The thesis examines the competence of mathematics teachers in private secondary schools in San Fernando City, La Union, aiming to design a two-pronged training program based on identified strengths and weaknesses. It finds that while teachers generally show good instructional skills, their content competence is average, particularly struggling with problem-solving and reasoning skills. The study concludes that despite limited training opportunities, the teachers perform well, and the proposed training program is crucial for enhancing their instructional efficacy and content knowledge.

1. COMPETENCE OF MATHEMATICS TEACHERS IN THE PRIVATE
SECONDARY SCHOOLS IN SAN FERNANDO CITY, LA UNION:
BASIS FOR A TWO-PRONGED TRAINING PROGRAM
A Thesis
Presented to the Faculty
of the Graduate School
College of Teacher-Education
Saint Louis College
City of San Fernando (La Union)
In Partial Fulfillment of
the Requirements for the DEGREE
MASTER OF ARTS IN EDUCATION
MAJOR IN MATHEMATICS
By
FELJONE GALIMA RAGMA
February, 2011

2. INDORSEMENT
This
thesis,
TEACHERS
IN
FERNANDO
CITY,
entitled,
THE
―COMPETENCE
OF
PRIVATE SECONDARY
LA
UNION:
BASIS
FOR
MATHEMATICS
SCHOOLS
A
IN
SAN
TWO-PRONGED
TRAINING PROGRAM,‖ prepared and submitted by FELJONE GALIMA
RAGMA in partial fulfillment of the requirements for the degree of
MASTER OF ARTS IN EDUCATION MAJOR IN MATHEMATICS, has
been examined and is recommended for acceptance and approval for
ORAL EXAMINATION.
MR.GERARDO L. HOGGANG, MAMT
Adviser
This
is
to
certify
that
the
thesis
entitled,
―COMPETENCE
OF
MATHEMATICS TEACHERS IN THE PRIVATE SECONDARY SCHOOLS
IN SAN FERNANDO CITY, LA UNION: BASIS FOR A TWO-PRONGED
TRAINING PROGRAM,” prepared and submitted by FELJONE GALIMA
RAGMA is recommended for ORAL EXAMINATION.
NORA A. OREDINA, Ed.D.
Chairperson
EDWINA M. MANALANG, MAEd
Member
MARILOU R. ALMOJUELA, Ed.D
Member
Noted by:
AURORA R. CARBONELL, Ed.D.
Dean, College of Teacher Education
Saint Louis College

3. APPROVAL SHEET
Approved by the Committee on Oral Examination as PASSED with
a grade of 96% on February 18, 2011.
NORA A. OREDINA, Ed.D.
Chairperson
EDWINA M. MANALANG, MAEd
Member
MARILOU R. ALMOJUELA, Ed.D
Member
ENGR. ANGELICA DOLORES, MATE-Math
CHED RO I Representative
Member
Accepted and approved in partial fulfillment of the requirements for
the
degree
of
MASTER
OF
ARTS
IN
EDUCATION
MAJOR
IN
MATHEMATICS.
AURORA R. CARBONELL, Ed.D.
Dean, College of Teacher Education
Saint Louis College
This is to certify that FELJONE GALIMA RAGMA has completed
all academic requirements and PASSED the Comprehensive Examination
with a grade of 94% in May, 2010 for the degree of MASTER OF ARTS
IN EDUCATION MAJOR IN MATHEMATICS.
AURORA R. CARBONELL, Ed.D.
Dean, College of Teacher Education
Saint Louis College

4. INDORSEMENT
This
thesis,
TEACHERS
IN
FERNANDO
CITY,
entitled,
THE
―COMPETENCE
OF
PRIVATE SECONDARY
LA
UNION:
BASIS
FOR
MATHEMATICS
SCHOOLS
A
IN
SAN
TWO-PRONGED
TRAINING PROGRAM,‖ prepared and submitted by FELJONE GALIMA
RAGMA in partial fulfillment of the requirements for the degree of
MASTER OF ARTS IN EDUCATION MAJOR IN MATHEMATICS, has
been examined and is recommended for acceptance and approval for
ORAL EXAMINATION.
MR.GERARDO L. HOGGANG, MAMT
Adviser
This
is
to
certify
that
the
thesis
entitled,
―COMPETENCE
OF
MATHEMATICS TEACHERS IN THE PRIVATE SECONDARY SCHOOLS
IN SAN FERNANDO CITY, LA UNION: BASIS FOR A TWO-PRONGED
TRAINING PROGRAM,” prepared and submitted by FELJONE GALIMA
RAGMA is recommended for ORAL EXAMINATION.
NORA A. OREDINA, Ed.D.
Chairperson
EDWINA M. MANALANG, MAEd
Member
MARILOU R. ALMOJUELA, Ed.D
Member
Noted by:
AURORA R. CARBONELL, Ed.D.
Dean, College of Teacher Education
Saint Louis College

5. APPROVAL SHEET
Approved by the Committee on Oral Examination as PASSED with
a grade of 96% on February 18, 2011.
NORA A. OREDINA, Ed.D.
Chairperson
EDWINA M. MANALANG, MAEd
Member
MARILOU R. ALMOJUELA, Ed.D
Member
ENGR. ANGELICA DOLORES, MATE-Math
CHED RO I Representative
Member
Accepted and approved in partial fulfillment of the requirements for
the
degree
of
MASTER
OF
ARTS
IN
EDUCATION
MAJOR
IN
MATHEMATICS.
AURORA R. CARBONELL, Ed.D.
Dean, College of Teacher Education
Saint Louis College
This is to certify that FELJONE GALIMA RAGMA has completed
all academic requirements and PASSED the Comprehensive Examination
with a grade of 94% in May, 2010 for the degree of MASTER OF ARTS
IN EDUCATION MAJOR IN MATHEMATICS.
AURORA R. CARBONELL, Ed.D.
Dean, College of Teacher Education
Saint Louis College

6. ACKNOWLEDGMENT
The researcher wishes to express his sincerest gratitude and warm
appreciation to the following persons who had contributed much in
helping him shape and reshape this valuable piece of work.
Mr. Gerry Hoggang, thesis adviser, for always giving necessary
suggestions to better this study.
Dr. Nora A. Oredina, chairwoman of the examiners, for her
valuable critique, and most especially, for inspiring the researcher to
pursue his Masterate degree.
Engineer Angelica Dolores, MATE-Math, CHED representative, for
her intellectual comments and recommendations.
Dr. Marilou R. Almojuela and Mrs. Edwina Manalang, panelists,
for their brilliant thoughts.
Dr. Jose P. Almeida, Mrs. Rica A. Perez, Mrs. Rosabel N. Aspiras
for validating the two sets of questionnaire.
Sr. Teresita A. Lara, Sr. Angelica Cruz, Mrs. Evangeline L.
Mangaoang, Mr. Danilo Romero, and Mrs. Loreta Cepriaso for validating
the two-pronged training program.
Principals, heads, teachers and students of the Private Secondary
Schools in the City Division of San Fernando, La Union for lending some
of their precious time in giving their responses to the questionnaires.

7. Mr. Amado I. Dumaguin, his former Mathematics Coordinator, for
always giving him inspiration and push; and for believing in the
researcher‘s capabilities.
Mr. & Mrs. Felipe and Norma Ragma, researcher‘s parents, for
always being there when the researcher needed some push.
And lastly, to God Almighty for giving the needed strength in the
pursuit of this endeavor.
F. G. R.

8. DEDICATION
To my Parents
Mr. & Mrs Felipe and Norma
Ragma
and
To my siblings
Darwin, Felinor and Nailyn
This humble work is a sign of my love to
you!
F.G.R.

9. THESIS ABSTRACT
TITLE: COMPETENCE OF MATHEMATICS TEACHERS IN THE
PRIVATE SECONDARY SCHOOLS IN SAN FERNANDO CITY,
LA UNION: BASIS FOR A TWO-PRONGED TRAINING
PROGRAM
Total Number of Pages: 230
AUTHOR: FELJONE G. RAGMA
ADVISER: MR. GERARDO L. HOGGANG, MAMT
TYPE OF DOCUMENT: Thesis
TYPE OF PUBLICATION: Unpublished
ACCREDITING INSTITUTION: Saint Louis College
City of San Fernando, La Union
CHED, Region I
Abstract:
The
study
aimed
at
determining
the
competence
level
of
mathematics teachers in the private secondary schools in San Fernando
City, La Union with the end goal of designing a validated two-pronged
training program.
Specifically, it looked into the profile of the mathematics teachers
along highest educational attainment, number of years in teaching
mathematics and number of mathematics trainings and seminars
attended; the level of competence of mathematics teachers along content

10. and instruction; the relationship between teacher‘s profile and content
competence, teacher‘s profile and instructional competence and content
and instructional competence; the major strengths and weaknesses of
the mathematics teachers along content and instruction and; the type
and validity of the training program.
The study is descriptive with two sets of questionnaire as the
primary data gathering instruments. It covered thirteen (13) private
secondary schools in San Fernando City, La Union with heads, faculty,
and students as respondents.
The study found out that all the mathematics teachers are licensed
and majority of them are pursuing graduate studies and had 0-5 years of
teaching experience; 84.62% had very inadequate and 15.39% had
slightly adequate attendance in seminars. It also found out that the
teachers‘ level of content competence was average with a mean rating of
16. They scored highest in conceptual and computational skills but
lowest in problem-solving skills. On the other hand, their level of
instructional competence was very good with a mean rating of 4.24. They
were rated highest in management skills but lowest in teaching skills.
Moreover, the study found that there is no significant difference in
the perceptions between students and teachers and between teachers
and heads but there is a significant difference in the perceptions between
students and heads. Also, there is no significant relationship between

11. profile and content competence and between content and instructional
competence. On the other hand, there is a significant relationship
between highest educational attainment and instructional competence;
but there is no significant relationship between number of years of
teaching and number of seminars attended to instructional competence.
The teachers‘ conceptual and computational skills are considered
as strengths. On the other hand, reasoning and problem-solving skills
are considered as weaknesses. All the other skills under teaching,
guidance, management and evaluation were considered strengths. The
weakness of Mathematics teachers along instructional competence was
on the quality of
utilization of information and communication
technology. In connection to the output of the study, the two-pronged
training program enhances the weaknesses and the sustainability of the
strengths. Its face and content validity was found high.
Based on the findings, the researcher concluded that the
mathematics teachers are all qualified in the teaching profession; they
are very young in the service and are exposed minimally to trainings and
seminars but they still perform well in their teaching; the teachers had
only average competence in terms of their content competence but were
perceived very skillful in teaching Mathematics.
Further, the heads rated instructional competence higher than the
students; but all the respondents considered the teachers very skillful in

12. teaching. Teachers who have higher educational attainment, number of
years in teaching and seminars do not have higher subject matter
competence and teachers who have higher educational attainment have
higher instructional competence; but, teachers who are more experienced
in teaching and have more seminars do not mean that they have higher
instructional competence than those who are younger and those who
have lesser seminars. It does not also mean that when a teacher has high
content competence, he has high instructional competence as well and
vice versa.
Further, teachers are not so skilled at analysis and problemsolving and they do not use ICT and other innovative instructional
technology much in their daily teachings but still have very good
teaching performance.
The validated two-pronged training program is timely for the new
and tenured teachers to update and upgrade their content and
instructional competence. Moreover, it is a helpful tool for them to
understand more their subject and know more about the ways on how to
present a subject matter, especially on the use of ICT.
Based on the conclusions, the researcher recommends that the
teachers should be encouraged to enroll in their graduate studies;
incentive scheme for outstanding performance should be devised by
administrators; teachers should always be sent to seminars and

13. workshops where their participation is necessary; teachers should use
ICT in their teaching and that the school has to provide such ICT
materials; a closer monitoring system has to be applied by the heads; the
proposed two-pronged training program for the Mathematics teachers
should be implemented in the private secondary schools in the City
Division of San Fernando, La Union; a study to determine the efficiency
or efficacy of the two-pronged training program should be undertaken;
and lastly, a parallel study should be undertaken in other subject areas
such as English and Science.

14. TABLE OF CONTENTS
Page
TITLE PAGE ………………………………………………………………
i
INDORSEMENT ………………………………………………………….
ii
APPROVAL SHEET ……………………………………………………...
iii
ACKNOWLEDGMENT …………………………………………………..
iv-v
DEDICATION ……………………………………………………………..
vi
THESIS ABSTRACT ……………………………………………………..
vii-xi
TABLE OF CONTENTS …………………………………………………
xii-xvii
LIST OF TABLES ………………………………………………………..
xviii –xix
FIGURE ……………………………………………………………………
xx
Chapter
1
The Problem ………………………………………………
1
Rationale …………………………………………….
Theoretical Framework …………………………..
7-14
Conceptual Framework ………………………….
15-17
Statement of the Problem ……………………….
19-20
Hypotheses…………………………………………
20-21
Scope and Delimitation …………………………
21-22
Importance of the Study ………………………..
22-23
Definition of Terms ………………………………..
2
1-7
23-26
Review of Related Literature …………………………
27

15. Profile of High School Mathematics Teachers ..
27
Highest Educational Attainment ……………….
27-28
Number of Years in Teaching Mathematics ….
29-30
Number of Seminars Attended …………………..
30-31
Level of Content and Instructional Competence ..
31
Subject Matter/Content …………………………….
32-33
Teaching Skills ……………………………………….
33-37
Guidance Skills ………………………………………
37-39
Management Skills …………………………………..
39-40
Evaluation Skills ……………………………………..
40-42
Comparison in Perceived Instructional Competence
Among Respondent Groups …………………………
42-43
Relationship of Profile and Content
Competence ……………………………………………
43-46
Relationship of Profile and Instructional
Competence …………………………………………….
46-48
Relationship between Content and
Instructional Competence ………………………..
48-50
Strengths and Weaknesses in Teachers‘
Competence ………………………………………….
Training Programs …………………………………..
3
50-52
52-53
Research Methodology ……………………………………..
54

16. Research Design …………………………………….
Sources of Data ……………………………………..
54-55
Instrumentation and Data Collection ………….
56-58
Validity and Reliability of the Instrument …….
58-60
Tools for Data Analysis ……………………………
60-64
Data Categorization ………………………………..
64-66
Proposed Training Program ………………………
66
Validity of the Training Program ………………..
4
54
66-67
Presentation, Analysis and Interpretation of Data…
68
Profile of Mathematics Instructors ………………
68
Highest Educational Attainment …………….
68-70
Number of Years in Teaching Mathematics…
70-71
Number of Seminars Attended ………………..
71-72
Summary of the Profile of Mathematics Teachers.. 73-74
Level of Content Competence ……………………….. 74
Conceptual Skills ………………………………….
74-76
Analytical Skills ……………………………………
76-78
Computational Skills ……………………………… 78-79
Problem-Solving Skills ……………………………. 79-81
Summary of Level of Content Competence.……. 81-83
Level of Instructional Competence ………………………………. 83
Teaching Skills ………………………………………….
83-86

17. Substantiality of Teaching ……………………….
86-87
Quality of Teachers‘ Explanation ………………
87
Receptivity to Students‘ Ideas
And Contributions ………………………………….
87-88
Quality of Questioning Procedure ………………
88
Selection of Teaching Methods ………………….
88
Quality of Information and Communication
Technology Used …………………………………..
89
Guidance Skills ….……………………………………
89-90
Quality of Interaction with Students ………….
90-91
Quality of Student Activity ………………………
91
Management Skills …………………………………..
91
Atmosphere in the Classroom …………………..
91-93
Conduct and Return of Evaluation
Materials ……………………………………………
Evaluation Skills ……………………………………..
Quality of Appraisal Questions………………….
93-94
94
94-96
Quality of Assignment/Enrichment
Activities …………………………………………….
96
Quality of Appraising Students
Performance …………………………………………
Comparison in the Perceived Instructional
97

18. Competence of the Groups of Respondents
Students and Teachers……………………………
97-98
Students and Heads……………………………….
99-100
Heads and Teachers……………………………….
100-101
Summary of Level of Instructional Competence ………
102-105
Relationship between Profile and
Content Competence ……………………………………….
105-108
Relationship between Profile and
Instructional Competence …………………………………
108-111
Relationship between Content and
Instructional Competencies ……………………………..
111-113
Summary of Relationship…………………………………….
113-114
Strengths and Weaknesses along Content Competence… 115-116
Strengths and Weaknesses along
Instructional Competence…………………….
116-121
Teaching Skills……………………………………
121-122
Guidance Skills ………………………………….
122
Management Skills ………………………………
122
Evaluation Skills …………………………………
122-123
Proposed Two-Pronged Training Program ………………
123-129
Level of Validity of the Proposed …………………………..
129-13)
Two-Pronged Training Program ………………………….
131-140

19. Sample Flyer of the Two-Pronged Training Program………. 141
5
Summary, Conclusions and Recommendations ……. 142
Summary …………………………………………
142-144
Findings ……………………………………………
144-145
Conclusions……………………………………….
146-147
Recommendations ………………………………
147-149
BIBLIOGRAPHY………………………………………….
150-161
APPENDICES …………………………………………….
162-219
CURRICULUM VITAE…………………………………….
210-213

20. LIST OF TABLES
Table 1……………………………………………………………
56
Table 2……………………………………………………………
69
Table 3……………………………………………………………
71
Table 4……………………………………………………………
72
Table 5……………………………………………………………
73
Table 6……………………………………………………………
75
Table 7……………………………………………………………
77
Table 8……………………………………………………………
79
Table 9……………………………………………………………
80
Table 10…………………………………………………………
82
Table 11…………………………………………………………
84-86
Table 12…………………………………………………………
90
Table 13…………………………………………………………
92-93
Table 14…………………………………………………………
94-96
Table 15…………………………………………………………
98
Table 16…………………………………………………………
99
Table 17…………………………………………………………
101
Table 18…………………………………………………………
103-104
Table 19…………………………………………………………
106
Table 20…………………………………………………………
109

21. Table 21…………………………………………………………
112
Table 22…………………………………………………………
114
Table 23…………………………………………………………
116
Table 24…………………………………………………………
117-121
Table 25 ………………………………………………………..
129-130

22. FIGURE
Figure
1
Page
The Research Paradigm …………………………………..
18

23. Chapter 1
THE PROBLEM
Rationale
The tremendous task of education today, under the enormous
influx of technological advances and innovations, is still the development
of a learner into a whole person, a complete human being capable of
understanding his own complexity and his intricate society. The teacher,
who is in charge of this global task, needs to cope with the challenges of
the modern times. He has to be equipped with the resources vital in
arousing and sustaining students‘ interest, in facilitating the learning
process, and in evaluating the learning outcomes. He should be a master
of his craft and is genuinely concerned with the total growth and
development of his students (Clemente-Reyes 2002).
Quality education is first and foremost a function of instruction.
Thus, for education to attain and sustain its quality, it should be coupled
with the best preparation for excellent instruction. It is then emphasized
that to be an excellent high school teacher, one should both have full
command of the subject and full knowledge of the teaching-learning
process including course structure and examination system. The
teacher, therefore, should not only have mastery of the subject matter
but also an in-depth understanding of the mind set and standards of

24. students within the class (http://www.dooyoo.co.uk/discussion/whatqualities-make-an-excellent-teacher/1039890/).
It is irrefutable that secondary education plays an essential part in
every nation‘s educational system (Darling-Hammond 2008). One high
school subject highly supportive of this is Mathematics.
No one can question the role being played by Mathematics in
education. In fact, Mathematics is one of the basic tool subjects in
secondary education. As such, mathematics teachers contend that the
place
of
mathematics
in
the
basic
education
is
indispensable
(http://wiki.answers.com/Q/Why_is_Mathematics_Indispensable).
It
has
been felt that mathematics has both utilitarian and disciplinary uses
necessary for everyone. By the very nature of the discipline, its
application to both science and technology and to the human sciences is
easily recognized by the layman. The bricklayer, the carpenter, and the
nuclear
scientist
use
mathematics
of
varied
complexities
(www.eric.edu/practicalities_mathed). Thus, the role of mathematics in
the holistic formation of every learner is vital (Sumagaysay 2001).
It can be gleaned, therefore, that it is important for students to
develop their potentials and capacities in mathematics to the fullest in all
possible means. In doing this, a sound mathematics curriculum that
would provide each learner the necessary skills and competence in
mathematics is hence necessary. The 2010 Secondary Mathematics

25. Education Curriculum Guide explicitly presents the Mathematics
Curriculum framework:
The goal of basic education is functional literacy for
all. In line with this, the learner in Mathematics should
demonstrate core competencies such as problem solving,
communicating mathematically, reasoning mathematically
and making connections and representations.
These competencies are expected to be developed
using approaches as practical work/ outdoor activities,
mathematical investigations/games and puzzles, and the
use of ICT and integration with other disciplines.
With these contents in the Secondary Mathematics Framework,
quality secondary mathematics education, reflective in the best practices
in instruction, would also entail the use of effective approaches and
techniques of teaching, which would equip each learner the needed skills
and competencies. On top of it all, a competent mathematics teacher who
empowers learners to achieve the goals of mathematics education, and
who is efficient and effective in providing quality mathematics instruction
is imperative (Gonzalez 2000).
The
country‘s
vision
for
quality
education
with
focus
on
Mathematics Proficiency is undoubted. But, our country, of course, is
not relieved from the crises. In fact, Dr. Milagros Ibe of the University of
the Philippines said that the result of a survey on the competence of
Science and Mathematics teachers showed that majority of the teachers
are not qualified to teach the subjects. With this issue at hand, Ibe

26. remarked that it is easy to understand why the achievement of Filipino
Students in Science and Mathematics was dismally low (Lobo 2000). In
the 2000 issue of the Philippine Journal of Education as cited by Aspiras
(2004), Ibe supports her contention of the connection of teachers‘
competence and students‘ achievement. She stressed that Filipino
students suffer from poor thinking skills; they are only able to recall
concepts but for questions beyond that or which require multiple-step
problem solving, our students appeared to have been stumped. As a
result, math and science skills of students from 42 countries showed
that Filipino students are biting the dust of their global counterparts.
These ideas prompted former President and now Congresswoman Gloria
Macapagal-Arroyo (Educator‘s Journal, 2003). She stressed that in order
for Filipino students to be globally competitive, the national aims to
improve the country‘s educational standards and to upgrade teachers‘
competence have to be pushed (Educator‘s Journal, 2003). Despite these
aims, recent LET results revealed that majority of the secondary teacherexaminees are not qualified to teach. In April, 2010 the passing rate for
secondary teachers was only 23.32% and in September, 2010 the
passing rate was 25.86%. These rates reveal that teachers, though
possess the needed degree/s are not yet qualified to teach; thus, they are
not competent. However, Lee (2010) clarified that passing the test does
not guarantee content competence. This is because majority of the

27. passers have rates of 75-79%. He highlighted that rates such as these
reflect fair or if not, poor competence.
On
the
light
of
mathematics
teacher‘s
qualification
and
competence, issues arise, too. First, Lobo (2000), as cited by Oredina
(2006) reveals in his article that only 71% of the Mathematics Teachers
claim to have formal preparation in Mathematics. This means that 29%,
who are unqualified to teach mathematics, still teach the subject. In
addition, the Civil Service Commission (CSC) has ruled that the
Department of Education (DepEd) may hire and retain teachers even if
they had not yet registered with Professional Regulation Commission
(PRC) as mandated by Republic Act No.7836 (Educator‘s Journal 2003).
This further implies that a non-registered math teacher or a non-major is
teaching math. Another, teacher handling the same subjects or in the
same year level develops the idea and practice to be stagnant-an ordinary
lecturer in a classroom (Farol 2000). Furthermore, many graduates of
teacher-education institutions, though received formal education, are not
prepared to handle a class of learners (Adams 2002).
Further, the UP
Institute of Science and Mathematics Education also revealed that ―many
teachers at all levels do not have the content background required to
teach the subjects they are teaching‖. The survey revealed that only 41%
of mathematics teachers are qualified to teach the subject (Cayabyab
2010). With this reality, it is not surprising why students performed

28. poorly in Mathematics Achievement Test. This is stressed by Roldan
(2004) in her assertion that students‘ mathematics low performance is
reflective of the weak mathematics teachers‘ influence. Roldan (2004)
revealed that secondary teachers in Region I were proficient only in
concepts and computations but they were deficient in their skills in
problem-solving and the use of teaching strategies. Thus, mathematics
teachers frequently find themselves focusing on mechanics, the answerresulting procedures-without really teaching what mathematics is all
about-where it came from, how it was labored on, how ideals were
perceived, refined, and developed into useful theories-in brief, its social
and human relevance (Cayabyab,2010).
It was also disclosed by Bambico (2002) in her dissertation that
that majority of the mathematics teachers in Region I scored 17 out of 35
simple mathematics problems; and their instructional competence
ranged from 54.71% to 78.03% only. These ratings were emphasized to
be weaknesses and the major reasons why the passing rate of the region
in the NAT has not even reached 80% and up.
In the City Division of San Fernando, particularly in the Private
secondary schools, quality mathematics teaching had been given much
emphasis. Several seminars and training-workshops had been organized
to update and upgrade teachers‘ competence.
One most recent
Mathematics Seminar was organized by the Association of the Private

29. Schools last July, 2010. The seminar-workshop on Trends in Teaching
High School Mathematics was an aim to improve the students‘
mathematics performance in the 2009 National Achievement Test (NAT)
(Eligio 2010). The seminar was attended by mathematics teachers in the
Private Schools in La Union where the researcher served as the resource
speaker. This brought out that majority of the teachers could not fully
analyze problems in higher Mathematics such as Geometry and
Trigonometry despite the fact they have graduated with a Mathematics
degree. They were also found to be very young in the service and that
they tend to teach mathematics word problems using one approach.
Even though seminars and trainings were conducted, these only
lasted for few hours and had no follow-ups. Another, only a few are sent
by the participating schools to attend such endeavor.
It is then with these predicaments that the researcher embarked
on the idea to appraise and evaluate the competence of mathematics
teachers along content and instruction. The results, in turn, will be the
foundations of proposing a validated two-pronged training program for
the Mathematics teachers in the Private Secondary Schools of the City
Division of San Fernando for the academic year 2010-2011.
Theoretical Framework
To put this study in its theoretical framework, a discussion on the
competence theories, theories of teaching and learning, the best practices

30. and approaches of an effective teacher, and the concept of training are
presented. Several theories on learning are also included since teachers
are learners, too. They need to learn first the fundamentals, the
strategies and techniques before they can actually impart knowledge to
their students.
Mathematics involves learning simple skills, calculations, facts and
procedures where memory, most especially practice are the most
essential. It requires a high level of creative and analytic thinking. Thus,
mathematics teachers should know when and what concepts to teach,
when and why students are having difficulties, how to make concepts
meaningful, when and how to improve skills and how to stimulate
productive and creative thinking in order to fully analyze what they are
doing (Subala 2006).
Piaget (1964) opined that as a child acquires knowledge of the
environment, he or she develops mental structures called concepts.
Concepts are rules that describe properties of environment events and
their relations with other concepts. As applied to teachers, when teachers
get familiar with certain concepts and routines, they are able to master
the skills.
Dewey‘s (1896) notion of knowledge for teaching is one that
features inquiry with, and practice as the basis for professional judgment
grounded in both theoretical and practical knowledge. If teachers

31. investigate the effects of their teaching on student learning and if they
study what others have learned, they come to understand teaching to be
an interesting endeavor. They become sensitive to variation and more
aware of the different purposes and situations. They are assessed on
contingent knowledge to become more thoughtful decision-makers.
According to Thorndike (1926), learning becomes more effective
when one is ready for the activity, practices what he has learned and
enjoys the learning experience. As applied to teachers, they cannot teach
effectively if they have not learned sufficiently.
Thorndike‘s law of exercise states that the more frequently a
stimulus response connection occurs, the stronger association and
hence, the stronger learning. Practice without knowledge of results is not
nearly effective as when the consequences become known to the learner.
Further, concepts are the substance of mathematical knowledge.
Students can make sense of mathematcs only if they understand its
concepts and their meanings or interpretations. An understanding of
mathematical concepts involves around more than mere recall of
definitions and recognition of common examples. The assessment of
students‘ understanding of concepts should be sensitive to the
development nature of concept acquisition. (Arellano 2004)
Bruner‘s (1968) most famous statement is that, any subject can be
taught effectively in some intellectually honest form to any child at any

32. stage of development. He insisted that the final goal of teaching is to
promote the general understanding of the structure of a subject matter.
To learn and use mathematics requires a substantial mastery of
computation. To master a skill of computation requires constant
practice, repetition and drill. Computational skills are essential in order
to facilitate the learning of new math concepts, to promote productive
thinking in problem solving, research and other creative thinking
activities.
Mathematics teachers have always viewed problem solving as a
preferential objective of mathematics instruction (Subala 2006). It was
not until the National Council of Teachers of Mathematics (NCTM)
published its position paper that problem solving truly came of age. As
its very first recommendation, the council proposed that problem solving
be the focus of school mathematics and performance in problem solving
be the measure of the effectiveness of the personal and national position
of mathematical competence (Taback, 1998).
Bruner (1968) believed that intellectual development is innately
sequential,
moving
from
inactive
through
iconic
to
symbolic
representation. He felt it is highly probable that this is also the best
sequence for any subject to take. The extent to which an individual finds
it difficult to master a given subject depends largely on the sequence in
which the material is presented. Further, Bruner also asserted that

33. learning needs reinforcement. He explained that in order for an
individual to achieve mastery of a problem, feedback must be reviewed as
to how they are doing. The results must be learned at the very time an
individual is evaluating his/her performance.
The above theories suggest that problems and applications should
be used to introduce new mathematical content to help students develop
both their understanding of concepts and facility with procedures, and to
apply and review processes they have learned.
Besides his abilities and competence, a teacher who is tasked to
facilitate the teaching-learning process, also needs a set of teaching
theories. These theories, which are based on the teachers‘ understanding
of the learner and the educative process, become the bases of his ways
on how to influence his students to learn. The 2010 Secondary
Mathematics Curriculum provide the three most important theories.
These
are
Experiential
Learning
by
David
Kolb
and
Rogers,
Constructivism and Cooperative Learning.
Experiential Learning by Kolb and Rogers presents that significant
learning takes place when the subject matter is relevant to students‘
experience and is purposeful to their personal interest. This further
connotes that human beings have the natural tendencies to learn; as
such, the task of the teacher is just to facilitate learning. Facilitating
learning revolves around (1) setting a positive climate, (2) clarifying the

34. purpose of the learner, (3) organizing and making available learning
resources, (4) balancing intellectual and emotional components of
learning and (5) sharing feelings and thoughts with learners but not
dominating. Thus, Experiential learning substantiates the Principle of
Learning by doing (http://oprf.com/Rogers).
On the other hand, constructivism roots from the idea that ―one
only knows something if one can explain it‖. This idea was formalized by
Immanuel Kant, who asserted that students are not passive recepients of
information;
rather,
they
are
active
learners
(www.wikipedia.com/ImmanuelKant). A basic theoretical proposition of
constructivism is that the students are eager participant in the
acquisition of knowledge. So, in the constructivist room, the teacher
serves not as the authority, but the pathfinder of knowledge.
Cooperative Learning Theory by Johnson and Johnson, in
addition, holds that learning is significant when students work together
to accomplish a task. The cooperative tasks are designed to elicit positive
interactions, provide students with different opportunities, and make
students engage in learning. This theory suppports the MultipleIntelligence Theory by Gardner (Montealegre 2003).
The Mathematical Framework also necessitates integration. As
such, the Reflective Teaching Theory is vital. This theory is based on the
Ignatian Pedagogy asserting that teaching experience should include

35. interaction from the students, which calls the plan to implement
reflections that give birth to new insights, knowledge and enlightenment
regarding one‘s self based upon the content of teaching (Crudo 2005).
In addition, in her dissertation on Mathematics Education,
Cayabyab (2010) theorized a mathematics stepping-stone theory. She
stressed that in teaching mathematics, students should be taught that
every mistake, every fault, every difficulty encountered becomes a
stepping-stone to better and higher things. She added that in teaching
and learning mathematics,skills on patience and accuracy are developed.
When a teacher has finished teaching, he therefore administers
strategies for assessment and evaluation to gauge learning. The theory of
Evaluation by Burden and Byrd, as mentioned by Oredina (2006),
pointed out that frequent, continuous and impartial evaluation of
academic performance is vital not only for the growth of institution but
also for the growth of the individual. Evaluation would tell whether
improvement is necessary.
If a teacher wants to be the best teacher for her students, he
should not fail to upgrade and update himself. The concept of training
enters the scene. Training is the process of acquiring specific skills to
perform a better job. It helps people to become qualified and proficient in
doing some jobs (Fianza,2009). Usually, an organization facilitates the
employees‘ learning through training so that their modified behavior

36. contributes to the attainment of the organization‘s goals and objectives
(Oredina 2006).
Further, training is a complex activity and must be clearly
planned. Design and preparation of training course usually consume
more time than delivery of the material. Successful training requires
careful planning by the trainer. Planning helps the trainer/s determine
that the appropriate participants have been invited to the training course
and that the training is designed to meet their needs in an effective way.
Thus steps in planning for effective training program are a requisite.
According to the PDF article accessed from the internet, the parts of a
training program include objectives, content , materials or resources,
methods
or
procedures,
and
evaluation
strategy
(www.jifsan.umd.edu/pdf/gaps-en/VI-Effective-Training-Com.pdf).
The abovementioned instructional competency dimensions find its
essence in the general areas cited in the questionnare.These serve as the
building blocks in structuring this research.
Moreover, the theories in teaching and learning, practices and
approaches,
and
the
principles
in
teaching
mathematics
show
parallelism in each of the content of the instructional dimensions. These
may also serve in the formulation of the recommendations of the study.
The concept of training serves as the core idea in designing the
output of this pursuit.

37. Conceptual Framework
The task of a teacher is complex and many-sided and demands a
variety
of
human
abilities
and
competencies.
The
abilities
and
competencies of a teacher, according to Nava (1999), as cited by
Clemente (2002), are subject matter – mastery of content-specific
knowledge for the effective instruction,
classroom management –
creation of an environment conducive to learning, facilitation of learning
– implicit and explicit knowledge of various teaching strategies and
methods to attain instructional objectives, and diagnostic – knowledge of
class needs and goals, abilities and achievement levels, motives,
emotions, which influence instruction and learning. These competence
dimensions were also mentioned by Lardizabal (2001). According to her,
the four dimensions are teaching skills, guidance skills, management
skills, and evaluation skills.
Effective high school mathematics teaching, therefore, involves
mastery of the subject matter on the part of the teacher, understanding
students‘ differences, interest and background, skills in the use of
appropriate methods and techniques, appropriate assessment strategies
and flexibility and sensitivity to adopt to the needs of students. Thus, the
nature of the task of a teacher is not easy. This then implies that the
teacher has to improve if his vision of influencing students to learn is of
prime concern.

38. One of the most time-tested ways for continuing development of
the professional teachers is the training and in-service educational
program. Its rationale is to help teachers carry out their job better. The
outcome of a well-planned training program is manifested in an
environment
of
learning
suited
to
the
needs
of
the
children
(www.britannicaonlineencyclopedia/training). This then connotes that
when teachers improve for the better, students improve for the better,
too.
Boiser (2000) extends his idea that if one aspires to continue
teaching effectively, he needs to continue upgrading himself. He opines
that to upgrade necessitates reading professional references, enrolling in
advanced courses and attending trainings, conferences and workshops.
Additionally, Lapuz (2007),as cited by Bello (2009), stresses the need for
training and retraining if teachers really wanted to be competent.
It is in this light that the study is thought of, formulated and set
up. This conceptualization is logically designed in the research paradigm
in Figure 1. The paradigm made use of the Input-Throughput-Output
model. The input is composed of the profile of mathematics teachers
along highest educational attainment, number of years in teaching, and
number of trainings and seminars attended. Further, it also contains the
variables on the level of competence along content and instruction. These
variables are indeed necessary to determine how competent the

39. mathematics teachers in the Private Secondary Schools in the City
Division of San Fernando, La Union are.
The throughput incorporated the processes of analyzing and
interpreting the variables in the input- profile (highest educational
attainment, number of years in teaching, number of seminars attended);
level of competence along content and instruction; the comparison in the
perceived instructional competence among the three respondent groups;
the culled-out strengths and weaknesses,and tests of correlation between
profile and the levels of competence along content and instruction; and
the relationship between the levels of competence along content and
instruction. It also holds the process of conceptualizing and validating
the output of the study.
The output of the study, therefore, is a validated two-pronged
training program for mathematics teachers in the Private Secondary
Schools in the City Division of San Fernando, La Union for academic year
2010-2011.

40. Input
A. Profile of mathematics teachers
along:
1. Highest educational
attainment;
2. Number of years in teaching
math; and
3. Number of seminars and
trainings
B. Level of competence of
mathematics teachers along:
1. Content
a. conceptual skills
b. reasoning/analytical
skills
c. computational skills
d. problem-solving skills;
and
2. Instruction
a. Teaching/
Facilitating Skills;
b. Guidance Skills;
c. Management
Skills; and
Throughput
Output
A. Analysis and interpretation of:
1. Teachers’ profile
2. Level of competence along
content and instruction
2.1 Comparison in the
perceived instructional
competence among the
respondent groups
3. Relationship between
a. teachers’ profile and
level of competence
along content;
b. teachers’ profile and
level of competence
along instruction; and
c. teachers’
competencies along
content and instruction
4. Strengths and weaknesses
on the level of competence
B. Development of a Proposed
Two-Pronged Training
Program for Mathematics
Teachers
C. Validation of the TwoPronged
Training Program
d. Evaluation Skills
1. face
2. content
Fig. 1
Research Paradigm
A Validated TwoPronged
Training Program
for Mathematics
Teachers

41. Statement of the Problem
This study aims primarily to determine the level of competence of
mathematics teachers in the Private Secondary Schools in San Fernando for
the academic year 2010-2011 as basis for a validated two-pronged training
program. Specifically, it aims to answer the following questions:
1. What is the profile of the mathematics teachers along:
a. highest educational qualification;
b. number of years in teaching mathematics; and
c. number
of
mathematics
trainings
and
seminars
attended?
2. What is the level of competence of mathematics teachers along:
a. Content
a.1. Conceptual Skills
a.2. Reasoning/ Analytical Skills
a.3. Computational Skills
a.4. Problem-Solving Skills ; and
b. Instruction
b.1.Teaching Facilitating Skills
b.2. Guidance Skills
b.3. Management Skills
b.4. Evaluation Skills?

42. 2.1 Is there a significant difference in the instructional competence
of the teachers as perceived by the students, heads and
teachers, themselves?
3. Is there a significant relationship between:
a. Teacher‘s profile and competence along content;
b. Teacher‘s profile and competence along instruction; and
c. Competence
along
content
and
competence
along
instruction?
4. What are the major strengths and weaknesses of the mathematics
teachers along:
a. Content; and
b. Instruction?
5. Based on the findings, what training program may be proposed to
enhance
the
content
and
instructional
competence
of
the
mathematics teachers?
5.1 What is the level of validity of the training program along:
a. face; and
b. content?
Hypotheses
The researcher is guided by the following hypotheses:
1. There is no significant difference in the perceived instructional
competence of the teachers among the three respondent groups.

43. 2. There is no significant relationship existing between:
a. Teacher‘s profile and competence along content
b. Teachers‘s profile and competence along instruction
c. Competence along
Scope and Delimitation
The primary aim of this study is to determine the level of
competence of high school mathematics teachers in the Private Schools
of the City Division of San Fernando for the academic year 2010-2011.
The 13 (thirteen) schools include Brain and Heart Center (BHC), Saint
Louis College (SLC), Christ the King College (CKC), Gifted Learning
Center, MBC Lily Valley School, La Union Cultural Institute (LUCI), La
Union Colleges of Arts, Sciences and Nursing (LUCNAS),Union Christian
College (UCC), San Lorenzo Science High Schoool (SLSHS), National
College of Science and Technology(NCST), Central Ilocandia College of
Science and Technology (CICOSAT), Felkris Academy, and Diocesan
Seminary of the Heart of Jesus (DSHJ). Further, there are three (3)
respondent groups: the Mathematics teachers, the heads, and the
students. Each Mathematics teacher in the private schools of San
Fernando is evaluated by one of his/her classes.
Based on the identified strenghts and weaknesses on the level of
content and instructional competence of the mathematics teachers, a
proposed two-pronged training program is formulated. The proposed

44. training program will be administered to the Private Secondary Schools
in the City Division of San Fernando, La Union. Since it involves
logistics, the administrators of the Private Secondary Schools in the City
Division of San Fernando are asked to validate the proposed two-pronged
training program for teachers.
Importance of the Study
This piece of work will greatly benefit the administrators, heads,
teachers, students, the researcher and future researchers.
To school administrators of the Private Secondary Schools in the
City Division of San Fernando, this study will provide them with data
that can help them formulate the in-service training programs. Further,
they will also be guided in structuring the Faculty Development Program
that is aimed at intensifying and sustaining the skills of the teaching
workforce;
To the Mathematics heads of the City Division of San Fernando,
this study will give them insights about the competence of their teachers.
This will also provide them data in designing the Human Resources
Development Plan;
To Mathematics teachers, this study will give them baseline data of
their strenghts and weaknesses in content and instruction. The output of
the study, on the other hand, will make them more competent, prepared,
directed and helped in carrying out their noble tasks;

45. To students of the Private Secondary Schools in San Fernando City
Division, this study will lead them to a thoughtful understanding of
mathematics for they are handled by more competent teachers;
To the researcher, a Mathematics teacher and at the same time the
Subject Area Coordinator for Mathematics of Christ the King College, this
study will help him in improving his mathematics teachers‘ competence;
and
To future researchers, who will be interested to conduct similar
studies, this study will motivate them to pursue their research since this
study can be used as basis.
Definition of Terms
To
better
understand
this
research,
the
following
items
are
operationally defined:
Content Competence. This pertains to the subject matter knowledge of
the
Mathematics
Mathematics
Algebra,
teachers
subjects:
Geometry,
in
the
Elementary
Advanced
four
(4)
Algebra,
Algebra,
secondary
Intermediate
Trigonometry
&
Statistics. Further, this also gauges the cognitive skills in
Mathematics along conceptual, analytical, computational and
problem-sloving.

46. Analytical
Skills.
This
pertains
to
the
skills
on
comprehension that requires investigative inquiry and
logical reasoning.
Computational Skills. This pertains to the skills that involve
the fundamental mathematical operations.
Conceptual Skills. This pertains to the skills on learning facts
and simple recall.
Problem-Solving Skills. This pertains to the skills that
require multiple-step plan to come up with a decision
or a solution.
Instructional Competence. This is divided into four dimensions:
teaching/facilitating skills, management skills, guidance skills
and evaluation skills.
Evaluation
skills.
This
is
an
area
on
instructional
competence which includes quality of appraisal questions,
quality of assignment/enrichment activities, and quality of
appraising students‘ performance.
Guidance skills. This is an area on instructional competence
which includes quality of interaction and quality of
activity.

47. Management
competence
skills.
This
which
is
an
area
includes
on
instructional
atmosphere
in
the
classroom,and conduct and return of evaluation materials.
Teaching skills. This is an area on intsructional competence
which includes substantiality of teaching, quality of
teacher‘s explanation, receptivity to students‘ ideas and
contributions, quality of questioning procedure, selection
of teaching methods, and quality of information and
communication technology utilized.
Heads. This pertains to the principals, academic coordinators, subject
area coordinators and department heads.
Level of Competence. This pertains to the degree or extent of
attainment along content and instruction of the Mathematics
teachers.
Mathematics students. These are the students duly enrolled in a private
high school in San Fernando for the academic year 2010-2011.
Mathematics teachers. These are the teachers handling secondary
mathematics in the Private Secondary schools in San Fernando for
the academic year 2010-2011.
Private Secondary schools in San Fernando. These are the nongovernment schools owned by private institutions and individuals
where the three groups of respondents came from.

48. Profile. This contains the variables on highest educational attainment,
number of years in teaching, and
number of trainings and
seminars attended.
Highest educational attainment. This pertains to the highest
academic qualification of the
high school mathematics teachers
for the academic year 2010-2011.
Number of years in Teaching. This refers to the length of service
a mathematics teacher has in the academe.
Number of Seminars attended. This refers to the frequency of
trainings undergone by a Mathematics teacher for the past 2 years.
Strength. This term refers to a content competence rating of 17 and
above and to an instructional competence rating of 3.51 and
above.
Two-Pronged Training Program. This refers to an action plan devised in
the study to enhance the content and instructional competence of
mathematics teachers of the Private schools in the City Division of
San Fernando.
Weakness. This refers to a content competence rating of below 17 and an
instructional competence rating of below 3.51.

49. Chapter 2
REVIEW OF RELATED LITERATURE AND STUDIES
A summary of professional literature and studies related to the
present study are presented in this chapter. These helped strengthen the
framework of this study and substantiated its findings.
Profile of Secondary Mathematics Teachers
According to the Executive Summary on Teachers and Institution,
teacher qualifications matter (www.sec.dost.gov.ph). It is with this idea
that the areas on teacher‘s profile are established. The areas include
Highest Educational Attainment, Years in teaching Mathematics and
Numbers of Trainings and Seminars Attended.
Highest Educational Attainment
Republic Act 9293, an act amending section 26 of RA 7836 states
that no person shall engage in teaching or act as a professional teacher
whether in preschool, elementary or secondary level unless the person is
duly registered.
Fianza (2009) revealed in her study that majority of the
respondents possessed the required eligibility to teach secondary
mathematics since most of the teachers were LET/PBET passers and
degree holders of mathematics. She further stressed that 40 out of 56
respondents were bachelor‘s degree holders, 15 had master‘s degree and
1 had doctorate degree.

50. Bautista, as cited by Binay-an (2002), stressed that teachers, in
general, met the educational requirements in accordance with the Magna
Carta for Public School Teachers. She also stressed that teachers didn‘t
want to remain stagnant in their field.
Eslava (2001) found out that out of the 40 teacher-respondents in
the secondary schools in La Union, only 12 or 30% were AB/BS
graduates, 19 or 47.5% were AB/BS with MA/MS units, or 8 or 20%
were MA/MS graduates and 1 or 2.5 was a PhD/EdD graduate. It was
pointed out that the mathematics teachers value continuing education to
further equip themselves in the issues and concerns about teaching.
In the Education Journal of the District of Thailand year 2009, the
study of Dr. Naree Aware-Achwarin (2005) was noted. The findings of this
published study disclosed that most of the teachers (92.88%) held
bachelor‘s degree; very few teachers (6.23%) held master‘s degree or
higher degrees.
Rulloda (2000), as cited by Oyanda (2003), expressed that teachers
did not want to remain stagnant in their undergraduate degrees. They
endeavored to improve their competencies by updating and upgrading
themselves through the formal process. It was necessary for them to
elevate their professional outlook to make them effective and worthy
members of the profession.

51. Number of Years in Teaching Mathematics
In the revised guidelines of the appointment and promotions of
teaching and related teaching group (DepEd order No.66, s 2007)
teaching experience is one of the criteria. Thus, the more experienced a
faculty member is the more confident and effective he is in teaching. This
was confirmed and affirmed by the study of Aware-Achwarin (2005). She
stressed that most of the teachers (71.07%) had teaching experience of
more than 10 years.
However,
several
local
studies
ran
nonparallel
to
these
international findings. Oyanda (2003) revealed that 136 high school
Mathematics teachers taught for 5-9 years, 132 taught for 0-4 years and
only a few had 20 years or more teaching experience. This implied that
majority of the teacher-respondents were quite young in the service.
Fianza (2009) also revealed that 67% of her respondents were very
young in teaching high school geometry. These respondents are in the
teaching service for less than 4 years.
According to Laroco (2005), 10% of the Private High School
Mathematics teachers in Urdaneta had been teaching for 15-19 years.
30% had 5-9 years of teaching and majority (60%) had taught for 4
years. The same implication was revealed.
Yumul (2001) noted that the length of teaching experience was a
valid indicator of performance. This is also seconded by the study of

52. Mallare (2001) stating that teaching experience is the best predictor of
mathematics achievement. These assertions can be easily established
since teachers develop their effectiveness as they become aware and
more experienced in the realities and complexities of teaching.
Number of Seminars and Trainings Attended
As teachers become the 21st century teachers, they need to
continually update and upgrade themselves to serve the needs of the socalled digital learners. One way of doing this is through attending
mathematics seminars or trainings.
Oyanda (2003) revealed that 6 (six) had attended international
trainings and 45 had national trainings. However, 4 revealed that they
had not attended any training. It was pointed out that only a few went to
international seminars/in-service trainings due to financial reasons
including lack of sponsorship from the government and private sectors.
Laroco (2005) brought out that most of the teacher-respondents
only attended seminars within the division level. The 2nd was regional.
The 3rd was at school and 4th was at the national level. This was due also
to financial constraints.
Fianza (2009) divulged that more than fifty percent of the
respondents attended trainings on curriculum, teaching strategies,
management, and assessment methods/ tools. Less than fifty percent of

53. the respondents attended trainings on content in Geometry. These
seminars are based on school and local.
Cabusora
(2004)
unveiled
that
attendance
of
his
teacher-
respondents to seminars and trainings were mostly local and regional.
Oredina (2006) disclosed that the instructors have attended a few
trainings and seminars for professional development. With these,
majority of the teacher-respondents have ―very inadequate‖ participation
in seminars and training workshops. The reasons she stressed were
financial constraints, non-availability of the instructors due to school
commitments and the distance of the seminar venue.
Level of Content and Instructional Competence
The significant factor in achieving quality Secondary Mathematics
Education is teachers‘ competence along content and instruction. Diaz
(2002) supports this by expressing that to be a successful mathematics
teacher, one must be competent in math and in mathematics
instruction. Thus, the levels of competence along the two dimensions
show teachers‘ strengths and weaknesses that serve as basis to develop
and
actualize
activities
that
will
further
improve
and
enhance
competence. Mathematics teachers can therefore improve the ability of
their learners when they have very good content knowledge of their
subject area and at the same time sound instructional skills.

54. Subject Matter/ Content
Cabusora (2004) stressed that the first essential of effective
teaching is teacher‘s thorough grasp of the subject matter he teaches.
According to Toledo (1992) and Bagaforo (1998), as cited by Diaz
(2000), teachers, in general, felt moderately competent in their knowledge
and ability in mathematics. It was disclosed that the teachers still lack
the
knowledge
of
mathematics
subjects,
particularly
the
higher
mathematics. Thus, it was concluded that teachers did not possess math
competence at level adequate for teaching secondary mathematics. Diaz
(2000) also found out in her study that teachers were moderately
competent in their knowledge in mathematics.
Gundayao (2000) found in her study that the teachers teaching
secondary mathematics in the Province of Quirino had ―good‖ level of
proficiency in Algebra, ―poor‖ in Geometry and ―poor‖ in Trigonometry. In
general, the results were poor because the teachers lacked the
competence in analyzing high level of category in analyzing problems.
Subala (2006) found out in her study that the graduating math
majors of teacher-training institutions in Region I were moderately
competent in Basic Math, fairly competent in Algebra and Statistics and
poorly competent in Geometry and Trigonometry.

55. Roldan (2004) revealed that her respondents were Above Average in
Math I and II and average in Math III and Math IV. She concluded that
the conceptual skills of the mathematics teachers were very important
and teachers need to consistently update and upgrade their capabilities
to enable them to cope with the challenges of the new millennium. Thus,
teachers needed to improve their skills in the topics of a particular
subject found to be weaknesses.
Teaching or Facilitating Skills
The shift of the teacher‘s role as provider of knowledge to facilitator
of learning or pathfinder of knowledge calls for proper application of
teaching methods to make the learning experiences vital and relevant.
Thus, the effectiveness of teaching Mathematics relies to a great extent
not only upon the teachers‘ educational attainment or skills but also
upon his competence in the subject.
Laroco (2005) unveiled that teachers mostly relied on textbooks to
facilitate the teaching-learning process. She also cited Yumul (2001)
revealing that the adequate instructional materials were not highly
utilized.
Sameon (2002) found out in his study that the most pressing
problems encountered by the instructors were inadequate facilities and
equipment; inadequate knowledge of teaching strategies and approaches.

56. Likewise, Bello (2009) also divulged that her respondents were
capable in teaching but had not yet achieved the level of competence for
optimum effectiveness. She stressed that teachers have more to enhance
such as on educational technology, technology integration, professional
relationship, community linkages and collaboration.
Also,
according
to
the
monitoring
and
evaluation
of
the
implementation of the basic education curriculum, there were gross
inconsistencies between the kind of graduates/learners that the schools
desire to produce and the strategies they employ. Instruction was still
predominantly authoritative and text-book based, learning was usually
recipient and reproductive, supervision was commonly prescriptive and
directive; and assessment was focused more on judging rather than on
simproving performance.
The second finding was that teachers wanted to know more about
integrative teaching. Teachers did not feel confident to use the
approaches because of the limited knowledge to operationalize them in
terms of lesson planning, instructional materials development, subject
matter organization, presentation and evaluation. There were still many
teachers who do not have enough knowledge about the key concepts and
approaches. However, they were willing to learn how to be more effective
in facilitating the full development of the students‘ potentials and to be
facilitator of the integrative learning process.

57. Thirdly, teachers had limited knowledge of constructivism as a
learning process. Learning as a construction process and the learner as a
constructor of meaning is among the basic concepts of the BEC.
Although the concept was unfamiliar to many teachers, it was observable
in some classes where problem solving, inquiry, or discovery approaches
were being used.
Another finding of the team was that several factors constrained
teachers from playing their role as facilitators of the learning process.
The factors that inhibited teachers from playing the facilitators‘ role
effectively were students‘ English deficiency, overcrowded classes, and
insufficient supply of textbooks, prescriptive supervision and an
examination system that encourages authoritative teaching.
However, there were also findings which revealed positive results.
One was the study of Aware-Achwarin (2005) on Teacher Competence of
Teachers at Schools in the Three Southern Provinces of Thailand which
revealed that teachers‘ competence was at high level. The highest was on
―teachership‖.
The second was that of Villanueva (1999), as cited by Binay-an
(2002), which revealed that the instructional abilities of the teachers
were rated high along ability to explain correctly, having a good
command of the language and sufficient knowledge of the subject matter.

58. Further, the findings of Acantilado (2002) showed that the faculty
members of Tertiary Accredited Programs of SUCs in Region I were highly
competent. Another, Roldan (2004) cited Subala revealing that teacherrespondents were competent. This finding revealed that the instructors
could be proper sources of assistance and guidance to their students in
analyzing different mathematical problems. She stressed that the more
competent the instructors are the better is the result in terms of the
teaching-learning process.
Grouws and Cebulla (2002), as cited by Fianza (2009) mentioned
that research findings indicated that certain teaching strategies and
methods should be worth careful consideration as teachers strive to
improve their mathematics teaching practice. Teachers should use
textbooks as just one instructional tool among many rather than feel
duty-bound to go through the textbook as one section per day basis. As
technology is used in mathematics classroom, teacher must assign tasks
and responsibilities to students in such a way that they have active
learning experiences with technological tools employed.
Research then suggests that teachers should concentrate on giving
opportunities for all students to interact in problem-rich situations.
Teachers must encourage students to find own solution method and give
opportunities to share and compare their solution method and answer in
small groups. Such solutions were presented by Roldan (2004) as she

59. cited Diaz (2000). The solutions were: (1) the administration must hire
only competent Mathematics Teachers to teach the subject. This step is
supported by Rivera (2010) citing an article posted on www.eric.ed.gov
conveying that schools are hiring teachers who are competent since
students‘ attainment level is hoped to improve; (2) the administration
should also be fully aware of the importance of faculty development
through the pursuit of graduate courses and attendance to seminars and
in-service training, for such are essential to the teachers‘ professional
growth and development, particularly on effective teaching; (3) teachers
should strive to elevate their level of attitudes along concept and
mathematics from above average to higher level; (4) rigid annual
evaluation of teachers may also be of help for them to assess their
weaknesses, make improvements on such and maintain and sustain
their strengths; (5) moderately competent and competent teachers attend
Saturday and summer classes or workshops to be able to upgrade their
competence; and (6) teachers should be encouraged to attend seminars
and workshops particularly in Mathematics to update them with recent
trends and educational innovations.
Guidance Skills
Educational Guidance is the process of helping students to achieve
the self-understanding and self-direction necessary to make informed
choices and move toward personal goals (Microsoft ® Encarta ® 2009).

60. One of the innate tasks of a teacher is to promote learning. He
does this by guiding the learning process of students through planning
and organizing meaningful learning experiences, creating a desirable
learning environment, using a variety of instructional materials,
providing for individual differences and appraising students‘ growth and
development.
Diaz (2000) expressed in her study that a teacher who is the
facilitator of learning should also have special knowledge and skills in
guiding, directing and advising learners. She stressed that doing so gives
substance to teacher-students relationship. Thus, in this special task,
the teacher must possess knowledge and skills in assisting students in
their problems.
Graycochea (2000) revealed in his study that his teacherrespondents were highly competent in providing an environment
conducive to learning. This had been perceived by the teachers, students
and their heads.
The study of Oredina (2006) exposed that mathematics teachers‘
guidance skills were perceived as strengths. She emphasized that the
teacher-respondents were very good in directing, supervising and guiding
the
learning
process
by
providing
an
atmosphere
which
is

61. nonthreatening. Further, they were able to provide appropriate level and
needs of the students. In addition, they can direct the work of the
students properly.
Management Skills
The principle of a favorable learning environment is of universal
acceptance. To teach effectively is to manage class effectively, too. This
principle suggests that learning becomes interesting and enjoyable under
favorable working conditions. Good classroom practices; thus, enter the
scene.
Bueno (1999), as cited by Tabafunda (2005), asserts that a sound
classroom can be maintained by employing classroom management
practices. These practices are: (1) structuring the learning environment;
(2) religious preparation of lessons; and (3) maintenance of constructive
pupil-behavior correction. Thus, a successful teacher is one who can
evaluate situations and then apply appropriate styles to address such
situations. (http//www.classroom%20management.03-29-10)
One of the most difficult problems that confront teachers is to
manage classrooms. This is because one cannot fully learn the
techniques of proper management from books or from earning a
bachelor‘s degree.

62. Achwarin
(2005)
reveals
that
among
the
dimensions
of
instructional competence, classroom management was rated the lowest.
Olbinado (2007) in her study entitled, ―Enhancement Program for
Secondary Teachers who are Non-math Majors‖ revealed that the
teacher-respondents were good at classroom management. She stressed
that even though the teachers were not holders of mathematics degree,
they were good at managing classes since most of them were seasoned
teachers.
Oredina (2006) underscored that the teacher-respondents were
very good at guidance skills. This means that the teachers were highly
aware of the importance of extrinsic motivation and strengthen positive
attitudes such as giving commendations and approval.
Evaluation Skills
When a teacher finishes the course of the discussion, he
automatically administers the tools to assess learning. It is through
assessment that students‘ performance is monitored. The purpose of
evaluation is hence necessary.
According to Laroco (2005) there are four principles of educational
assessment. These are: (1) educational assessment always begins with
educational values and standards. Assessment is not an end in itself but
a vehicle for attaining educational goals; (2) educational assessment

63. works best when it accurately reflects the students‘ achievement/
attainment and understanding of educational goals and standards; (3)
educational assessment works best when it is ongoing, not episodic and
when varied measures are used; and (4) effective educational assessment
provides students with information (e.g. goals, standards, feedback) to
motivate and enable them to attain educational targets. Students should
be aware of what they are being assessed for and should also be given
information on what is needed to attain the expected outcomes.
Sameon (2002) revealed that his respondents perceived themselves
as very competent in assessment. He stressed that the teachers
understood the underlying theories and practices to improve students‘
performance.
Rivera and Sambrano (1999), as cited by Tabafunda (2005),
stressed that effective teaching should be coupled with the art of
questioning. Good questions served as essential in developing students‘
ability to define and exercise judgments.
Oredina (2006) found out in her study that the teacherrespondents were perceived ―very good‖ in evaluation and assessment.
She revealed that along the four competence dimensions, the skill on
evaluation had the highest rating. This means that the respondents were

64. highly capable in formulating questions with the purpose of developing
critical thinking; mathematics teachers were competent in providing
reasonable, appropriate, practical and challenging enrichment activities
to substantiate what had been taken in class.
Comparison in the Perceived Instructional Competence Among the
Groups of Respondents
According
to
the
article
accessed
from
http://en.wikipedia.org/wiki/individual_differences_psychology,
―Every
man is in certain respect (1) like all other men, (2) like some other men
and (3) like no other men‖. Thus, two contrasting ideas are revealed –
individual similarities and differences. This means that any two
individuals may have same perceptions at a time; but they may also have
opposing perceptions at another time. The adage, ―Everyone experiences
different time and space than everyone else but can still find
commonalities at a certain time in space with everyone else‖ supports
this
thoughts
and
contentions
very
well
(http.//www.newton.dep.anl.gov/askasci/gen06/gen06327.htm).
Commonalities among perceptions exist because there is a
common code (shared representations) for perceptions and actions. This
is
contained
in
the
Common
Coding
(www.en/wikipedia.org/wiki/common_coding_theory).
On
Theory
the
other
hand, differences exist because of different status of people, needs,

65. personalities, and beliefs. Further, individuals differ in terms of
perception
because
of
selective
perception
(www.ask.com/questions_about_selective_perception).
The aforecited thoughts are revealed in a study published in the
web revealing that there is a significant difference in the perceptions
along skills between the teachers and managers/heads. This is due to
the observation that when one holds a position, he has a certain degree
of confidence. He is sure of his capabilities and enjoys certain status
higher than others.
This can be supported through the educational thought presented
by Johnson (2010) on administrative support and cordial teacherstudent relationships. He stresses that these educational principles
integrate the concepts on backing-up, lending hands and sharing
appreciation.
Relationship of Profile and Level of Competence along Content
A teacher cannot share what he does not have. He has to be a
subject matter expert when he intends to instill lasting thoughts in the
minds of his learners.
Several articles posted on the World Wide Web implicitly and
explicitly cite the relationship between profile variables along highest

66. educational attainment, teaching experiences and number of seminars
attended and subject matter competence.
One article contends that subject matter/ content knowledge is
rooted from teaching experiences and the number of degrees a teacher
holds.
(http://doconnor.edublogs.org/finding-e-learning-and-online-
teaching-jobs/)
Another supports this thought by mentioning that subject matter
competence can be attained and maintained through continuing
professional education. It also extended that teachers who are subject
matter expert are the ones who have stayed in service for quite some
time. (jobs.stanlake.co.uk/recruiter/users/jobs.php?id=22).
A published research on Teacher Certification was also accessed.
The study revealed that teachers who had certification, longer years of
professional service and more frequencies of degrees show subject matter
competence (http://www.sedl.org/pubs/policyresearch/resources/ARA2004.pdf).
Another web article reveals that instructor-led training workshops
also
enhance
subject
(http://doconnor.edublogs.org)
matter
expertise
and
skills.

67. A national study on teaching expertise, though in the HEIs, by
Clemente-Reyes (2002) expresses that subject matter expertise is gained
through
possessing
educational
achievements,
gaining
years
of
professional teaching service and attending training. She mentioned that
earning a bachelors‘ degree was not sufficient; thus, recommending for
continuing professional education since majority of the teacher experts
were masters degree holders or even doctorate degree holders. Also,
when a teacher is exposed in the teaching profession, he is likely to
expand his horizons in his field; thus, contributing to teaching expertise.
Lastly, she asserted that training helped a lot in gaining additional input.
Such input met or not met by teachers in her formal education can affect
his content knowledge.
Further , the Australian Government commissioned the Australian
Council for Educational Research (2001) to conduct an investigation of
effective mathematics teaching and learning in Australian secondary
schools. The research revealed that teacher knowledge and educational
background is positively, but weakly related to teacher effectiveness. The
more this education has to do with mathematical content and pedagogy,
the more likely it is that teachers will be effective.
Keneddy (2001) also wrote in her article that a prospective teacher
majoring a subject like mathematics or science does not guarantee that

68. teachers will have the kind of subject matter knowledge they need for
teaching. She further stressed that college-level professional subjects do
not address the most fundamental concepts in disciplines. Instead,
professors provide massive quantities of information, with little attention
given to significance or fundamentals on how to deal with teaching.
Relationship of Profile and Level of Competence along Instruction
Teaching is a systematic presentation of facts, skills and
techniques. It needs certain competencies in order to teach effectively.
One way of assuring this is having a degree in education or any related
degrees. If a teacher wishes to teach in secondary, a field of specialization
is required in order to teach more competently. But having a degree does
not guarantee that one can teach well, he needs constant upgrading of
what he knows.
The study of Estoesta (1999), as cited by Fianza (2009) reveals that
there was a strong relationship between educational attainment and
teaching experiences to instructional competence. She stressed that the
teachers who had higher educational attainment and teaching experience
had high performance rating, thus higher competence. This study is
seconded by the study of Sameon (2002). According to him, teaching
competence is highly correlated to highest educational attainment and
teaching experience.

69. These findings were also supported by the international study of
Achwarin (2005) arguing that teachers‘ qualification is positively and
significantly related to teachers‘ competence.
Binay-an (2002) extended that length of service and number of
seminars and trainings were significantly related to competence.
Davis (2000), as cited by Binay-an (2002), claimed that teachers
who are younger in the service are more likely to possess greater
competence since they have greater inquisitive mind and zest for
teaching. However, this was not in congruence to the study of Laroco
(2005) claiming that teachers who had longer years in service are in
better position to adjust themselves to different classroom situations;
thus, they are more competent. She concluded that teaching experiences
add to the teaching competence.
Oredina (2006) accentuated that highest educational attainment is
significantly correlated to teaching skills but not significantly correlated
to guidance, management and evaluation skills. She also extended that
number of years in teaching, performance rating and number of
seminars attended are not significantly correlated to the four core
dimensions of instructional competence. These imply that teacher with
higher performance rating, with more number of years of teaching and
seminars were not necessarily more competent than those with less.

70. Soria (1995), as cited by Laroco (2005), found out that there was
no significant relationship between highest educational attainment and
number of years in teaching and their professional proficiency.
Parrochas (1998) also supported this contention, as cited by
Laroco (2005), by claiming that there is no significant relationship
between highest educational attainment of teachers and mastery level of
pupils.
Relationship of Subject Matter and Instructional Competence
Global goals of education stress the connection between how
teachers let the students know and what the teachers actually know.
Some of these goals are (1) all children should be taught by teachers who
have the knowledge, skills, and commitment to teach children well; (2)
for all teachers to have access to high-quality professional development;
and (3) for teachers and principals to be hired and retained based on
their ability to meet professional standards of practice. It is only with
these clearly stated and directed goals that teaching-learning process will
be meaningful.
Leinhardt, as cited by Subala (2006), disclosed that teaching
practices were often considered as one of the reasons why American
students were not currently demonstrating top achievement in science
and mathematics. He further stressed that teacher‘s knowledge of the
subject
matter
necessarily
influenced
their
classroom
practices.

71. Moreover,
linkages
between
teacher‘s
personal
knowledge
and
instructional activity had proven elusive despite the considerable level of
concern expressed regarding low levels of mathematics and science
knowledge possessed by pre and in-service teachers.
Binay-an
(2002),
in
her
study,
―Determinants
of
Teaching
Performance‖, pointed out that subject matter expertise is significantly
related to teaching expertise. He made use of the adage, ―One can‘t give
what he does not have‖ to substantiate this.
Cabusora (2004) asserted that subject matter expertise and
exemplary instruction are significantly correlated. He stressed that when
teachers have thorough grasp of the teaching-learning process, they are
likely to perform in instruction.
Diaz (2000) also stressed that teachers who are competent in
instruction are the ones who are competent in their field of expertise.
In the study of Dr. Flordeliza Clemente-Reyes (2002) on ―Unveiling
Teaching Expertise: A showcase of 69 Outstanding Teachers in the
Philippines‖, it was revealed that subject matter expertise was a
contributory factor to teaching expertise. It was stressed that mastery of
content-specific knowledge and the organization of this knowledge affect
effective instruction. If the teachers were not experts in their field, it is
unlikely for them to possess teaching expertise

72. An international study was cited by an article posted on the
Harvard Educational Review. This study was by Reynolds (1999). In the
study, he exposed that subject matter expertise was not contributory to
success in teaching. With these she expanded the meaning of subject
matter expertise to include an awareness of that expertise as learned.
(http://www.hepg.org/her/abstract/164).
Strengths and Weaknesses in Teachers’ Competence
The teacher is always confronted with different challenges that he
needs to face. Challenges of a teacher might be extrinsic or intrinsic.
Teachers might encounter problems on students‘ population, sizes of
classroom and the like. It can also be that a teacher finds preparing for
a class meaningless. These challenges are undoubted to be contributory
to the teacher‘s success in teaching.
Ordas (2000), as cited by Olbinado (2007), disclosed that schools
were not only faced with great lack of teachers; but with the massive
deficiency in qualified and competent teachers. She further stressed that
teacher training was deficient in terms of frequency and accessibility for
teachers.
Roldan (2004) concluded that secondary mathematics teachers in
Region I were proficient in concept and computations but they were
deficient in their skills in problem-solving and the use of teaching
strategies.

73. Oyando (2003) revealed in her investigation that teachers were
highly competent in basic mathematics; but were moderately competent
in higher mathematics.
Almeida (1998) and Diaz (1998) revealed that their respondents, in
separate studies, have moderate competence in their field. Diaz (1998)
added that mathematical analysis was wanting.
Verceles (2009) revealed that the use of calculators, especially
computers were all weaknesses. Lecture method was very dominant.
Nuesca (2006) indicated that Philippine Instruction is highly
teacher-centered. She supported this by enumerating the three most
common methods used by Filipino teachers: lecture, discussion and
demonstration.
Fianza (2009) disclosed that math instruction is often approached
in terms of stating and emphasizing rules- the ―tell, show and do‖ model.
Graycochea
teaching
technique;
were
(2000)
somewhat
motivational
revealed
serious.
strategies
that
problems
on
She
stressed
that
and
management
mathematics
questioning
were
the
contributory factors in this finding.
Cristobal (2004) found out that Instructors of Lorma Colleges
exhibited
capabilities
along
teaching
procedure,
substantiality
of
teaching and evaluation. The only expressed need is in the use of varied
instructional materials.

74. Roldan (2004) exposed that the secondary mathematics teachers in
Region I were deficient in the use of teaching strategies. Binay-an (2002)
supported this finding when she exposed that her respondents were not
so competent in using methods and approaches.
Alano (2003) of the Philippine Normal University mentioned that
studies showed that almost half of the teachers teaching the core
subjects have computer units, but only a few among them use such for
classroom instruction.
Oredina (2006) in her dissertation revealed that teacher‘s level of
instructional competence was very good. The evaluation skills were rated
highest while their teaching skills were the lowest.
Two-Pronged Training Programs
To be a successful math teacher, one needs to continually upgrade
himself. With this belief, the Congressional Commission in Education, as
cited by Olbinado (2007), recommended that a periodic assessment of
training needs of school teachers in both public and private schools is
imperative.
Eslava
(2001)
pointed
out
that
attending
service
trainings
enhances, with no doubt, the professional qualities of teachers. Laroco
(2005) added this thought expressing that when teachers wanted to
continue improving on their teaching performance, they needed to
undergo necessary training.

75. Cristobal (2004) claimed that while training remains only one of a
number of alternative approaches towards human resource development,
it remains to be the most utilized instrument for the development of
adults, professionals and paraprofessionals alike in a wide variety of
specific areas.
Fianza (2009) believed that training is a very good approach to staff
development.
She
opined
that
quality
instruction,
especially
in
mathematics, can be attained and delivered through enhancing teachers‘
competence.
Roldan (2004) claimed that training should be of prime concern
when quality of education is of prime concern, too. Such training has to
be done before any plan for assigning longer period to the teaching of
Mathematics is implemented.
Lastly, Oredina (2006) discoursed that training allows teachers to
show and share ideas, ask questions, make decisions and share personal
experiences in teaching Mathematics. She stated that this program will
make teachers change their traditional method of teaching to that of a
facilitator of learning.

76. Chapter 3
RESEARCH METHODOLOGY
This chapter presents, incorporates and discusses the research
design, the sources of data, instrumentation, procedure and the tools for
data analysis.
Research Design
The descriptive method of investigation was used in the study. This
design aims at gathering data about the existing conditions. Calmorin
(2005) describes descriptive design as a method that involves the
collection of data to test hypothesis or to answer questions regarding the
present status of a certain study. Further, Deauna (2003) defines such
design as one that includes all studies that purport to present facts
concerning the nature and status of anything.
Since the comparison on the perceptions of the respondents along
instructional competence and the relationship of the data on the
teachers‘ profile, content and instructional competence were established,
the descriptive-comparative and the descriptive-correlational methods
were employed, respectively.
Sources of Data
The population of this study is composed of three (3) groups of
respondents: (1) heads, (2) High school mathematics teachers in the

77. Private City schools of San Fernando (3) high school mathematics
students for the academic year 2010-2011.
All the heads with the mathematics teachers were considered. For
the students, one-third of the class population was considered. This is
equivalent to thirty- three and one-third percent (33 1/3 %) of the total
number of students in a class. According to Gay, as mentioned by
Oredina (2006), ten percent (10%) of the population is an acceptable
sample but twenty percent (20%) is required from a small population.
However, to make the findings of this study more reliable and acceptable,
the researcher preferred to implement the statistical idea that the bigger
the sample, the more valid are the results.
The total population of three hundred and fifty-seven (357)
constituted the respondents of this study, broken down as follows: three
hundred eighteen (318) students, twenty six (26) teachers and thirteen
(13) heads. Substitute teachers or on-leave teachers are not considered
as respondents of the study.
Table 1 shows the distribution of the
number of specified respondents from the thirteen (13) Private Secondary
Schools of the City Division of San Fernando, La Union for the academic
year 2010-2011.

78. Table 1
Distribution of Respondents
SCHOOLS
Brain and Heart of a Christian (BHC)
Central Ilocandia Institute of Technology
(CICOSAT)
Christ the King College (CKC)
Diocesan Seminary of the Heart of Jesus
(DSHJ)
Felkris Academy
Gifted Learning Center (GLC)
La Union Cultural Institute (LUCI)
La Union Colleges of Nursing, Arts and
Sciences (LUCNAS)
MBC Lily Valley School
National College of Science and Technology
(NCST)
Saint Louis College (SLC)
San Lorenzo Science School (SLSS)
Union Christian College (UCC)
TOTAL
Number of
Students Teachers Heads
33
2
1
20
2
1
75
3
5
1
1
1
8
7
14
7
1
1
2
1
1
1
1
1
7
7
1
1
1
1
90
11
24
318
6
1
2
26
1
1
1
13
Instrumentation and Data Collection
To gather the data essential to the realization of this study, two
sets of data gathering instrument were utilized. One was a 60-point
researcher-made mathematics competence test for mathematics teachers
whose content was based on the 2010 Secondary Mathematics
Curriculum. The other is a questionnaire-checklist, the key instrument
in obtaining the data in evaluating the instructional competence of high
school mathematics teachers in the Private Secondary Schools.

79. The mathematics competence test is divided into 4 areas of
Secondary Mathematics (Elementary Algebra, Intermediate Algebra,
Geometry, Advanced Algebra, Trigonometry and Statistics). Each area
includes 15 questions; each question corresponds to one (1) point.
Further, it was made following the Bloom‘s Taxonomy of Cognitive Skills
for Mathematics (Conceptual, Reasoning/Analytical, Computational, and
Problem-Solving). (Please see appended Table of Specifications)
On
the
other
hand,
such
questionnaire
on
instructional
competence was composed of two parts: Part I elicited the profile of the
mathematics teachers along the highest educational attainment, years of
teaching mathematics and number of mathematics trainings and
seminars attended; Part II, on the other hand, drew out the level of
instructional
competence
skills/facilitating
skills,
along
the
management
four
skills,
areas
guidance
─
teaching
skills,
and
evaluation skills. The statements in the questionnaire for studentrespondents were rephrased in such a way that these are parallel to the
statements in the questionnaires for teachers and heads. This rewording
ensured that the student-respondents clearly understood the details for
assessment.
Each of the teacher-respondent took the mathematics competence
test not exceeding one hour or sixty (60) minutes in one sitting/ session.
The administration of the test was conducted during their free periods,

80. lunch breaks, and after the class hours as agreed upon by the researcher
and the teacher-respondents, themselves. Such being the case, the
researcher took him almost 2 months to gather the required data. Also,
each teacher was evaluated by his/ her students in one of his/her
classes, heads and himself.
With the permission of the school heads of the thirteen private
secondary schools, copies of the two sets of instrument were given to the
respondents to accomplish. In the mathematics competence test,
teachers were not allowed to use calculators. This was made sure by the
researcher during his proctoring of tests. The fully accomplished
questionnaires were retrieved personally by the researcher.
Validity and Reliability
The mathematics competence test was a researcher-made test
whose content was based on the 2010 UBD-Secondary Education
Curriculum. The questionnaire-checklist, on the other hand, was a
combination of the FAPE Performance Evaluation Tool, Institutional
Supervisory Instrument of Christ the King College and the questionnairechecklist utilized by Oredina (2006) in her study, ―Mathematics
Instruction in the HEIs in La Union: Basis for a Training Program‖. Since
the key instruments were based on several manuscripts, their validity
and
reliability
were
established.
The
Education
Supervisor
for
Mathematics; a Master Teacher II of La Union National High School; the

81. Academic Coordinator of Christ the King College and the members of the
reading committee served as the validators of the two sets of
questionnaires. The computed validity rating for the Mathematics
competency
test was
4.63,
which means
that
the Mathematics
competency test is of very high validity. On the other hand, the computed
validity rating for the Instructional competence test was 4.71 indicating a
very high validity, too. Further, all the suggestions cited by the validators
were incorporated, especially on the competence test where the radical
symbols and fractional bars have to be encoded using the equation editor
to
avoid
unnecessary
misconception.
Conversely,
their
internal
consistency or reliability was determined using the Kuder-Richardson 21
formula. The first one was used to get the reliability of the content
competence test while the second was used to get the reliability of the
instructional competence checklist.
The formulas are (Monzon-Ybanez
2002):
𝐾𝑅21 =
𝑘
𝑘−1
1−
𝑥 𝑘−𝑥
𝑘𝜎 2
where:
k = number of items
𝑥 = mean of the distribution
𝜎 2 = the sample variance of the distribution
or

82. (Garett 1966): 𝐾𝑅21 =
[𝑛𝜎 2 −𝑀(𝑛 −𝑀)]
𝑡
(𝑛−1)(𝜎 2 )
𝑡
where:
n = product of the number of items in the test and the highest
scale
𝜎 2 = variance
𝑡
𝑀 = mean
Through
the
assistance
of
the
Education
Supervisor
for
Mathematics, Dr. Jose P. Almeida, a dry run of the questionnaires was
administered to 20 students, 5 mathematics teachers and 1 Mathematics
head of La Union National High School. The mathematics competence
test had a reliability coefficient of 0.93, denoting that the competence test
was very highly reliable. Alternatively, the questionnaire checklist was
found to have very high reliability having a computed coefficient of 0.96.
Tools for Data Analysis
The data which were gathered, collated and tabulated were
subjected for analysis and interpretation using the appropriate statistical
tools. The raw data were tallied and presented in tables for easier
understanding.
For problem 1, frequency counts and rates were used to determine
the status of the profile of the respondents along highest educational

83. attainment, years in teaching mathematics. A scoring scheme seen in
data categorization together with frequency counts and rates were used
to treat the number of seminars and trainings attended. The rates were
obtained by using the formula below:
R= n
N
where:
x 100
R - rate
n - number of frequencies gathered by each item
N - the total number of cases
100 – constant
For problem 2.a, mean and rates were utilized to determine the
mathematics competence; whereas for problem 2.b., weighted mean was
employed to determine the level of instructional competence along the
four areas.
The formula for mean is as follows (Ybanez 2002):
M = ∑x
N
Where: M – mean
x – sum of the product of the extent of the variables and
their corresponding frequency
N – number of respondents

84. For problem 2.1, t-test independent (t-test between means), taken
two at a time was used to determine the difference in the perceptions of
the
respondents.
The
formula
for
t-test
for
means
(http://en.wikipedia.org/wiki/Student%27s_t-test) is:
where:
= estimator of the common standard deviation of the two
samples
n = number of participants, 1 = group one, 2 = group two.
n – 1 = number of degrees of freedom for either group
n1 + n2 – 2 = the total number of degrees of freedom, which is used
in significance testing.
t = degree of difference
For problem 3.a, 3.b and 3.c, the Pearson-r moment of correlation
was used to determine the significance of relationship between teachers‘
profile
and
teachers‘
level
of
content
competence,
profile
and

85. instructional
competence
and
level
of
content
competence
and
instructional competence. The formula (Ybanez 2002) is:
N ∑XY − ∑X (∑Y)
𝑟=
(N∑X 2 − ∑X 2 )(N ∑2 – ∑Y 2 )
where: X – observed data for the independent variable
Y – observed data for the dependent variable
N – size of sample
r – degree of relationship between X and Y
The
computed
significance;
correlation
thus
coefficients
the
were
formula
subjected
to
used
(http://faculty.vassar.edu/lowry/ch4apx.html) is:
𝑡=
r
1 − r2
n−2
where: r – computed correlation coefficient
n-2 – degree of freedom
t – degree of significance for r
For problem 4, the major strengths and weaknesses were deduced
based on the findings, particularly on the level of competence (content
and instruction) through statistical ranking. An area was considered
strength when it received a descriptive rating of very good or excellent;
otherwise, the area was considered a weakness.

86. The MS Excel Data Analysis Tool and STATEXT were employed in
treating the data.
Data Categorization
For the mathematics competence test, the Scale System is utilized.
Ave. No. of
Teachers who
Got the correct
Answer
Descriptive Equivalent rating
DER class
22-26
Outstanding
strength
17-21
Above Average Competence
strength
12-16
Average Competence
weakness
7-11
Fair Competence
weakness
0-6
Poor Competence
weakness
For the mathematics trainings and seminars attended by teachers,
data were categorized according to levels: school, local, national and
international. Each level corresponds to a particular number of points.
The scales below clarify the categorization:
Level
Frequency
Point Equivalent
School
1
1
Local
1
2
Regional
1
3
National
1
4
International
1
5

87. No. of points
Descriptive Equivalent rating
40 and above
Very Adequate (VA)
31-40
Moderately Adequate (MA)
21-20
Fairly Inadequate (FA)
11-20
Slightly Inadequate (SI)
1-10
Very Inadequate (VI)
For the level of instructional competence, the 5-point Likert Scale
below is incorporated:
Points
Ranges
DER
DER Class
5
4.51-5.00
Excellent (E)
Strength
4
3.51-4.50
Very Good (VG)
Strength
3
2.51-3.50
Good ( G)
Weakness
2
1.51-2.50
Fair (F)
Weakness
1
1.00-1.50
Poor (P)
Weakness
Moreover, the major strengths and weaknesses are drawn out from
the ratings given. Such ratings are ranked; hence, the ranking system
was used. The item that gets the highest mean value in the strengths
was ranked first indicating that it is regarded as the foremost strength.
These procedures also apply in the items considered as weaknesses.
Finally, the scales for interpretation on the degree of relationship of
the identified correlates are as follows (Ybanez 2002):
±1.00
-perfect correlation

88. ±0.91-0.99
-very high correlation
±0.71-±0.90
-high correlation
±0.41-±0.70
-marked correlation
±0.21-±0.40
-low correlation
±0.01-±0.21
- negligible correlation
0.00
- no correlation
Proposed Training Program
The proposed training program includes the following parts:
rationale,
objectives,
content,
methodology,
training
management,
participants, duration, logistics and success indicator (Cayabyab, 2010).
A training program is set for content competence; another program
is set for instructional competence. The trainers considered for the
training program were some of the speakers met by the researcher in the
seminars/workshops
he
attended,
the
Education
Supervisor
for
mathematics, and some of his professors in mathematics.
Validity of the Training Program
To establish the validity, acceptability and functionality of the
proposed training program, it was presented to the Administrators of the
Private Secondary Schools in the City Division of San Fernando, La
Union.

89. The validation was guided by the following point assignments:
Points
Ranges
DER
5
4.51-5.00
Very High (VH)
4
3.51-4.50
High (H)
3
2.51-3.50
Moderate (M)
2
1.51-2.50
Fair/Slight (F/S)
1
1.00-1.50
Low/Poor (L/P)

90. Chapter 4
PRESENTATION, ANALYSIS AND INTERPRETATION OF DATA
In this chapter, the data gathered were subjected to statistical
analysis and systematically presented to manifest the levels of content
competence
along
conceptual
skills,
reasoning/analytical
skills,
computational skills and problem-solving skills; and instructional
competence of the mathematics instructors along teaching skills,
management skills, guidance skills and evaluation skills. The identified
strengths and weaknesses were the foundations for formulating and
structuring
a
proposed
two-pronged
training
program
for
the
Mathematics teachers in the City Division of San Fernando, La Union.
Profile of the Mathematics Teachers
The first problem of the study focused on the profile of the
Mathematics Teachers in the Private Secondary Schools in the City
Division of San Fernando to provide basic but relevant information on
teachers‘ competence both for content and instructional competence.
Highest Educational Attainment
Table 2 shows the highest educational attainment of Mathematics
Teachers. Out of the 26 teacher-respondents, 11 or 42.31% are licensed
teachers, 14 or 50.00% are pursuing graduate studies and 2 or 7.69%

91. Table 2
Distribution of Teacher-Respondents
According to Highest Educational Attainment
Educational Attainment
Frequency
Rate
BSED/BSE/AB/BS graduate
(Non-licensed)
0
0%
BSED/BSE/AB/BS graduate
(Licensed)
11
42.31%
BSED/BSE/AB/BS graduate
13
50.00%
MS/MA graduate
2
7.69%
with EDd/PHd units
0
0%
EDd/Phd graduate
0
0%
26
100%
w/ MS/MA units
Total
are Master‘s degree holders. This means that the Mathematics teachers
are qualified to teach in the Secondary schools since they have met the
necessary requirements stipulated in the Magna Carta for Public School
Teachers and Republic Act 9293, which both require secondary teachers
to be duly registered before engaging themselves in the teaching
profession. It is also noticeable that majority of the teachers value
continuing education since half of the total population are currently
enrolled in their Master‘s program. This finding accepts the null

92. hypothesis that 50% of the respondents are pursuing their graduate
studies. Also, it runs parallel to the studies of Fianza (2009), Eslava
(2001) and Rulloda (2000) stressing that generally, the teachers meet the
basic requirements for teaching and do not want to be stagnant because
they want to elevate their professional outlook to make them effective
and worthy members of the profession.
Number of Years in Teaching Mathematics
Table 3 reveals the distribution of teacher-respondents according
to the number of years in teaching Mathematics. It further reveals that
18 or 65.38% have been teaching from 0-5 years, 2 or 7.69% from 6-10
years, 1 or 3. 85% from 11-15 years, 4 or 15.39% from 16-20 years, 1 or
3.85% from 21-25 years, and 1 or 3.85% has been teaching for more
than 25 years. These data give a general impression that the
Mathematics teachers of the Private Schools in San Fernando City, La
Union are very young in the profession. It means that the general turnover of teachers in the private schools is high, especially in small schools
where teachers stay only up to 1-2 years since they desire to be
employed in the
public schools
or
work abroad, where
higher
compensation, more incentives and other benefits abound. Therefore, it
rejects the null hypothesis of the study that 50% of the teacherrespondents have teaching experience of below 5 years. This finding runs
parallel to the studies of Oyanda (2003) and Fianza (2009) revealing that

93. the teachers are generally quite young in the service. Their findings
revealed that more than half of their respondents have less than 5-year
teaching experience.
Table 3
Distribution of Teacher-Respondents
According to Number of Years in Teaching Mathematics
Years
Frequency
Rate
0-5 years
17
65.38%
6-10 years
2
7.69%
11-15 years
1
3.85%
16-20 years
4
15.39%
21-25 years
1
3.85%
26 years and above
1
3.85%
Total
26
100%
However, the finding of this study does not support the finding of
Aware-Achawarin (2005) when he revealed that 71.07% of his teacherrespondents were tenured in the teaching profession since they have
been teaching for more than 10 years.
Number of Seminar/Trainings Attended (for the last two years)

94. Table 4 presents the distribution of the teacher-respondents
according to the number of seminars/trainings attended for the last two
years.
Out of the 26 respondents, 22 or 84.62% have ―very inadequate‖
attendance or participation in trainings and seminars while the
remaining 4 or 15.39% have ―slightly adequate‖ attendance to seminars
and trainings. This finding rejects the null hypothesis of the study
stating that 50% of the teacher-respondents have adequate attendance to
Table 4
Distribution of Teacher-Respondents
According to Seminars Attended
No. of Points Earned
for the past 2 years
Descriptive Equivalent
Frequency of
Teachers
Rate
0-10
Very Inadequate
22
84.62%
11-20
Slightly Adequate
4
15.39%
21-30
Adequate
0
0%
31-40
Moderately Adequate
0
0%
40 and above
Very Adequate
0
0%
26
100%
Total
seminars/trainings for the past two years. This implies that the teachers
have not been sent to seminars and trainings where their participation

95. was highly expected. This is caused by financial constraints, nonavailability of teachers due to school commitments and the distance of
the venue of the seminar.
The finding of the current study is supported by the finding of
Oredina (2006), which disclosed that majority of the teacher-respondents
have
―very
inadequate‖
participation
in
seminars
and
training
workshops. This was due to financial constraints. However, it does not
jibe with the finding of Fianza (2009), which revealed that more than 50%
of her respondents have attended trainings on curriculum, teaching
strategies, management and assessment methods.
Summary of Profile of Mathematics Teachers in the Private
Secondary Schools in San Fernando City, La Union
Table 5 reveals that majority of the Mathematics teachers in the
Private Secondary Schools in the City Division of San Fernando possess
the necessary requirements in the teaching profession. Thus, they are
Table 5
Summary Table of Profile of Mathematics Teachers in the Secondary
Schools in San Fernando City, La Union
Variables
A. Highest Educational Attainment
Frequency
Rate
0
0%

96. BSEd/AB/BS Graduate (Non-licensed)
BSEd/AB/BS Graduate (Licensed)
11
42.31%
BSEd/AB/BS Graduate w/ MS/MA units
13
50.00%
MS/MA graduate
2
7.69%
With EDd/PHd units
0
0%
EDd/PHd graduate
0
0%
26
100%
17
65.38%
6-10 years
2
7.47%
11-15 years
1
3.85%
16-20 years
4
15.39%
21-25 years
1
3.85%
26 years and above
1
3.85%
26
100%
(0-10) Very Inadequate
22
84.62%
(11-20) Slightly Inadequate
4
15.39%
(21-30) Fairly Inadequate
0
0%
(31-40) Moderately Adequate
0
0%
(41 and above) Very Adequate
0
0%
26
100%
Total
B. No. of Years in Teaching Mathematics
0-5 years
Total
C. No. of Seminars Attended
Total

97. qualified to teach in the secondary schools. Also, they value continuing
education by enrolling in graduate school programs; however, they are
very young in the service and their attendance to seminars is very
inadequate.
Level of Subject Matter/ Content Competence
The succeeding tables present the subject matter/ content
competence of the Mathematics teachers in the private secondary schools
in the City Division of San Fernando as revealed in the results of the
Mathematics competence test along conceptual skills, reasoning/
analytical skills, computational skills and problem-solving skills.
Conceptual Skills
Table 6 shows the subject matter competence of the teacherrespondents along conceptual skills. There are twenty-four (24 or
92.31%) teachers who got the items correctly in Elementary Algebra,
eighteen (18 or 69.23%) in Intermediate Algebra, fourteen (14 or 53.85%)
in Geometry, and seventeen (17 or 65.38%) in Advanced Algebra,
Trigonometry and Statistics. Thus, the teachers have ―outstanding‖
competence‖ in Elementary Algebra, ―above average competence‖ in
Intermediate Algebra, ―average competence‖ in Geometry
and ― above
average competence‖ in Advanced Algebra, Trigonometry and Statistics.
Generally, there are eighteen (18 or 69.23%) teachers who got the items
correctly for conceptual skills; thus, they have above average competence

98. Table 6
Subject Matter Competence of the Teacher-Respondents along
Conceptual Skills
Area of Mathematics
Average no.
of teachers
who got the
items
correctly
Rate
DER
Elementary Algebra
24
92.31%
Excellent
Intermediate Algebra
18
69.23%
Above Average
Geometry
14
53.85%
Average
Advanced Algebra, Trigonometry,
and Statistics
17
65.38%
Average
18
69.23%
Above Average
Mean
in conceptual skills. This rejects the null hypothesis of the study that the
teachers have average competence in content along conceptual skills.
This means that the teachers have mastered the basic mathematical
terms, definitions and concepts in mathematics. This is attributed to the
reason that they have finished their degrees in Mathematics and that
majority of them are continuing their graduate studies. Such being the
case, the teachers can impart to the students the basic mathematical
concepts needed in the understanding of more complex analysis of
mathematical problems. It is very true that definitions, theorems,

99. postulates and other facts in mathematics should be well understood by
anyone first before he/she can fully understand the rudiments of
Mathematics. As Mina (2002) explained, knowledge, concepts, principles
and ideas are very necessary in teaching because these start the
acquisition of further learning. Further, it implies that the teachers need
to continually upgrade and update their knowledge in the subject they
are teaching to be able to achieve excellent competence. Roldan (2004)
stressed this in her study that conceptual skills of the teachers are very
important because these serve as the foundations of their math skills.
The finding of the study does not jibe with the studies of Toledo
and Bagaforo, as cited by Diaz (2000), revealing that the teachers felt
moderately competent in their knowledge in mathematics. It was
concluded that the teachers did not possess mathematics competence at
a level very adequate for teaching secondary mathematics.
Reasoning/ Analytical Skills
Table 7 shows the subject matter competence of the teacherrespondents along reasoning/ analytical skills. There are twelve (12 or
46.15%) teachers who got the items correctly in Elementary Algebra,
sixteen (16 or 61.54%) in Intermediate Algebra, nineteen (19 or 73.08%)
in Geometry, and fourteen (14 or 53.85%) in Advanced Algebra,
Trigonometry
and
competence‖
in
Statistics.
Elementary
Thus,
the
algebra,
teachers
―average
have
―average
competence‖
in

100. Intermediate Algebra, ―above average competence‖ in Geometry and
―average competence‖ in Advanced Algebra, Trigonometry and Statistics.
Generally, there are fifteen (15 or 57.69%) teachers who got the item for
Table 7
Subject Matter Competence of the Teacher-Respondents along
Reasoning/Analytical Skills
Average no. of
teachers who got
the items
correctly
Rate
DER
Elementary Algebra
12
46.15%
Average
Intermediate Algebra
16
61.54%
Average
Geometry
19
73.08%
Above Average
Advanced Algebra, Trigonometry, and
Statistics
14
53.85%
Average
15
57.69%
Average
Area of Mathematics
Mean
reasoning/ analytical skills correctly; thus, the teachers have ―average
competence‖ in terms of their reasoning/ analytical skills. This accepts
the null hypothesis of the study that the teachers have average
competence in content along reasoning/analytical skills. This implies
that the teachers can satisfactorily lead the students in comprehending
mathematical problems.
Further, it is evident that in Geometry, the
subject that requires more analysis and probing, the teachers achieved

101. higher competence than the other subjects. It means that they received
more training in reasoning in this subject than the other subjects. This is
very true since Geometry focuses much on deductive reasoning as a tool
in analyzing geometric problems and illustrations. This finding also
means that the teachers needed upgrading of their reasoning competence
to be able to lead students to analyze all types of problems, especially the
most complex ones. Roldan emphasized this in her study that teachers
really needed to be excellent in comprehension. This finding does not
corroborate with the study of Gundayao (2000) when she generalized
that the teachers lacked the reasoning competence since they have poor
skills in analyzing different categories of mathematical problems.
Computational Skills
Table 8 discloses the subject matter competence of the teacherrespondents along computational skills.
The table divulges that there are nineteen (19 or 73.08%) teacherrespondents who got the items correctly in Elementary Algebra, nineteen
(19 or 73.08%) in Intermediate Algebra, twenty-one (21 or 87.50%) in
Geometry, and twelve (12 or 46.15%) in Advanced Algebra, Trigonometry
and Statistics. Thus, the teachers possess ―above average competence‖ in
Elementary
Algebra,
Algebra,
―above
Competence‖
in
―above
average
average
competence‖
Advanced
Algebra,
competence‖
in
in
Geometry
Trigonometry
Intermediate
and
and
―Average
Statistics.

102. Generally, there are eighteen (18 or 69.23%) teachers who got the item
correctly in computational skills; thus, they have ―average competence‖
in terms of their computational skills. This accepts the null hypothesis of
the study that the teachers have average competence in content along
computational skills. This means that the teachers are good sources of
processes, procedures, and techniques in solving items in Mathematics.
Table 8
Subject Matter Competence of the Teacher-Respondents along
Computational Skills
Average no. of
teachers who got
the items
correctly
Rate
DER
Elementary Algebra
19
73.08%
Above Average
Intermediate Algebra
19
73.08%
Above Average
Geometry
21
87.50%
Above Average
Advanced Algebra, Trigonometry, and
Statistics
12
46.15%
Average
18
69.23%
Above Average
Area of Mathematics
Mean
Subala (2006) stressed this when she concluded that when teachers have
average competence or above, they can satisfactorily direct students in
the correct process of solving mathematical items. Roldan stressed that
mathematics teachers needed to be experts in computation because

103. when teachers are experts of this skill, it is expected that students can
master this skill, too.
A closer look at the table makes it evident that the teachers have
much
lower
computational
competence
in
Advanced
Algebra,
Trigonometry & Statistics than the other subjects. This is due to the fact
that this is a more complex subject than the other subjects.
Problem-Solving Skills
Table 9 illustrates the subject matter competence of the teacherrespondents along problem-solving skills.
Table 9
Subject Matter Competence of the Teacher-Respondents along
Problem-solving Skills
Average no. of
teachers who got
the items
correctly
Rate
DER
Elementary Algebra
11
42.31%
Fair
Intermediate Algebra
10
38.46%
Fair
Geometry
13
50.00%
Average
Advanced Algebra, Trigonometry, and
Statistics
12
46.15%
Average
12
46.15%
Average
Area of Mathematics
Mean

104. It demonstrates that there are eleven (11 or 42.31%) teachers who got
the items correctly in Elementary Algebra, ten (10 or 38.46%) in
Intermediate Algebra, thirteen (13 or 50.00%) in Geometry, and twelve
(12 or 46.15%) in Advanced Algebra, Trigonometry and Statistics. Thus,
the teachers possess ―fair competence‖ in Elementary Algebra, ―fair
competence‖ in Intermediate Algebra, ―average competence‖ in Geometry
and ―average competence‖ in Advanced Algebra, Trigonometry and
Statistics. Generally, there are twelve (12 or 46.15%) teachers who got
the items correctly in problem-solving skills; thus, they have ―average
competence‖ in problem solving skills. This accepts the null hypothesis
of the study that the teachers have average competence in content along
problem-solving skills. This means that the teachers can guide their
students in analyzing, interpreting and solving word problems in
Mathematics. Since this is the case, it can be inferred that the students
in the Private Secondary Schools is San Fernando City can analyze, solve
and interpret word problems. This is rooted to their average competence
in analyzing skills and above average competence in computation skills
since a good foundation of analytical and computational skills are
necessary in solving word problems.
Further, among the four subject matter skills, this is the area that
received the lowest mean score. This is due to the fact that these skills
require more rigorous analysis and computation before one can actually

105. come up with an approach to the problem and eventually a correct
solution.
Summary on the Level of Content Competence of the Mathematics
Teachers
Table 10 reveals that the teachers have above average competence
in Elementary Algebra, average competence in Intermediate Algebra,
above average competence in Geometry; and average competence in
Advanced Algebra, Trigonometry and Statistics. Generally, the teachers
have ―average subject matter competence‖ in Mathematics. This accepts
the null hypothesis of the study that the teachers have average subject
matter competence. This means that the teachers know what to teach
since they have ―good‖ proficiency in the Mathematics subjects offered in
the Secondary schools. Since they have average
Table 10
Summary on the Level of Content Competence of the Mathematics
Teachers along Conceptual, Reasoning /Analytical, Computational and
Problem-solving Skills
Area of
Mathematics
Conceptual Reasoning/ Computational
Analytical
Skills
Skills
Skills
ProblemSolving
Skills
Mean
DER
Elementary Algebra
24
12
19
11
17
Above
Average
Intermediate
18
16
19
10
16
Average

106. Algebra
Geometry
14
19
21
13
17
Average
Advanced Algebra,
Trigonometry, and
Statistics
17
14
11
12
14
Average
Grand Mean
18
15
18
12
16
DER
Above
Average
Average
Above
Average
Average
Average
competence in Mathematics, it can be inferred that they know what to
teach; hence, they are qualified to teach secondary mathematics. Since
they are qualified to teach, the students can get adequate concepts and
skills in mathematics.
The finding of this study is supported by the findings of Toledo
and Bagaforo, as cited by Diaz (2000), which asserted that the teachers
have average competence in their knowledge and ability in mathematics.
They emphasized that the teachers needed updating and upgrading of
subject matter competence to possess the needed competence situated at
a level very adequate for teaching secondary mathematics. This was even
stressed by Roldan (2004) that even if the teachers have average or above
average competence, the teachers need to consistently upgrade their
knowledge and capabilities in teaching so as to cope with the challenges
of the new millennium. However, this does not jibe with the study of

107. Gundayao (2000) which revealed that the teachers, in general, have poor
proficiency in the Mathematics subject they are teaching. He stressed
that the competence was poor because the teachers lacked the
competence in analyzing complex mathematical principles, concepts and
problems.
Level of Instructional Competence
The subsequent tables reflect the instructional competence of the
Mathematics Teachers in the Private Secondary Schools in the City
Division of La Union as perceived by themselves, heads and the students.
There were four areas in which the teachers were appraised, namely:
teaching/facilitating skills, guidance skills, management skills and
evaluation skills.
Teaching/ Facilitating Skills
Table 11 shows the mathematics teachers‘ level of instructional
competence along teaching/ facilitating skills. The table reveals that the
teachers have high level of competence as shown by the mean rating of
4.07, which is interpreted as very good.
Table 11
Level of Instructional Competence of the Teacher-Respondents Along
Teaching/ Facilitating Skills

108. Instructional Competence Dimensions
Students Teachers Heads WM
DER
1. Substantiality of Teaching
a. show confidence and exhibit mastery of the
subject matter
4.41
4.33
4.63
4.46
Very
Good
b. show awareness of the developments of the
subject matter as seen in the utilization of key
concepts, relationships, and different
perspectives related to the content area
c. align classroom instruction with national
standards, school’s vision-mission and
educational philosophy
d. focus on and cover all important aspects of
the subject matter
4.28
4.30
4.48
4.35
Very
Good
3.99
4.19
4.41
4.19
Very
Good
4.26
4.22
4.37
4.28
Very
Good
e. connect students’ prior knowledge, life
experiences, and interests in the instructional
process
f. provide values clarification and integration
considering the applications of the subject
area to the students’ practical life
g. engage students in in-depth and varied
experiences that meet the diverse needs and
promote holistic growth
h. relate ideas and information within and across
content areas
4.15
4
4.19
4.11
Very
Good
4.08
3.96
4.22
4.09
Very
Good
4.23
4.04
4.26
4.18
Very
Good
3.79
4.04
4.26
4.03
Very
Good
4.15
4.14
4.35
4.21
Very
Good
a. make abstract concepts clear for students’
understanding
4.18
4.37
4.33
4.29
Very
Good
b. ask students how they got a particular answer
4.29
4.48
4.37
4.38
Very
Good
c. encourage students to probe into reactions,
answers and responses
4.35
4.33
4.30
4.33
Very
Good
Sub-mean
2. Quality of teacher’s explanation
I…

109. d. use knowledge of students’ development to
make learning experiences meaningful and
accessible for every student
Sub-mean
4.13
4.19
4.37
4.23
Very
Good
4.24
4.34
4.34
4.31
Very
Good
3. Receptivity to students’ ideas and
contributions
I…
a.
lead students to ask or initiate thoughtprovoking questions
3.95
4.15
4.07
4.06
Very
Good
b.
integrate and elaborate students’ questions
and contributions into the class discussion
4.14
4.22
4.11
4.16
Very
Good
c.
demonstrate flexibility and responsiveness in
adjusting instruction to meet students’ needs,
ideas and contributions
Sub-mean
4.1
4.19
4.22
4.17
Very
Good
4.06
4.19
4.13
4.13
Very
Good
a. pose thought-provoking questions that
promote high-order thinking skills
4.24
4.15
4.33
4.24
Very
Good
b. encourage students to explain ideas and ask
questions about the content
4.19
4.22
4.22
4.21
Very
Good
c. provide time for student to think, ponder on
and express response
4.25
4.22
4.30
4.26
Very
Good
d. pose follow-up questions to clarify initial
question when a student is unable to respond
effectively
e. emphasize on essential ideas and problems
4.20
4.15
4.37
4.24
Very
Good
4.24
4.19
4.37
4.27
Very
Good
f.
ensure that factual information and skills are
applied to ideas and problems
4.25
4.15
4.19
4.20
Very
Good
Sub-mean
4.23
4.18
4.30
4.24
Very
Good
4. Quality of questioning procedure

110. 5. Selection of teaching methods
a. determined on behavioral objectives and
appropriate to the content area
4.16
4.04
4.22
4.14
Very
Good
b. used in expressing ideas and problems
(projects, themes, panel discussion,
demonstration, etc)
c. emphasizing on and eliciting students’ inquiry
4.21
3.85
4.15
4.07
Very
Good
3.94
3.89
4.15
3.99
Very
Good
d. used to address individual differences and
develop multiple intelligences
3.94
3.78
4.15
3.96
Very
Good
e. intended to engage students in learning and
supportive of theories of collaborative and
cooperative learning
Sub-mean
4.14
4.07
4.26
4.16
Very
Good
4.08
3.93
4.19
4.07
Very
Good
a. computers for designing and printing
instructional materials
3.54
3.59
3.85
3.66
Very
Good
b. the principles of computer-aided and
computer-based instruction
c. multi-media resources, including technologies
such as the internet, in the development and
sequencing of instruction
d. computerized grading sheets (without received
corrections)
3.26
3.33
3.77
3.45
Good
3.08
3.33
3.7
3.37
Good
3.53
3.70
4.04
3.76
Very
Good
e.
3.19
2.96
3.56
3.24
Good
Sub-mean
3.32
3.38
3.78
3.49
Good
Grand Mean
4.01
4.03
4.18
4.07
Very
Good
6. Quality of information and communication
technology used
I use…
overhead/LCD projector
Legend:
WM – Weighted Mean

111. DER – Descriptive Equivalent Rating
This finding is beyond the null hypothesis that the teachers have good
performance
levels
in
their
instructional
competence
along
teaching/facilitating skills.
Substantiality
of
Teaching.
This
aspect
of
the
teaching/facilitating skills received an average rating of 4.21, which is
interpreted as very good. This is the area rated third highest among the
areas under this skill. It means that the teachers exhibit the subject
matter competence required in teaching secondary mathematics. This is
even supported by the result of the mathematics test that the teachers
have average subject matter competence. Being subject matter experts,
the teachers were perceived to be skillful in the utilization of key
concepts, relationships, and different perspectives related to the content
area.
Thus,
it
implies
that
the
students
can
have
adequate
comprehension of the subject matter. This slightly affirms the result of
the
competence
test
revealing
that
the
teachers
have
―average
competence‖ in the Mathematics subject they are teaching.
The Quality of Teacher’s Explanation.
This area received a
rating of 4.31, interpreted as ―very good‖. This is the area with the
highest rating among the areas under teaching/facilitating skills. It can
be inferred that the teachers are able to explain mathematical concepts

112. since they have mastered the mathematical facts and concepts needed in
their subject. With their mastery, the teachers are able to make abstract
concepts clear. Further, the teachers were also perceived to be skillful in
involving students in finding and explaining how they got their answers
and in probing into their answers, reactions and responses. This is
supported by the study of Villanueva (1999), which revealed that the
teachers were rated very high along ability to explain correctly as evident
in their content of the answer and command of the language of
instruction.
Receptivity to students’ Ideas and Contributions. This area was
rated a mean value of 4.13, interpreted as very good. This finding
suggests
that
the
teachers
can
demonstrate
flexibility
and
responsiveness in adjusting teaching to meet students‘ needs, ideas and
contributions. Furthermore, the teachers are skilled in leading students
in initiating thought-provoking questions. Rivera (2010) stressed that
when teachers want students to learn, they have to provide opportunities
for all students to interact in problem-rich situations, ask questions and
probe into each question. Thus, teachers have to encourage students to
find their own solution methods and give occasions for students to share
and compare solution methods and answers in the groups.
Quality of Teaching Procedure. The very high rating of 4.24
signifies that the teachers have the ability to ask thought-provoking

113. questions to find out if the students have understood the lesson very
well. This means further that the teacher can formulate questions that
develop the critical thinking ability of the students. If questions are
understood, the teachers are able to follow up to find out the extent of
students‘ understanding; if questions are unanswered, the teachers are
able to reformulate or rephrase the questions so as to fit students‘
understanding.
Selection of Teaching Methods. In connection to the selection of
teaching methods, the teachers were perceived ―very good‖ in all the
identified skills with a mean value of 4.07. This means that the teachers
are highly skilled in employing several approaches, methodologies and
techniques with emphasis on student inquiry and on collaborative and
cooperative learning. Grouws and Cebulla (2002), as cited by Fianza
(2009), mentioned that when teachers want to improve mathematics
teaching, certain strategies and methods of teaching should be
considered to a great extent by the teachers, themselves.
Quality of Information and Technology Utilized.
The lowest
mean rating of 3.49, interpreted as good, was given to the quality of
information and communication technology used. This implies that the
teachers recognize to a lower degree the relevance of technology in
teaching mathematics. They do not often use instructional gadgets such
as the overhead projector, LCD projector and the like, although they have

114. received very good rating in terms of computerization of grades and some
instructional materials.
This finding corroborates with the study of Bello (2009) stressing
that the instructors have to improve more on educational technology and
technology integration.
This also finds support from the study of Oredina (2006) asserting
that the lowest area rated by her respondents was on quality of
information and communication technology used since utilization of ICT
was seldom.
Guidance Skills
Relative to the guidance skills, the mathematics teachers were
evaluated along quality of interaction with students and quality of
students‘ activity. As revealed in Table 12, level of Instructional
competence of the Teacher-Respondents along guidance skills, the
mathematics teachers were rated a grand mean of 4.24, which is
interpreted as very good.
Table 12
Level of Instructional Competence of the Teacher-Respondents Along
Guidance Skills
Instructional Competence Dimensions
1. Quality of Interaction with students
Students Teachers Heads
WM
DER

115. a. arouse, maintain and sustain students’
interests
b. give students recognition (phrases and
reinforcements)
c. regard students’ errors/mistakes as fruitful
opportunities for learning
d. make use of teaching as guide in helping
students improve their work
e. communicate high and realistic expectations
from students
Sub-mean
3.98
4.19
4.48
4.22
Very Good
4.18
4.22
4.41
4.27
Very Good
4.06
4.3
4.48
4.28
Very Good
4.25
4.37
4.44
4.35
Very Good
4.10
4.07
4.33
4.17
Very Good
4.11
4.23
4.43
4.26
Very Good
4.2
4.37
4.26
4.28
Very Good
4.1
4.19
4.37
4.22
Very Good
4.05
4.22
4.37
4.21
Very Good
4.06
4.11
4.44
4.20
Very Good
4.12
4.07
4.37
4.19
Very Good
4.11
4.19
4.36
4.22
Very Good
4.11
4.21
4.40
4.24
Very Good
2. Quality of students’ activity
a. activities are purposeful, relevant and
experiential
b. students are developing increased selfreliance and responsibility
c. learning activities are appropriate for
students’ developmental tasks
d. time allocation is flexible to allow continuity
of productive activities
e. resources and facilities are appropriate for
the learning activities
Sub-mean
Grand Mean
Legend:
WM – Weighted Mean
DER – Descriptive Equivalent Rating
Quality of Interaction with Students. The teachers were
perceived to have very good competence in helping students improve on
their work, in providing encouragement, recognition and in developing
self-reliance and responsible self-direction to students for a more
effective learning. This means that the teachers are highly aware of the

116. importance of extrinsic motivation to maintain, strengthen and sustain
positive attitudes such as giving commendations and approval. Also, they
excel in encouraging students to learn and improve their performance.
This finding is supported by the study of Graycochea (2000) which
revealed that teachers were very highly competent in providing an
environment conducive to learning.
Quality of Students’ Activity. As regards the quality of students‘
activity, the rating received by the teachers was 4.22, interpreted as very
good. This implies that the teachers are highly capable in providing
learning activities that are appropriate for students‘ developmental tasks.
The highest area rated was the area on ―activities are purposeful,
relevant and experiential‖. Kolb and Rogers stressed that significant
learning takes place when the subject matter is relevant to students‘
experience and is purposeful to their personal interest.
Management Skills
Table 13 presents the instructional competence of the mathematics
teachers in terms of their management skills. It is revealed that the level
of management skills of the mathematics teachers was very good with a
grand mean rating of 4.37.
Atmosphere in the classroom. The three respondent groups
indicated their highest response on the ability of the teacher to instill
mutual respect, order and discipline as attested by the mean of 4.42.

117. This entails that the teachers are skilled classroom managers. They have
the ability to create and sustain desirable behavior during classroom
instruction. They also have that certain ―command‖ over the class that
effective classroom managers possess. According to Bueno, as cited by
Tabafunda (2005), a sound classroom can be achieved and maintained
through maintenance of constructive student-behavior correction.
The teachers are also found to be skilled in establishing,
communicating, modeling and maintaining standards of responsible
behavior by incorporating creative and constructive discipline techniques
rather than coercive and restrictive ones. This means that there is a
thriving harmonious relationship existing between the teachers and their
students. A genuine expression of care on the part of the teacher makes
an atmosphere conducive to learning, a learning atmosphere of safety
and free of threat (Lardizabal, 1991).
Table 13
Level of Instructional Competence of the Teacher-Respondents Along
Management Skills
Instructional Competency
Students Teachers Heads
WM
DER
4.32
Very
Good
1. Atmosphere in the classroom
I…
a. create and encourage positive social interaction,
active engagement and self-regulation for
every student
4.27
4.26
4.44

118. b. am enthusiastic and maintain a warm friendly
atmosphere conducive to learning
4.24
4.33
4.30
4.29
Very
Good
c. establish, communicate, model, and maintain
standards of responsible student behavior
4.32
4.33
4.30
4.32
Very
Good
d. instill mutual respect, order and discipline
4.32
4.41
4.52
4.42
Very
Good
e.
incorporate creative and constructive discipline
techniques rather than coercive and restrictive
discipline techniques
f. develop and implement classroom procedures
and routines that support learning and enforce
school policies among students
g. cultivate students’ deep sense of controlling for
their direction
4.28
4.19
4.30
4.26
Very
Good
4.23
4.30
4.37
4.30
Very
Good
4.15
4.22
4.37
4.25
Very
Good
h. am organized, punctual and manage class time
well; accomplish the objectives and procedures
set for the time period
Sub-mean
4.15
4.22
4.33
4.23
Very
Good
4.25
4.28
4.37
4.30
Very
Good
a. correct test papers, quizzes,
assignments/requirements carefully
4.31
4.56
4.52
4.46
Very
Good
b. return corrected test papers, quizzes,
requirements promptly
4.25
4.30
4.56
4.37
Very
Good
c. conduct efficiently quizzes/ examinations to
avoid cheating
4.31
4.44
4.59
4.45
Very
Good
Sub-mean
4.29
4.43
4.56
4.43
Very
Good
Grand Mean
4.27
4.36
4.47
4.37
Very
Good
2.
Conduct and return of evaluation materials
I…
Legend:

119. WM- Wieghted Mean
DER – Descriptive Equivalent Rating
Conduct and Return of Evaluation Materials. In connection to
the conduct and return of evaluation materials, the teachers were
perceived to be very good in all the areas included. This reflects that the
teachers conduct efficiently quizzes to avoid cheating, and after the
administration of tests, the teachers are able to correct and return the
said evaluation materials. Cabusora (2001) emphasized that competence
and efficiency of a teacher is also reflected in his ability to return
promptly corrected test papers.
Evaluation Skills
Table 14 presents the instructional competence of the mathematics
teachers along evaluation skills. It is reflected that the teachers have very
good evaluation skills as attested by the mean value of 4.32. This implies
that the teachers are able to maintain, enhance and sustain learning
through their skill in evaluating learning outcomes; thus, they are able to
determine students‘ strengths and weaknesses as basis for an improved
classroom interaction.
Quality of Appraisal Questions. The teachers are found to be well
adept in the preparation of well-framed test questions covering the

120. subject matter taken in the class and in asking questions that lead to the
summary of the salient points of the lesson. These bring out the idea that
Table 14
Level of Instructional Competence of the Teacher-Respondents Along
Evaluation Skills
Instructional Competence Dimensions
Students Teachers Heads WM
DER
1. Quality of Appraisal questions
I am able to…
a. frame questions to find out students’
understanding
4.33
4.33
4.44
4.37
Very
Good
b. ask questions, integrated in varying
techniques, that lead to the synthesis of the
salient points of the lesson
c. prepare well-framed questions covering the
subject matter taken in class
4.28
3.70
4.30
4.09
Very
Good
4.20
4.37
4.37
4.31
Very
Good
d. guide students in goal setting and assessing
their own learning
4.16
4.15
4.44
4.25
Very
Good
e. provide students substantive, timely, and
constructive feedback for specific area for
improvement (write comments on paper/talk
to students privately)
Sub-mean
4.01
4.15
4.22
4.13
Very
Good
4.20
4.14
4.36
4.23
Very
Good
a. varying authentic assessments to gauge the
extent of authentic learning
4.20
4.08
4.37
4.22
Very
Good
b. assignment/ enrichment activities to
supplement the day’s lesson and/or
aligned to classroom instruction
4.25
4.22
4.48
4.32
Very
Good
2. Quality of assignment/
activities
I provide and consider…
enrichment

121. c. subject requirements that are practical and
challenging
4.25
4.19
4.44
4.29
Very
Good
d. adequate time for students to complete
assignments/ requirements
4.27
4.41
4.59
4.42
Very
Good
e. availability of materials in giving
assignments and subject requirements
4.19
4.37
4.52
4.36
Very
Good
4.23
4.25
4.48
4.32
Very
Good
a. observe the standard grading system of
the school
b. grade/ score students objectively and
accurately
c. encourage students’ participation in
creating rubrics
4.37
4.52
4.74
4.54
Excellent
4.37
4.48
4.70
4..52
Excellent
4.15
4.04
4.30
4.16
Very
Good
d. utilize criteria/
requirements
4.21
4.30
4.56
4.36
Very
Good
Sub-mean
4.28
4.34
4.58
4.40
Very
Good
Grand Mean
4.24
4.24
4.47
4.32
Very
Good
Sub-mean
3. Quality of
performance
I…
appraising
rubrics
students’
in
checking
Legend:
WM- Weighted Mean
DER – Descriptive Equivalent Rating
the teachers are well-skilled in directing the class to probe into situations
that develop critical analysis through the formulation of very good
questions. This finding corroborates with study of Sameon (2002) which

122. stressed that teachers perceived themselves as very competent in
assessment. It means, therefore, that the teachers understood the
underlying principles and theories in test construction to improve
students‘ performance. According to Rivera and Sambrano (1999), as
cited by Tabafunda (2005), effective teaching should be coupled with the
art of questioning. Good questions serve as essential in developing
students‘ ability to define and exercise judgments.
Quality of Assignment/Enrichment Activities. The teachers
were perceived very good in providing quality assignment/ enrichment
activities as attested by the mean rating of 4.32. This means that the
teachers are highly capable in providing varying authentic assessments
to gauge the extent of learning. Further, they were also found to be wellskilled in providing activities that supplement the day‘s lesson. Similarly,
they were found very good in providing time to complete requirements
and projects that are practical and challenging. This finding is supported
by the finding of Oredina (2006) divulging that her respondents were very
competent
in
providing
reasonable,
appropriate,
practical
and
challenging enrichment activities to substantiate what the students have
learned in class.
Quality of Appraising Students’ Performance. Relative to the
quality of appraising students‘ performance, the mathematics teachers
were perceived very good in observing the grading system of the school,

123. in grading students objectively, in encouraging students in creating,
utilizing rubrics/ criteria in checking requirements. This finding suggests
that the teachers are skilled evaluators, interpreters and users of
evaluation results or learning outcomes. This study is supported by the
study of Sameon (2002) revealing that the respondents perceived
themselves as very competent in assessment. He stressed that the
teachers
understood
the
underlying
principles
and
practices
in
evaluation and assessment.
Comparison on the Perceived Instructional Competence between
Students and Teachers
Table
15
presents
the
comparison
between
the
perceived
instructional competence between the students and teachers. The
perceptions have ―insignificant‖ difference in the teaching skills,
―significant‖ difference in guidance skills, ―insignificant‖ in management
skills and ―insignificant‖ in evaluation skills. Generally, there is no
significant difference in the perceptions of students and teachers as
regards the teachers‘ instructional competence. This finding accepts the
null hypothesis of the study that there is no significant difference in
perceptions of the group of respondents.
Table 15
Comparison on the Perceived Instructional Competence between
Students and Teachers

124. Instructional Skills
Mean
(Students)
Teaching/
Mean
(Teachers)
4.01
4.03
Computed t-
0.07
Decision
Interpretation
Do not
Not
reject Ho
value
t- critical
significant
@ 0.05
2.23
Facilitating
Guidance
4.11
4.21
5.00
4.30
Reject Ho
Significant
Management
4.27
4.36
1.10
4.3
Do not
Not
reject Ho
significant
Do not
Not
reject Ho
significant
Do not
Not
reject Ho
significant
Evaluation
Grand Mean
4.24
4.12
4.24
4.17
0.65
0.5
2.78
2.06
This means that the students and teachers evaluated the teachers‘
competence without discrepancy. This is rooted to the fact the teachers
and the students are the ones who interact with each other on a daily
basis, so they know very well what transpires and what does not in the
classroom. This can also be explained using the educational thought by
Johnson (2010) on teacher-student relationships. He stressed that
backing up, sharing and appreciation helped maintain commonalities in
perceptions of teachers and their students.

125. Comparison on the Perceived Instructional Competence between
Students and Heads
Table
16
presents
the
comparison
between
the
perceived
instructional competence between the students and heads. There exists
an ―insignificant‖ difference in the teaching skills, ―significant‖ difference
in guidance skills, ―insignificant‖ difference in management skills and
―significant‖ difference in evaluation skills. Generally, there is a
significant difference in the perceptions of the students and heads as
regards the instructional competence of the mathematics teachers. This
rejects the null hypothesis of the study on the difference of the
perceptions.
Table 16
Comparison on the Perceived Instructional Competence between
Students and Heads
Instructional Skills
Mean
(Students)
Teaching/
Mean
(Heads)
4.01
4.03
Computed t-
1.01
Decision
Interpretation
Do not
Not
reject Ho
value
t- critical
significant
@ 0.05
2.23
Facilitating
Guidance
4.11
4.40
8.14
4.30
reject Ho
Significant
Management
4.27
4.47
2.01
4.31
Do not
Not
reject Ho
significant

126. Evaluation
4.24
4.47
3.50
2.78
reject Ho
significant
Grand Mean
4.12
4.33
2.28
2.06
reject Ho
significant
This means that the heads rated the teachers comparatively higher than
the students. This is rooted to the period of interactions of the two
groups of respondents: the students on a daily basis; while the heads on
occasional basis. The students interact with the teachers daily during
class interactions. They could assess when a teacher comes to class
prepared or not. On the other hand, the head sees the class interaction
during observation, a period when the teacher has prepared much for the
teaching-learning process. This is supported by the thought presented by
the article on www.ask.com that differences exist because of the different
status of people, needs, personalities, interactions and beliefs.
Comparison on the Perceived Instructional Competence between
Teachers and Heads
Table 17 manifests the comparison on the perceived instructional
competence between the teachers and their heads. There exists an
―insignificant difference‖ in terms of teaching skills, ―significant‖ in
guidance skills, ―insignificant‖ in management skills and ―insignificant‘
in evaluation skills. Generally, there exists an insignificant difference in
the perceptions of the two respondents. This finding accepts the null
hypothesis of the study that there is no significant difference in the

127. perceptions of the respondents. This can be explained through citing the
Common Coding Theory. According to the theory, commonalities among
perceptions of two groups of respondents exist because there is a
Table 17
Comparison on the Perceived Instructional Competence between
Teachers and Heads
Instructional Skills
Mean
(Teachers)
Teaching/
Mean
(Heads)
4.03
4.18
Computed t-
0.94
Decision
Interpretation
Do not
Not
reject Ho
value
t- critical
significant
@ 0.05
2.23
Facilitating
Guidance
4.21
4.40
4.59
4.30
reject Ho
Significant
Management
4.36
4.47
0.91
4.30
Do not
Not
reject Ho
significant
Do not
Not
reject Ho
significant
Do not
Not
reject Ho
significant
Evaluation
Grand Mean
4.24
4.16
4.47
4.33
2.68
1.83
2.78
2.06
common code or shared representations for perceptions and actions.
(www.en/wikipedia.org/wiki/common_coding_theory). Thus, the teachers
and their heads share a common goal in instruction, that is, to impart

128. quality education to the students. The insignificant difference can also be
explained by citing an excerpt in the Magna Carta for Public School
Teachers asserting that teachers should always need to back up each
other as sign of professionalism (Magna Carta for Public School
Teachers: Teacher as Professionals).
Summary of the Level of Instructional Competence of Mathematics
Teachers in the Private Secondary Schools in the City of San
Fernando, La Union
Table 18 reflects the summary of instructional competence of
mathematics teachers. It is gleaned from the table that the instructional
competence of the teachers obtained a grand mean of 4.24, interpreted
as very good. This rejects the null hypothesis of the study that the
teachers have only average/moderate instructional competence.
All the levels of skills were rated very good with management skills
as the highest and teaching skills as the lowest. Along teaching skills,
one indicator was rated good only, that is on the quality of
communication and information technology used. This implies that the
teachers are not very familiar and unskillful in utilizing instructional
technology; thus, they are not very competent along this area. This is
also rooted to the access to such technologies. In the researcher‘s
observation during the proctoring of tests, teachers, especially the ones

129. in the big schools, own laptops. This gives an idea that the math
teachers have limited access to projectors since other math teachers and
teachers
of
other
subjects
also
desire
to
use
information
and
communication technology in facilitating the teaching-learning process.
Preparation of instructional technology is also a cause of this. Creating
interactive slides, researching up-to-date clips including the setting up of
the gadgets is also a complex task. Reinhardt, as cited by Oredina
(2006), emphasizes that using ICT in teaching develops the proficiency
desired among the students since features of computers such as video
presentations; animations and the like are better instructional objects
than chalkboards and transparencies.
Table 18
Summary of the Level of Instructional Competence of Mathematics
Teachers in the Private Secondary Schools in the City of San Fernando,
La Union
Level of Instructional
Competence
A. Teaching/ Facilitating Skills
Students
Teachers
Heads
Mean
DER
4.15
4.14
4.35
4.21
Very
Good
4.24
4.34
4.34
4.31
Very
Good
4.06
4.19
4.13
4.13
Very
1. Substantiality of Teaching
2. Quality of Teachers’
Explanation
3. Receptivity to students’ ideas

130. and contributions
Good
4. Quality of questioning
procedure
4.23
4.18
4.30
4.24
Very
Good
5. Selection of teaching methods
4.08
3.93
4.19
4.07
Very
Good
6.Quality of information and
communication technology used
3.32
3.38
3.78
3.49
Good
Sub-Mean
4.01
4.03
4.18
4.07
Very
Good
4.11
4.23
4.43
4.26
Very
Good
4.11
4.19
4.36
4.22
Very
Good
4.11
4.21
4.40
4.24
Very
Good
1.Atmosphere in the Classroom
4.25
4.28
4.37
4.30
Very
Good
2.Conduct and return of
evaluation materials
4.29
4.43
4.56
4.43
Very
Good
4.27
4.36
4.47
4.37
Very
Good
4.20
4.14
4.36
4.23
Very
Good
4.23
4.25
4.48
4.32
Very
Good
B. Guidance Skills
1. Quality of interaction with
students
2. Quality of students’ activity
Sub-Mean
C. Management Skills
Sub-Mean
D. Evaluation Skills
1. Quality of appraisal questions
2.Quality of
assignment/enrichment

131. activities
3.Quality of appraising students’
performance
4.28
4.34
4.58
4.4
Very
Good
Sub-Mean
4.24
4.24
4.47
4.32
Very
Good
Grand Mean
4.16
4.21
4.38
4.24
Very
Good
Legend:
WM- Weighted Mean
DER – Descriptive Equivalent Rating
The very good evaluation given by the respondent groups to almost
all the skills is pinpointing to a laudable instructional competence of the
mathematics teachers in the Private schools in the City Division of San
Fernando. This means that the mandate of the Department of Education
(DepEd) to provide Quality Education for All (EFA) is present such that
the realization of the goals and objectives of Mathematics teaching is
achievable, especially in the Secondary schools.
The studies of Acantilado (2002), Subala, as cited by Roldan (2004)
and Oredina (2006) support the finding of the study. Their studies
emphasized that their teacher-respondents were highly competent.
Subala explained that since the teachers were competent, they can be
proper sources of assistance and guidance to their students in analyzing

132. different mathematical concepts. It is noteworthy that the perceived
instructional competence of teachers is in line with the goal of DepEd of
achieving and providing sound functional literacy to the students.
(Secondary Education Curriculum Framework, 2010).
Relationship Between Profile and Level of Content Competence
Table 19 manifests the relationship existing between profile
variables and content competence variables. It further reveals that
highest
educational
attainment
is
significantly
correlated
to
computational skills but not with conceptual skills, analytical and
problem-solving skills. This means that when a math teacher has higher
educational attainment, he has higher computational skills; but not
necessarily conceptual, analytical and more so with problem-solving skill
since such skill requires complex analysis with accurate solutions to deal
with certain mathematical problems. This can be explained through
citing an article by Keneddy (2001). Her article explained that a
prospective teacher majoring a subject like mathematics or science does
not guarantee that teachers will have the kind of subject matter
knowledge and skills they need for teaching.
Moreover, the table shows that number of years of teaching is
significantly correlated to problem-solving skills but not conceptual,
analytical and computational skills. Thus, a teacher who is more tenured
Table 19

133. Relationship Between Profile and Level of Content Competence
Profile
Conceptual
Skills
Analytical Skills
Computational
Skills
Problem-solving
Skills
Highest Educational
Attainment
0.23 Low
0.32 Low
0.57* marked
0.05 Negligible
t= 1.16
t= 1.90*
t= 3.40*
t=0.25
Number of Years in
Teaching
0.37 Low
0.19 negligible
0.27 low
0.42 * marked
t= 1.95*
t= 0.95
t= 1.37
t= 2.27*
Seminars Attended
0.49* marked
0.31Low
0.19 Negligible
0.06 Negligible
t= 2.75*
t= 1.60
t= 0.95
t= 0.29
Legend *- The relationship is significant
df = n-2 = 24; t critical value = 1.711
in teaching mathematics has higher competence in problem solving. It is
true that when someone is more exposed to certain routine, he is able to
master it.
The table also presents that the number of seminars attended is
significantly correlated to conceptual skills but not to analytical,
computational and problem-solving. This implies that when a teacher
frequently attends seminar-workshops, he has more content knowledge
of a certain discipline. It is with attending seminars that changes or
developments of an area of learning are taught and learned.
A further examination of the table reveals that all the marked or
substantial correlations (highest educational attainment- computational

134. skills, number of years in teaching-problem solving skills, seminars
attended- conceptual skills) had been found to be significant. This means
that the relationship existing among the cited variables are significant. It
can be strongly inferred that once a teacher has higher educational
qualifications, he is more competent in terms of computational skills;
once a teacher becomes more tenured in the teaching profession, he is
more competent along problem-solving skills; and, once a teacher has
attended more seminars, he is more competent in terms of conceptual
skills.
It can also be noted that even the correlations between highest
educational
attainment-analytical
skills
and
number
of
years
in
teaching- conceptual skills, which were found to be low, are significant.
This means that there is really no strong connection between having
higher educational qualifications and competence along analytical skills,
and number of years in teaching and conceptual skills.
The finding of this study is supported by the ideas of web-article
writers suggesting that subject matter competence can be attained and
sustained through continuing professional education and teaching
experiences. Also, the data fully support the contention of ClementeReyes (2002) in her study. Reyes expresses that subject matter expertise
is gained through possessing educational achievements, gaining years of
professional teaching service and attending training. She mentioned that

135. earning a bachelors‘ degree was not sufficient; thus, recommending for
continuing professional education since majority of the teacher experts
were masters degree holders or even doctorate degree holders. Also,
when a teacher is exposed in the teaching profession, he is likely to
expand his horizons in his field; thus, contributing to teaching expertise.
Lastly, she asserted that training helped a lot in gaining additional input.
Such input met or not met by teachers in her formal education can affect
his content knowledge.
Relationship Between Profile and Level of Instructional Competence
Table 20 discloses the relationship existing between profile
variables and instructional competence variables. It shows that highest
educational attainment is significantly correlated to teaching skills,
guidance skills, management skills and evaluation skills. This implies
that when a teacher has higher educational achievement, he is likely a
master of the teaching-learning process— he can facilitate classroom
instruction, can provide needed guidance to his students, is an effective
classroom manager, and a good evaluator of learning outcomes. Since
the computed correlation coefficients were found to be significant, there
exists a strong relationship between the variables correlated. It can be
strongly expressed that when a teacher possesses higher educational
attainment, he is likely more competent in instruction.

136. Table 20
Relationship Between Profile and Level of Instructional Competence
Profile
Teaching
Skills
Guidance Skills
Management
Skills
Evaluation Skills
Highest Educational
Attainment
0.71 * high
0.54 * marked
0.51 * marked
0.61* marked
t = 4.94*
t=3.14*
t=2.90*
t=3.77*
Number of Years in
Teaching
0.18 low
0.24 Low
0.28 Low
0.33 Low
t=0.90
t=1.21
t=1.43
t=1.71*
Seminars Attended
0.21 low
0.41* marked
0.24 Low
0.41 * marked
t=1.05
t=2.20*
t=1.21
t=2.20*
Legend *- The relationship is significant
df = n-2 =24; t critical value= 1.711
This finding is supported by the study of Sameon (2002) stating that
highest educational attainment is strongly correlated to teaching
competence. Also, this corroborates with the international study of
Achwarin (2005) arguing that teachers‘ qualification is positively and
significantly related to teachers‘ instructional competence.
The table also illustrates that number of years of teaching does not
correlate with teaching, guidance, management and evaluation skills.
This means that the skills under instructional competence (teaching,
guidance, management, evaluation) are not necessarily brought about by
the number of years a teacher has spent in teaching. Further, a teacher

137. who has a 30-year teaching experience is not necessarily more competent
than a teacher who is still earning his teaching experience.
Moreover, the correlation between number of years of teaching to
teaching skills, guidance skills and management skills were found to be
insignificant. This means that the relationship is not strong enough to
contend that a teacher who stayed long in the service does not
necessarily have higher competence along teaching, guidance and
management skills. On the other hand, the correlation between the
number of years of teaching to evaluation skills was found to be
significant. This means that it is safe to assert that a teacher who stayed
in the service for a longer period of time does not necessarily have higher
evaluation skills.
These findings run parallel to the study of Oredina (2006)
revealing that number of teaching experience is not significantly
correlated to the four instructional competence dimensions. However,
these findings do not corroborate with the study of Davis (2000), as cited
by Binay-an (2002), which claimed that teachers who are younger in the
service are more likely to possess greater competence since they have
greater inquisitive mind and zest for teaching. Further, these were not
also in congruence to the study of Laroco (2005) claiming that teachers
who had longer years in service are in better position to adjust
themselves to different classroom situations; thus, they are more

138. competent. She concluded that teaching experiences add to the teaching
competence.
Same table also exposes that the number of seminar-workshops
attended by the teachers is significantly related to guidance and
evaluation skills but not to teaching and management skills. This means
that the more seminar-workshops a teachers attends, the teacher
becomes more competent in guiding students and in evaluating their
learning. This can be strongly asserted since the correlation for these
variables have been found to be significant.
It further means that a teacher who has more seminars or
trainings is not more competent in teaching and managing a class
compared to a teacher with less number of seminars.
Relationship Between Content and Instructional Competence
Table 21 unveils the relationship existing between content and
instructional competence of the mathematics teachers. It relates that
conceptual skill is significantly related to guidance skills. Thus, a teacher
who is more competent along concepts is more likely a good source of
guidance. However, conceptual skill is not correlated to teaching skills,
management and evaluation skills; thus, a teacher who possesses more
conceptual skills does not necessarily mean that he can teach well,
manage class effectively and evaluate learning outcomes accurately.

139. Table 21
Relationship Between Content and Instructional Competence
Cognitive Skills
Teaching
Skills
Guidance Skills
Management
Skills
Evaluation
Skills
Conceptual Skills
0.25 Low
0.45* marked
0.31 Low
0.33 Low
t=1.26
t=2.47*
t=1.60
t=1.71*
0.23 Low
0.37 Low
0.27 Low
0.33 Low
t=1.15
t=1.95*
t=1.37
t=1.71*
0.35 Low
0.37 Low
0.21 Low
0.25 Low
t=1.83*
t=1.95*
t=1.05
t=1.27
0.22 Low
0.16 Negligible
0.17 Negligible
0.14 Negligible
t=1.10
t=0.79
t=0.85
t=0.69
Analytical Skills
Computational Skills
Problem-Solving skills
Legend *- The relationship is significant
df=n-2=24; t critical value = 1.711
Moreover, analytical, computational and problem-solving skills do not
correlate with teaching, guidance, management and evaluation skills.
This means that when teachers possess high skills along analysis,
computational and problem-solving, they do not necessarily possess
skills along teaching-facilitating, guidance, management and evaluation
lls. An international study which was cited by an article posted on the
Harvard Educational Review supports this finding very well. This study
was by Reynolds (1999). In the study, he exposed that subject matter

140. expertise was not contributory to success in teaching. With these she
expanded the meaning of subject matter expertise to include an
awareness
of
that
expertise
(http://www.hepg.org/her/abstract/164).
as
learned.
This means that when a
teacher has more content competence, it does not necessarily follow that
he can teach better. On the other hand, these findings do not support
several studies, which include that of Binay-an (2002), Cabusora (2004),
Diaz (2000), and Clemente-Reyes (2002)
which revealed that subject
matter expertise was a contributory factor to teaching expertise. It was
stressed that mastery of content-specific knowledge and the organization
of this knowledge affect effective instruction. If the teachers were not
experts in their field, it is unlikely for them to possess teaching expertise.
Summary on the Relationship existing among Profile, Instructional
and Subject Matter Competence
Table 22 summarizes the relationship existing between profile and
content
competence,
profile
and
instructional
competence,
and
competence along content and instruction.
It further reveals that the computed correlation coefficients
between the profile variables and content competence profile are all
below the substantial coefficient of 0.41; thus profile (highest educational
attainment, number of years of teaching and number of seminars
attended) is not significantly related to content competence.

141. Summary on the Relationship existing among Profile, Instructional and
Subject Matter Competence
Table 22
Highest
Number of Years
Number of
Instructional
Educational
of Teaching
Seminars Attended
Competence
Attainment
Content
0.40 low
0.38 low
0.31 low
0.38 low
Competence
t = 3.10*
t = 2.01*
t = 1.60*
t = 2.01*
Instructional
0.64* Marked
0.28 low
0.35 low
t = 4.08*
t = 1.43
t = 1.83*
Competence
Legend: * Significant
df=n-2=24; t critical value = 1.711
Moreover, it divulges that highest educational attainment is
significantly correlated to instructional competence with a correlation
coefficient of 0.64, which is interpreted as marked or substantial
correlation. However, the number of teaching experience and number of
seminars attended do not correlate with instructional competence.

142. It also reveals that the computed correlation coefficient between
instructional competence and content competence is 0.38, interpreted as
low correlation. This means that instructional competence and content or
subject matter competence are not significantly related.
Strengths and Weaknesses of Mathematics Teachers Along Content
Competence
Table
23
manifests
the
strengths
and
weaknesses
of
the
mathematics teachers along the content/subject matter competence
dimensions such as conceptual skills, analytical/reasoning skills,
computational skills and problem-solving skills. As basis for determining
the strengths from weaknesses, a mean rating lower than 17 is
considered a weakness; otherwise, it is considered as strength. They are
ranked accordingly for an organized presentation. The strengths are
ranked in such a way that the item that garnered the highest mean value
obtained the first rank to indicate that it is regarded as the foremost
strength; the lowest mean value under the strength is ranked first
indicative that it is a foremost weakness.
Analytical
skills
and
problem-solving
skills
are
considered
weaknesses; conceptual and computational skills are considered as
strengths. Generally, the teachers have a grand mean below 17; thus, the
teachers are found to be weak in terms of their subject matter/ content
competence. This accepts the null hypothesis of the study that the

143. teachers‘ weaknesses are on analytical and problem-solving skills and
their strengths are on conceptual and computational.
Table 23
Strengths and Weaknesses of Mathematics Teachers along Content
Competence
Area of Content
Competence
Conceptual Skills
Strength
Rank
18
Weakness
1.5
15
Computational
Skills
18
1
1.5
Problem-Solving
Skills
Grand Mean
2
12
Analytic/Reasoning
Skills
Rank
16
The foremost weakness is problem-solving. This is due to the fact
that this skill encompasses all the other skills. One should know enough
mathematical facts, should know how to reason out and probe deeper,
and of course, should know how to compute before he can actually deal
with mathematical problems.

144. Strengths and Weaknesses of Mathematics Teachers Along
Instructional Competence
Table
24
manifests
the
strengths
and
weaknesses
of
the
mathematics teachers along the instructional competence dimensions
such as teaching/facilitating skills, guidance skills, management skills
and evaluation skills. As basis for determining the strengths from
weaknesses, all items rated 3.50 and above are strengths; otherwise,
weaknesses. They are ranked accordingly for an organized presentation.
The strengths are ranked in such a way that the item that garnered the
highest mean value obtained the first rank to indicate that it is regarded
as the foremost strength; the lowest mean value under the strength is
ranked first indicative that it is a foremost weakness.
Table 24
Strengths and Weaknesses of Mathematics Teachers
Instructional Competence
Instructional Competency
A. Teaching / Facilitating Skills
Strength Rank Weakness Rank
1. Substantiality of Teaching
I...
a. show confidence and exhibit mastery of the
subject matter
b. show awareness of the developments of the
subject matter as seen in the utilization of key
concepts,
relationships,
and
different
perspectives related to the content area
4.46
1
4.35
2

145. c. align classroom instruction with national
standards, school’s vision-mission and
educational philosophy
d. focus on and cover all important aspects of the
subject matter
e. connect students’ prior knowledge, life
experiences, and interests in the instructional
process
f. provide values clarification and integration
considering the applications of the subject area
to the students’ practical life
g. engage students in in-depth and varied
experiences that meet the diverse needs and
promote holistic growth
h. relate ideas and information within and across
content areas
4.19
4
4.28
3
4.11
6
4.09
7
4.18
5
4.03
8
a. make abstract concepts clear for students’
understanding
b. ask students how they got a particular answer
4.29
1
4.38
2
c. encourage students to probe into reactions,
answers and responses
d. use knowledge of students’ development to
make learning experiences meaningful and
accessible for every student
4.33
3
4.23
4
4.06
3
4.16
2
4.17
1
2. Quality of teacher’s explanation
I…
3. Receptivity to students’ ideas and contributions
I…
a. lead students to ask or initiate thoughtprovoking questions
b. integrate and elaborate students’ questions and
contributions into the class discussion
c. demonstrate flexibility and responsiveness in
adjusting instruction to meet students’ needs,
ideas and contributions
4. Quality of questioning procedure
I…

146. e.
a. pose thought-provoking questions that promote
high-order thinking skills
b. encourage students to explain ideas and ask
questions about the content
c. provide time for student to think, ponder on and
express response
d. pose follow-up questions to clarify initial
question when a student is unable to respond
effectively
emphasize on essential ideas and problems
4.24
4
4.21
5
4.26
2
4.25
3
4.27
1
f.
4.20
6
a. determined on behavioral objectives and appropriate
to the content area
4.14
2
b. used in expressing ideas and problems
(projects,
themes,
panel
discussion,
demonstration, etc)
c. emphasizing on and eliciting students’ inquiry
4.07
3
3.99
4
d. used to address individual differences and
develop multiple intelligences
e. intended to engage students in learning and
supportive of theories of collaborative and
cooperative learning
3.96
5
4.16
1
3.66
2
ensure that factual information and skills are applied
to ideas and problems
5. Selection of teaching methods
I use teaching methods which are…
6. Quality of information and communication
technology used
I use…
a. computers for designing and printing
instructional materials
b. the principles of computer-aided and computerbased instruction
c. multi-media resources, including technologies
such as the internet, in the development and
sequencing of instruction
d. computerized grading sheets (without received
corrections)
e. overhead/LCD projector
3.45
3.37
3.76
3
2
3.24
1
1

147. B. Guidance Skills
1. Quality of Interaction with students
I…
a. arouse, maintain and sustain students’ interests
4.22
4
b. give students recognition (phrases and
reinforcements)
c. regard students’ errors/mistakes as fruitful
opportunities for learning
d. make use of teaching as guide in helping
students improve their work
e. communicate high and realistic expectations
from students
4.27
3
4.28
2
4.35
1
4.17
5
4.28
1
4.22
2
4.21
3
4.20
4
4.19
5
4.32
2.5
4.29
5
4.32
2.5
2. Quality of students’ activity
I ensure that…
a. activities are purposeful, relevant and
experiential
b. students are developing increased self-reliance
and responsibility
c. learning activities are appropriate for students’
developmental tasks
d. time allocation is flexible to allow continuity of
productive activities
e. resources and facilities are appropriate for the
learning activities
C. Management Skills
1. Atmosphere in the classroom
I…
a. create and encourage positive social
interaction, active engagement and selfregulation for every student
b. am enthusiastic and maintain a warm friendly
atmosphere conducive to learning
c. establish, communicate, model, and maintain
standards of responsible student behavior

148. d.
instill mutual respect, order and discipline
e.
incorporate creative and constructive discipline
techniques rather than coercive and restrictive
discipline techniques
f. develop and implement classroom procedures
and routines that support learning and enforce
school policies among students
g. cultivate students’ deep sense of controlling for
their direction
h. am organized, punctual and manage class time
well; accomplish the objectives and procedures
set for the time period
3.
4.42
1
4.26
6
4.30
4
4.25
7
4.23
8
4.46
1
4.37
3
4.45
2
4.37
1
4.09
5
4.31
2
4.25
3
4.13
4
Conduct and return of evaluation materials
I…
d. correct
test
papers,
quizzes,
assignments/requirements carefully
e. return corrected test papers, quizzes,
requirements promptly
f. conduct efficiently quizzes/ examinations to avoid
cheating
4. Evaluation Skills
1. Quality of Appraisal questions
I am able to…
a. frame questions to find out students’
understanding
b. ask questions, integrated in varying techniques,
that lead to the synthesis of the salient points of
the lesson
c. prepare well-framed questions covering the subject
matter taken in class
d. guide students in goal setting and assessing their
own learning
e. provide students substantive, timely, and
constructive feedback for specific area for
improvement (write comments on paper/talk to
students privately)
2. Quality of assignment/ enrichment activities

149. I provide and consider…
a. varying authentic assessments to gauge the
extent of authentic learning
b. assignment/ enrichment activities to supplement
the day’s lesson and/or aligned to classroom
instruction
c. subject requirements that are practical and
challenging
d. adequate time for students to complete
assignments/ requirements
e. availability of materials in giving assignments and
subject requirements
4.22
5
4.32
3
4.29
4
4.42
1
4.36
2
a. observe the standard grading system of the
school
b. grade/ score students objectively and accurately
4.54
1
4.52
2
c. encourage students’ participation in creating
rubrics
d. utilize criteria/ rubrics in checking requirements
4.16
4
4.36
3
3. Quality of appraising students’ performance
I…
Teaching/ Facilitating Skills
In general, teaching skills were considered as strengths of the
teachers as regards substantiality of teaching, quality of teacher‘s
explanation, receptivity to students‘ ideas, quality of questioning
procedure and selection of teaching methods. However, the quality of
information and communication technology used was regarded as
weakness. Thus, it entails that the teachers are very good facilitators of
the teaching learning process. They are able to execute their function

150. effectively. They are effective pathfinders of knowledge who can instill the
essentials of their subject in the students. But, they need to improve
along the quality of information and communication technology utilized
the mere fact that they were found wanting along this area. The reason
for this weakness may be the accessibility of the teachers to these kinds
of technology.
Guidance Skills
All the indicators under this area were perceived as strengths. This
implies that the Mathematics teachers are very good in directing,
supervising, and guiding the teaching-learning process. They are able to
provide an atmosphere conducive to humane learning. Also, they provide
activities which are relevant and purposeful for the students, and which
they can direct and control to aim for optimum learning. Such being the
case, the students are trained to become responsible element of the
teaching-learning process.
Management Skills
The indicators of this skill are all perceived as strengths. A further
comparison of the four skills gives an idea that this area is the skill rated
the highest, the foremost strength. This means, in general, that the
teachers are very good classroom managers. As such they are able to
instill mutual respect, good behavior and discipline among students
since they, themselves, model good behavior that their students emulate.

151. Evaluation Skills
Like all the indicators under guidance and management skills, all
the indicators under evaluation skills are perceived strengths by the
three groups of respondents. This means that the teachers are able to
gauge the extent of learning of their students.
In synthesis, all the identified skills along teaching, guidance,
management and evaluation were perceived to be strengths by the three
groups of respondents, except in the quality of information and
communication utilized, which is considered a weakness; thus, a
primary concern.
The finding of the current study runs parallel to the studies of
Cirstobal (2004), Oredina (2006), and Bello (2009). In their studies, all
the other areas were perceived strengths such as in teaching procedure,
methodologies, assessment strategies, guidance, and management but
the three divulged that the teachers lacked the necessary competence in
technology utilization and integration.
Proposed Two-Pronged Training Program for Mathematics Teachers
of the Private Secondary Schools in the City Division of
San Fernando, La Union
I. Rationale
The task impressed by the educative process on the shoulders of
the teachers is not easy. Despite this, teachers still strive for the best to

152. provide the quality education every student deserves. Teachers still
desire to be the best for their students. If this ideal holds greater than
the challenges, then the teacher should not fail to upgrade and update
himself. In doing so, teachers certainly improve their weaknesses and
sustain or intensify their strengths. Indeed, training is necessary.
. Training is the process of acquiring specific skills to perform a
better job. It helps people to become qualified and proficient in
performing their tasks. Through training, people‘s behavior towards a
task becomes modified. Such modified behavior contributes to the
successful attainment of goals and objectives.
The proposed two-pronged training program is based upon the
identified strenghts and weaknesses of the mathematics teachers‘
competence along content and instruction. The items rated the lowest in
content competence dimensions (reasoning/analytical and problemsolving skills which were average competence),
and instructional
competence dimensions (Information and Communication Technology
(ICT)
utilization)
are considered priorities. The other
dimensions
considered very good are still included for sustainability and possible
enhancement.
The insufficiency of Information and Communication Technology
used in the private secondary schools in the City Division of San
Fernando is theorized to be a contributory factor in the low rating given

153. to the quality of ICT used. To improve such, each school should upgrade
its facilities in terms of technology, besides training the teachers in the
use of such technology.
The training program shoud be implemented during the preservices of the institution so that the attendance of the teachers will be
assured. The teachers will simultaneously have their training. Follow-up
will be done, if necessary. Assessment will be done on the last day of the
program.
Post-test will be done to ensure mastery of the subject matter.
Demonstration lesson, on the other hand, will be conducted to see the
extent of manifestation of instructional competence. In the selection of
topics to be taught, the area with the lowest competency rating will be
considered.
II. General Objectives
1. Improve content and instructional pedagogical competencies;
2. Apply and adopt technology and utilize varied instructional
materials in teaching mathematics;
3. Utilize
the
different
motivating
techniques
and
classroom
interactive activities;
4. Develop the proper techniques in the art of questioning and
classroom management; and

154. 5. Construct reliable and valid evaluative materials to measure
students‘ achievement.
III. Training Course Contents
A. Content Competence
1. Problem-Solving Skills
2. Reasoning/Analytical Skills
3. Computational Skills
4. Conceptual Skills
B. Teaching Skills
1. Information and Communications Technology
2. Instructional Aids and Devices
3. Methodology/Strategies
and
Approaches
Interaction
4. Art of Questioning
C. Guidance Skills
1. Motivating Techniques
D. Management Skills
1. Classroom Management and Discipline
E. Evaluation Skills
1. Evaluative Techniques
IV. Methodologies
in
Classroom

155. Lectures integrated with Interactive discussion with, application,
skill builders, and follow-up workshops will be the main methodologies of
the training course. Partcipants will be engaged in different set-ups:
individual for the lecture, solving and application, pair for the
brainstorming and group for the workshops.
The teacher-participants can sometimes be asked to share their
know-how and procedures about certain situations so that the
discussion will be more substantial, fruitful and participative.
V. Training Management
The mathematics training shall be under the over-all management
of the prinicipal with the assistance of the academic coordinator and the
mathematics coordinator.
The facilitators for the proposed training program were chosen
based on their qualifications, trainings and seminars attended and
organized, and competence along the different areas of concern. Most of
the facilitators were speakers of the different seminar-workshops
attended by the researcher. Such being the case, their expertise have
really been considered in choosing their area for training.
For Content Competence Training
Name
Position
Mr. Gerry Hoggang
Head, Mathematics
Saint Louis College
High School
Experiences/Qualifications/
Area/s of Concern
BSEd, MAMT
Elementary Algebra

156. Dr. Jose Almeida
Education Supervisor I
Mathematics, DepEd
BSEd, MATE, PHd
Mrs. Edwina Manalang
Faculty
Saint Louis College
BSED, MAED
Geometry
Dr. Ramir Austria
Head, Mathematics Instruction
University of the Cordilleras
BSEd, MAEd-Math, EDd.Mgt.
For Instructional Competence
Intermediate
Algebra
- Advanced Algebra, Trigo and Stat
Mr. Jayson Toquero
Instructional Media Center-In charge BSIT, MS Comp Ed Units
CKC-High School
- Info. and Com. Tech utilized
Dr. Nora A. Oredina
Head, Mathematics
Saint Louis College
BSEd, MATE, EDd
Principal
St Paul College, Manila
BSED, MAED
Principal
STC, QC
BEED, MAED
Mrs. Debbie Graffil
Mrs. Gloria Cruz
-test construction
-classroom management
-guidance skills, lesson planning
VI. Participants
All mathematics teachers of the Private Secondary Schools in the
City Division of San Fernando, La Union
VII. Duration
5 days (refer to the proposed program of activities)
VIII. Logistics
Honoraria for speakers (1,500/speaker)
P12000.00
Meals/Snacks for the speakers (P150/speaker)
P 1200.00
Seminar Kits (P50/teacher)
P 1300.00

157. Others:
Documentation, LCD projectors
Laptop (c/o IMC officer)
Certificates (c/o secretary)
TOTAL
P14,500.00
IX. Success Indicator
The mathematics teachers of the private secondary schools in the
City Division of San Fernando, La Union shall improve on their content
competence:
conceptual,
reasoning/analytical,
computational
and
problem-solving skills; and instructional: teaching/facilitating, guidance,
management and evaluation skills by 25 percent.
Level of Validity of the Two-Pronged Training Program
It can be seen from the Table that the level of face and content
validity of the proposed two-pronged training program as perceived by
the validators was high. This suggests that the proposed program is
highly functional, acceptable, appropriate, timely, implementable and
sustainable.
Table 25
Level of Validity of the Two-Pronged Training Program
Level of Validity
Weighted
Descriptive
Mean
Equivalent

158. I.
Face
4.17
High
II.
Content
4.50
High
b. Acceptability
4.50
High
c. Appropriateness
4.33
High
d. Timeliness
4.17
High
e. Implementability
3.83
High
f. Sustainability
3.83
High
Average
4.20
High
Over-all Rating
4.19
High
a. Functionality

159. Area of
Concern
A. Content
Competence
Problem
Solving
Skills
A VALIDATED TWO-PRONGED TRAINING PROGRAM FOR MATHEMATICS TEACHERS
Materials
Time
Human
Objectives
Methods/
Content
Needed
Frame
Resource
Strategies
Through the
conduct of
lecture, testretest, skill
builders
strategies, the
mathematics
teachers
should be
able to:
- examine
different word
problems,
mathematics
illustrations or
items
accurately
- solve
Outcomes
Snacks:
Algebra I
Logistics
There is a
significant
increase in
the
mathematics
competence
pretest and
Participants:
All math
teachers
-real number
system
-First degree
equations and
inequalities in
one variable
Speaker:
Mr. Gerry
Hoggang
-rational
algebraic
expressions
-linear
equations in 2
variables
-lecture
-Skill-building
-systems of
linear
equations
P 300.00
Problem Sets
1 day
May 24, 2011
Compass
(Morning)
Honorarium

160. mathematical
problems with
ease and
accuracy
-develop
additional
techniques in
solving word
problems
exercises
P3000.00
Algebra II
-sharingdiscussion
Test-retest
strategy
-Quadratic
Equations
-variations
-Sequences
and Series
Supplemental
Materials
Participants:
Overhead/
All math
teachers
or LCD
projectors
Speaker:
Laptops
Dr. Jose P.
Almeida
Geometry
-Writing Proofs
-Triangle
congruence
Participants:
1 day
All math
Snacks:
posttest

161. -inequalities
May 24, 2011
-Similarity
teachers
(Afternoon)
-Circles
Speaker:
-Coordinate
Geometry
Mrs. Edwina
Manalang
P 300.00
Math IV
-Functions
Quadratic
Polynomial
Participants:
Exponential
All math
teachers
Logarithmic
Circular
-trigonometric
Identities and
Equations
-Counting
techniques and
Speaker:
Dr. Ramir
Austria
Honorarium
P3000.00

162. probability
-Intro to
Statistics
Area of
Concern
Objectives
A. Content
Competence
Through the
conduct of
lecture, testretest, skill
builders
strategies, the
mathematics
teachers
should be
able to:
Methods/
Content
Strategies
- examine
different word
problems,
mathematics
illustrations or
Algebra I
-real number
system
-First degree
equations and
inequalities in
one variable
Materials
Needed
Time
Frame
Human
Resource
Logistics
Outcomes
Snacks:
There is a
significant
Participants:
All math
teachers
Speaker:
Mr. Gerry
Hoggang
-rational
algebraic
expressions
-linear
equations in 2

163. Reasoning/
Analytical
Skills
items
accurately
-use
deductive or
inductive
reasoning in
solving
exerices
increase in
the
mathematics
competence
pretest and
Honorarium posttest
variables
-lecture
-systems of
linear
equations
-Skill-building
exercises
P 300.00
Problem Sets
1/2 day
May 23, 2011
Compass
(morning)
P3000.00
Algebra II
-sharingdiscussion
Test-retest
strategy
Supplemental
Materials
-Quadratic
Equations
-variations
Overhead/
-Sequences
and Series
or LCD
projectors
Laptops
Geometry
-Writing Proofs
-Triangle
Participants:
All math
teachers
Speaker:
Dr. Jose P.
Almeida

164. congruence
Participants:
-inequalities
1 /2day
-Similarity
May 23, 2011
-Circles
All math
teachers
(afternoon)
-Coordinate
Geometry
Speaker:
Mrs. Edwina
Manalang
Math IV
-Functions
Quadratic
Polynomial
Exponential
Logarithmic
Participants:
All math
teachers
Circular
-trigonometric
Identities and
Equations
-Counting
Speaker:
Dr. Ramir
Austria

165. techniques and
probability
-Intro to
Statistics
Area of
Concern
Objectives
A. Content
Competence
Through the
conduct of
lecture, testretest, skill
builders
strategies, the
mathematics
teachers
should be
able to:
Methods/
Content
Strategies
Algebra I
-real number
system
-First degree
equations and
inequalities in
one variable
-rational
algebraic
Materials
Needed
Time
Frame
Human
Resource
Participants:
All math
teachers
Speaker:
Mr. Gerry
Hoggang
Logistics
Outcomes

166. Conceptual
Skills
Computational skills
- restate on
their own the
different basic
mathematical
concepts,
theorems,
postulates,
laws and
properties/
axioms
- solve
mathematical
problems
mentally
expressions
-linear
equations in 2
variables
-lecture
-systems of
linear
equations
1 day
Overhead/
-Skill-building
exercises
Algebra II
-panel discussion
-Quadratic
Equations
Laptops
May 25, 2011
or LCD
projectors
-variations
-improve
performance
in the
mathematics
competency
test
There is a
significant
P 300.00
increase in
the
mathematics
competence
pretest and
Honorarium
posttest
P3000.00
Snacks:
-sharingdiscussion
-Sequences
and Series
Problem sets
Participants:
All math
teachers
Speaker:
Test-retest
strategy
Geometry
Dr. Jose P.
Almeida

167. -Writing Proofs
-Triangle
congruence
-inequalities
-Similarity
Participants:
All math
teachers
-Circles
-Coordinate
Geometry
Speaker:
Mrs. Edwina
Manalang
Math IV
-Functions
Quadratic
Polynomial
Exponential
Participants:
Logarithmic
All math
teachers
Circular
-trigonometric
Identities and

168. Equations
Speaker:
-Counting
techniques and
probability
Dr. Ramir
Austria
-Intro to
Statistics
Area of
Concern
Objectives
B.
Through the
Methods/
Strategies
Content
Materials
Needed
Time
Frame
Human
Resource
Logistics
Outcomes

169. Instructional
Competence
conduct of
lecture,
seminarworkshop,
demonstration
panel
discussion,
and hands-on
activities, the
mathematics
teachers should
be able to:
Teaching
Facilitating
Skills
(utilization of
ICT)
- use ICT
gadgets such
as projectors,
laptops,
computers and
the like
-acquaint
themselves in
the basic usage
of the features
of MS
PowerPoint
-lecture
Basic features
of MS
PowerPoint,
Excel, MS
1 day
LCD
Projector
Participants
Snacks:
All Math
teachers
P600.00
95% of the
teachers have
improved on
the use of ICT

170. slides such as
hyperlinking,
videos, photos,
and the like
-use MS Excel,
Geogebra, MS
Math, MathLab
and Statext
-familiarize
themselves
with the
different
interactive
classroom
activities that
supplement
classroom
instruction
-structure
thought
provoking
questions that
-workshop
Math, Math
Lab, Geogebra,
Internet
Statext
Speaker:
Mr. Jayson
Toquero
-demonstration
-panel discussion
in instruction
May 26, 2011
Mathematical
Softwares
Honorarium
P1500.00

171. develop the
critical and
analytical
thinking of the
students
Area of
Concern
Objectives
B.
Instructional
Competence
Through the
conduct of
lecture,
seminarworkshop,
demonstration
panel
discussion,
and hands-on
activities, the
mathematics
teachers
should be
able to:
Methods/
Strategies
Content
Materials
Needed
Time
Frame
Human
Resource
Logistics
Outcomes

172. - use the
varied
motivating
techniques in
instruction
Guidance
Skills
-lecture
(Motivating
techniques)
-workshop
-demonstration
-panel discussion
-acquire and
utilize skills
and
techniques in
improving
classroom
instruction
1 day
Motivating
techniques
LCD
Projector
Laptop
Internet
Mathematical
Softwares
May 27, 2011
Participants
All Math
teachers
Speaker:
Mrs.Gloria
Cruz
95% of the
teachers have
P800.00
improved on
motivating
techniques,
classroom
discipline,
Honorarium
assessment
P1500.00 strategies)
Snacks:

173. Management
skills
(Classroom
discipline)
-construct wellframed test
questions with
table of
specifications
Classroom
Discipline
techniques
Articles on
Classroom
situations
Participants
All Math
teachers
Speaker:
Mrs. Deffie
Graffil
Evaluation
skills
(assessment
strategies)
-Authentic
assessment
Strategies
Honorarium
P1500.00
Test samples
Participants
All Math
teachers
Honorarium
P1500.00

174. Speaker:
Dr. Nora A.
Oredina
Prepared by:
Noted by:
Approved by:
MR. FELJONE G. RAGMA
Researcher
MRS. EVANGELINE L. MANGAOANG
HS Principal
SR. TERESITA A. LARA, ICM
School Directress

175. Chapter 5
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
This chapter incorporates the summary, findings, conclusions and
recommendations of the study.
Summary
The study aimed at determining the competence of Mathematics
teachers in the private secondary schools of San Fernando City, La
Union as basis for a proposed two-pronged training program.
Specifically, it sought to find answers to the following questions:
6. What is the profile of the mathematics teachers along:
a. highest educational qualification;
b. number of years in teaching mathematics; and
c. number
of
mathematics
trainings
and
seminars
attended?
7. What is the level of competence of mathematics teachers along:
a. Content
a.1. Conceptual Skills
a.2. Reasoning/ Analytical Skills
a.3. Computational Skills
a.4. Problem-Solving Skills ; and
b. Instruction
b.1.Teaching Facilitating Skills

176. b.2. Guidance Skills
b.3. Management Skills
b.4. Evaluation Skills?
2.1 Is there a significant difference in the instructional competence
of the teachers as perceived by the students, heads and
teachers, themselves?
8. Is there a significant relationship between:
a. Teacher‘s profile and competence along content;
b. Teacher‘s profile and competence along instruction; and
c. Competence
along
content
and
competence
along
instruction?
9. What are the major strengths and weaknesses of the mathematics
teachers along:
a. Content; and
b. Instruction?
10.
Based on the findings, what training program may be
proposed to enhance the content and instructional competence of
the mathematics teachers?
5.1 What is the level of validity of the training program along:
a. face; and
b. content?

177. The descriptive survey method was used in this study. Data were
gathered with the use of two sets of questionnaire. One is a teacher-made
competence test to determine the content competence. The other one is
questionnaire-checklist to determine the instructional competence.
Respondents were heads, teachers and their students.
Findings
The following are the salient findings of the study:
1. a) All the mathematics teachers are licensed and majority of them
are pursuing graduate studies.
b) Majority of the teacher-respondents, 17 or 65.38%, had 0-5
years of teaching experience.
c) 84.62% had very inadequate and 15.39% had slightly adequate
attendance in seminars.
2. a) The teachers‘ level of subject matter/content competence was
average with a mean rating of 16. They scored highest in
conceptual and computational skills but lowest in problem-solving
skills.
b) The teachers‘ level of instructional competence was very
good with a mean rating of 4.24. They were rated highest in
management skills but lowest in teaching skills.
2.1) There is no significant difference in the perception between
students and teachers; there is a significant difference in the

178. perception between students and heads; and there is no significant
difference in the perception between teachers and heads.
3.
a) There is no significant relationship between profile (highest
educational attainment, number of years of teaching, number of
seminars attended) to content competence.
b)
There
is
a
significant
relationship
between
highest
educational attainment and instructional competence; but there is
no significant relationship between number of years of teaching
and number of seminars attended to instructional competence.
c) There is no significant relationship existing between content
competence and instructional competence.
4. a) Conceptual skills and Computational skills are considered as
strengths. On the other hand, reasoning/analytical skills and
problem-solving skills are considered as weaknesses.
b) All the other skills under teaching, guidance, management
and evaluation were considered strengths. The weakness of
Mathematics teachers along instructional competence was on the
quality of utilization of information and communication technology.
5. The two-pronged training program enhances the weaknesses
and the sustainability of the strengths.
5.1 The training program along face and content validity was
high.

179. Conclusions
In the light of the above-cited findings, the following conclusions
are drawn:
a) The mathematics teachers in the secondary schools of the City
Division of San Fernando, La Union are all qualified in the teaching
profession.
b) The teachers are very young in the service because of the high
turn-over rate of the private schools. The rate may be rooted to the
teachers‘ desire to be employed abroad or in the public schools.
c) The mathematics teachers are exposed minimally to trainings
and seminars but they still perform well in their teaching.
2. The teachers had only average competence in terms of their
content competence but were perceived very skillful in teaching
Mathematics.
2.1 The heads rated instructional competence higher than the
students; but all the respondents consider the teachers very skillful
in teaching.
3. a) Teachers who have higher educational attainment, number of
years in teaching and seminars attended do not have higher subject
matter competence.
b) Teachers who have higher educational attainment have higher
instructional competence; but, teachers who are more experienced in

180. teaching and have more seminars do not mean that they have higher
instructional competence than those who are younger and those who
have lesser seminars.
c) It does not mean that when a teacher has high content
competence, he has high instructional competence as well and vice
versa.
4. Teachers are not so skilled at analysis and problem-solving and
they do not use ICT and other innovative instructional technology
much in their daily teachings but still have very good teaching
performance.
5. The proposed two-pronged training program is timely for the new
and tenured teachers to update and upgrade their content and
instructional competence. Moreover, it is a helpful tool for them to
understand more their subject and know more about the ways on
how to present a subject matter, especially on the use of ICT.
5.1 The administrators of the private secondary schools in the City
Division of San Fernando, La Union considered the two-pronged
training program valid.
Recommendations
Based on the conclusions of the study, the researcher recommends
the following:

181. 1. The teachers have to be encouraged to enroll in their graduate
studies, especially in line with their fields of specialization so that
their competence will be elevated.
2. Incentive Scheme for outstanding performance should be devised
by administrators to enhance or sustain teaching performance;
and keep outstanding teachers in the service.
3. Teachers should always be sent to seminars and workshops where
their participation is necessary. If funding isn‘t enough, there
should be mechanisms such as improving faculty development
plan to remedy the predicament. Further, if a teacher is sent for a
seminar, he has to echo the essentials of the seminar to his/her
area members.
4. Teachers should use ICT in their teaching. On the other hand,
the school has to provide the materials in order for the teacher to
integrate technology to instruction.
5. A closer monitoring system has to be applied by the heads to
ensure that teachers utilize ICT in their teaching. If materials are
scarce, scheduling should be done.
6. The proposed two-pronged training program for the Mathematics
teachers should be implemented in the private secondary schools
in the City Division of San Fernando, La Union.

182. 7. A study to determine the efficiency or efficacy of the two-pronged
training program should be undertaken.
8. A parallel study should be undertaken in other subject areas such
as English and Science.

183. BIBLIOGRAPHY

184. BIBLIOGRAPHY
A. BOOKS
Calmorin, Laurentina. Methods of Research and Thesis Writing.
Manila: Rex Book Store, 2001.
Clemente-Reyes, Flordeliza. Unveiling Teacher Expertise. Manila: De la
Salle University Press,Inc., 2010.
Devela, Mileah. Strategies for Teaching. Sampaloc, Manila: Rex
Publishing, 2000.
Esclabanan, Corazon. Teaching the High School Subjects. Quezon
City, Philippines: Phoenix Publishing House, 2001.
Galton, M. Teaching in the Primary Schools. London: David Fulton
Publishers, 2001.
Lardizabal, Amparo. Principles and Methods of Teaching. Quezon City:
Phoenix Press, Inc., 2001.
Isidro, Antonio. The Philippine Educational System. Manila,
Philippines: Bookman, Inc, 2000.
Sanchez, Custodia A. Methods and Techniques of Research. Manila:
Rex Book Store, 2002.

185. Shulman, L.S. Knowledge and Teaching: Foundations of the New
Reform. Harvard Educational Review, 2001.
Sumagaysay, Lourdes. "Mathematics in the Secondary Curriculum." In
Teaching the High School Subjects, by C Esclabanan, 89-100.
Quezon: Phoenix Publishing Houise, 2001.
B.JOURNALS/PERIODICALS
Adams, S.K. "The Ethnographic stuidy of outstanding Veteran teachers."
Dissertation Abstracts International. 2002.
Berliner, D.C. "In Pursuit of the Expert Pedagogue." Educational
Researcher, 2006: 5-13.
"Consolidated Results of the Monitoring and Evaluation of the
Implementation of the Basic Education Currciulum." Department
of Education, 2002.
"CSC Ruling: DepEd Can hire Unregisered Teachers." Educator's
Journal, 2003: 1-2.
Darling-Hammond, Linda. "Creating Excellent and Equitable High
Schools." Educational Leadership, May 2008: 14-19.
Dizon-Andres, Jenny. "The Government in the high School Scene."
Educational Leadership, May 2009: 7-11.

186. Eligio, Janet. "Seminar on Trends in Teaching Mathematics." Rationale
on the Seminar on Teaching Trends. San Fernando, City, July
2010.
Esperanzate, Estrella. "Making Mathematics Class Enjoyable." The
Modern Teacher, 2006: 146-147.
Farol, Isaac. "Make Teaching More Fun." Educator's Journal, 1999: 2-3.
Gonzalez, Andrew. "Development Imperatives in Education." Tanglaw,
2002: 1-6.
Gonzalez, Andrew. "DECS Secretary's Desk: Preparation of the
Philippine Educational System to the Challeges of the 21st
Century." The Philippine Journal of Education, 2000: 2.
Gubrud, Allan. "Learning Achievement and Efficiency of Learning the
Concepts of Vector Addition at Three different Grade Levels."
Science Education, 2003: 2-5.
Ibe, Milagros. "Filipino Studes lack Math and Science Skills." The
Philippine Journal of Education, 1998: 1-3.
Kennedy, Mary. "How Teachers Learn to Teach." Educator's Journal,
2001: 6-8.

187. Lee, Mariano. "Great Ideas for teaching Mathematics." Philippine
Journal of Education, 2010: 6-7.
Lobo, Fred. "The Effective Mathematics Teacheer." Philippine Daily
Inquirer, 1995: 12-15.
Montealegre, Ma. Antoinette. "Cooperative Learning Activities."
Educator's Journal, 2003: SIBS Publishing.
Nava, F.J.G. "Effective Teaching Behaviors." Paper Presented at the
International Conference on Teacher Education. Hongkong: The Hongkong
Institute of Education, February 23, 1999.
Scherer, Marge. "The High School Scene." Educational Leadership,
2008:
7-9.
"Secondary Mathematics Education Curriculum Guide." Educational
Manuscripts. 2010.
C.PUBLISHED /UNPUBLISHED RESOURCES
Achwarin, Naree A. ―Teachers‘ Competence at the Schools in the
Southern Provinces of Thailand.‖ Published Dissertation.
Assumption University of Thailand-Graduate School of
Education, 2005.

188. Aspiras, Rosabel Rizalinda N. ―Predictors of Performance of the Second
Year Students of Christ the King College.‖ Unpublished Master’s
Thesis. Don Mariano Marcos Memorial State University Graduate
College, City of San Fernando, La Union, 2004.
Bambico, Teresita A. ―INSET as a Tool for Improving Mathematical
Competence: Analysis of the Teachers‘ Performance in Region I‖.
Unpublished Dissertation. Pangasinan State University.2002
Bello, Elizabeth Constancia F. ―Competence of Teacher Educators: Input
for Capacity Building Program‖. Unpublished Dissertation. Saint
Louis Colege, City of San Fernando, La Union, 2009
Binay-an, Imelda N. ―Determinants of Teaching Performance of
Secondary School English Teachers.‖ Unpublished Master’s
Thesis. Don Mariano Marcos Memorial State University-SLUC,
Agoo, La Union, 2002.
Cabusora, Edmund A.‖A Model for the Enhancement of Professors‘
Competence in the Graduate Schools.‖ Unpublished
Dissertation. Don Mariano Marcos Memorial State University
Graduate College, City of San Fernando, La Union, October 2004.
Cayabyab, Vanessa P.‖Mathography: A Basis in Making a Learning
Program for Future Mathematics Teachers.‖ Unpublished

189. Dissertation. Don Mariano Marcos Memorial State University
Graduate College, City of San Fernando, La Union, 2010.
Crisrtobal, Joseph M. ―Capabilities and Needs of the Faculty of Lorma
Colleges along Instruction, Research and Instruction: Basis for a
Training Program.‖ Unpublished Master’s Thesis. Saint Louis
College, City of San Fernando, La Union, 2004
Eslava, Perpetua M. ―A Proposed Training Program for Mathematics
Teachers in the Secondary Schools of La Union, SY 2002-2005.‖
Unpublished Master’s Thesis. Don Mariano Marcos Memorial
State University Graduate College, City of San Fernando, La
Union, 2001.
Diaz, Patricia U. ―Predictors of Mathematical Competencies of the Public
and Private Secondary Mathematics Teachers of the Division of
La Union.‖ Unpublished Dissertation. Don Mariano Marcos
Memorial State University Graduate College, City of San
Fernando, La Union, 2000.
Fianza, Ester T. ―Competencies and Needs of Geometry Teachers: Input
to a Training Program.‖ Unpublished Dissertation. Don Mariano
Marcos Memorial State University Graduate College, City of San
Fernando, La Union, 2009

190. Graycochea, Leonardo F. ―Math Teaching in the Secondary Schools in La
Union, SY 1999-2000: A Model for DMMMSU-Graduate School.‖
Unpublished Master’s Thesis. Don Mariano Marcos Memorial
State University Graduate College, City of San Fernando, La
Union, 2000.
Hoggang, Nancy. ―Physics Teaching in the City Division of San
Fernando, La Union‖ Unpublished Master’s Thesis. Saint Louis
College, City of San Fernando, La Union,2001
.
Laroco, Marlyn R. ―Mathematics of Instruction Plan for the Private
Secondary Schools of the City Division of Urdaneta: Basis for an
Instruction Plan.‖ Unpublished Master’s Thesis, 2005.
Mallare,L. ‗A Proposed Three-Year Action Plan for the Bachelor of
Science in Computer Science in Lorma Colleges.‖ Unpublished
Master’s Thesis. DMMMSU-GC,2001
Olbinado, Emily M. ―Enhancement Program for Secondary Teachers
Who are Non-math Majors.‖ Unpublished Master’s Thesis. Don
Mariano Marcos Memorial State University Graduate College,
City of San Fernando, La Union, 2007.

191. Oredina, Nora A. "Mathematics Instrcution in the HEIs in La Union:
Basis for a Training Program." Unpublished Dissertation. Saint
Louis College, San Fernando City, La Union, June 2006.
Oyanda, Emy F. ―Extent of Knowledge of Secondary Mathematics
Teachers in the Division of La Union: Input to an Instructional
Plan.‖ Unpublished Master’s Thesis. Don Mariano Marcos
Memorial State University Graduate College, City of San
Fernando, La Union, 2003
Ramos, Delilah P. ―The Effectiveness of Games and Puzzles in Secondary
Mathematics I Instruction.‖ Unpublished Master’s Thesis. Saint
Louis College, San Fernando City, La Union.2009.
Rivera, Imelda Lyn R. ―instruction Plan in Contemporary Mathematics for
Teacher Education.‖ Unpublished Master’s Thesis. Don Mariano
Marcos Memorial State University Graduate College, City of San
Fernando, La Union, 2010.
Roldan, Jinkee. ― Achievement and Competence of Mathematics Teachers
in the Division of La Union: Basis for a Proposed Training
Program.‖ Unpublished Dissertation. Saint Louis College, San
Fernando City, La Union.2004.
Subala, Gloria Filomena. ―Competence of the Graduating Math Majors in
the Teacher Training Institutions in Region I.‖ Unpublished

192. Dissertation. Saint Louis College, San Fernando City, La Union,
2006.
Tabafunda,
L.
―Level
of
Effectiveness
of
Secondary
Mathematics
Teachers:Input to A Training Program.‖ Unpublished Master’s
Thesis. Benguet State University, 2005
Verceles, Joan. ―Mathematics Instruction in the College of Technology of
DMMSU-MLUC:
Basis
for
an
Enriched
Math
Instruction.‖
Unpublished Master’s Thesis. Don Mariano Marcos Memorial
State University Graduate College, City of San Fernando, La Union,
2009
D.ON-LINE RESOURCES
Australian Government: Department of Education, Employment and
Workplace Relations. (2001). Retrieved July 31, 2010, from Investigation
of Effective Mathematics Teaching and Learning in Australian Secondary
Schools:http://www.dest.gov.au/sectors/school_education/publications
_resources/other_publications/effective_mathematics_teaching_learning.
htm
http://www.dooyoo.co.uk/discussion/what-qualities-make-an-excellentteacher/1039890/ (accessed 13, July 2010)
http://wiki.answers.com/Q/Why_is_Mathematics_Indispensable

193. http://oprf.com/Rogers (accessed 12 August 2010).
http://doconnor.edublogs.org/finding-e-learning-and-online-teachingjobs/ (accessed 01 September 2010)
jobs.stanlake.co.uk/recruiter/users/jobs.php?id=22
(accessed
02
September 2010)
http://www.sedl.org/pubs/policyresearch/resources/AERA-2004.pdf
(accessed 11 September 2010)
Dersal, Van. 2006. http://www.fao.orhg/docrep/w5030e/w583eoh.htm
(accessed August 10, 2010).
"eric edu." 2009. www.eric.edu/practicalities_mathed (accessed August
15, 2010).
"www.deped.gov." 2010. www.deped.gov/basic_education (accessed July
31, 2010).
www.britannicaonlineenyclopedia.com
http://world.bank.org (accessed 13 2010, August)
http://www.thejournal.com/articles2009
http://www.psypdx.edu/PSIcafe/keytheorist/Gagne.html

194. www.jifsan.umd.edu/pdf/gaps-en/VI-Effective-Training-Com.pdf
(accessed July 17, 2010)
www.ask.com/questions_about_selective_perception. (accessed October
01, 2010)
(www.en/wikipedia.org/wiki/common_coding_theory). (accessed October
01, 2010)
(http.//www.newton.dep.anl.gov/askasci/gen06/gen06327.htm).
(accessed October 01, 2010)
http://en.wikipedia.org/wiki/individual_differences_psychology(accessed
October 01, 2010)
http//www.classroom%20management.(accessed March-29-10)
www.sec.dost.gov.ph (accessed June 2010)
Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All
rights reserved.

195. APPENDICES

196. Sample Computation of Reliability of the Questionnaires
For the College Algebra test:
𝐾𝑅21 =
𝑘
𝑘−1
1−
𝑥 𝑘−𝑥
𝑘𝜎 2
where:
k = number of items
𝑥 = mean of the distribution
𝜎 2 = the sample variance of the distribution
𝐾𝑅21 =
𝐾𝑅21 =
r = 0.79
𝑘
𝑘−1
30
30−1
1−
1−
𝑥 𝑘−𝑥
𝑘𝜎 2
8.9 30−8.9
30 5.15 2

197. CRITERIA
Validators
Sample Computation on the Validity
College Algebra Test
Mean

198. A
B
C
D
E
1. The directions are
specific and can be
understood well by the
students.
4.8
2. The questions are
encoded correctly. There
are no grammatical errors
and lapses.
4.8
3. The sentences are
formulated in a manner
that the target students
can understand.
4. Mathematical
expressions and equations
are encoded correctly. They
are easily understood for
easier calculations.
4.4
5. The test items cover the
course contents as
indicated in the table of
specifications.
4.6
7. There are provisions for
students to write solutions
on the question sheets.
4.6
6. Generally, the test items
are representations of what
they are ought to measure.
4.6
4.6
Overall Mean
4.0 5.0 4.43 4.71 5.0
4.63

199. Summary of Suggestions:
Sample Computation on the Validity of the
Instructional Competence Questionnaire-Checklist
Criteria
Validators
A
B
C
D
E
Mean
1. Are the items representative
of the concepts being
measured?
4
5
5
5
5
4.8
2. Are the questions free from
grammatical error?
4
5
5
5
5
4.8
3. Are the items perfectly clear
and unambiguous? Is the
general frame and reference
from which these are asked,
and from which the answers
should be given clear?
4
5
5
4
5
4.6
4. Are the test items stable,
relatively deep-seated, wellconsidered, non-superficial,
non-ephemeral, but
something which is typical of
the subject area?
4
5
5
5
5
4.8
5. Do the test item pull? That
is, can these be responded
to by a large enough
proportion of examinees to
permit validity? Are the test
items engaging enough to
get response with some
4
5
5
5
5
4.8

200. depth and reality?
6. Are the options of reasonable
range of variations?
4
5
5
4
5
4.6
7. Are the test items sufficiently
inclusive? Are full scope and
intent of the test items so
clearly indicated that the
test takers will not omit
parts of the options through
lack of certainty as to what
the test items desired.
4
5
4
5
5
4.6
Overall Mean
4.0
5.0
4.86
4.71
5.0
4.71
Sample Computation on the Validity of the
Two-Pronged Training Program
Criteria
Validators
Mean
A
B
C
D
E
F
4
5
5
4
4
3
4.17
a.Functionality
5
5
5
5
4
3
4.50
b.Acceptability
5
5
5
5
4
3
4.50
c.Appropriateness
5
5
5
4
4
3
4.33
d.Timeliness
5
5
5
4
4
2
4.17
e.Implementability
4
4
5
4
4
2
3.83
f.Sustainability
4
4
4
5
4
2
3.83
I. Face
II. Content

201. Average
4.67
4.67
4.83
4.5
4.0
2.50
4.20
Overall Mean
4.34
4.83
4.92
4.25
4.0
2.78
4.19
MATHEMATICS COMPETENCE TEST
NAME:________________________________SCHOOL_______________:SCORE::______
INSTRUCTIONS: Select the letter of the correct answer. Write your answers on the space provided for.
CALCULATORS ARE NOT ALLOWED! (30)
_____1.Which axiom supports the idea that 2x +y = y +2x?
a. commutative b. associative
c. inverse
d. identity
_____2. Which of the following statements is always true?
a. The quotient of two numbers is not always an integer.
b. The quotient of two numbers is not always a fraction.

202. c. The quotient of two number is not always rational
d. All statements are true except a
e. Statements a, b and c are true.
_____3. San Fernando’s temperature, which is 40◦C, is how many ◦F?
a.104
b. 77
c. 400
d. 273.4
_____4. Len borrowed P10,000 at 10% simple interest. If she paid an interest and principal at the end of 18
mos., how much did she pay?
a.P11,550
b. P18000
c.P11500
d. P10010
_____5. From a 100cm x 100cm x 60cm block of marble, a pyramid with square base of 100cm and a
height of 60cm is carved. What is the volume of the marble carved in scientific notation?
a. 2x105
b. 4x104
c. 4x105
d. 5x102
_____6.If the sum of x and y is subtracted from the sum of their squares, the answer is N. What is the
relevant equation?
a. x+y- x2+y2 =N b.(x2+y2)-(x+y)=N
c.(x+y)2 -(x+y)=N
d. (x-y) + (x+y)2=N
_____7. Which of the following is not a polynomial?
a. 5x2 +2x -1
b. x3- 3.4x+7
c.
4
𝑥−2𝑥 3 −5
d.
𝑥2
2
_____8.Which of the following describes an identity equation?
a.4a-7=1
b. x= y+1
c.3(8-10)=-8+2 d. 4(7-2) =18
_____9. RJ and JR are traveling north in separate cars on the same highway. RJ is at 65kph and JR is at
70kph. RJ passes Dau Exit at 2:30p.m. JR passes the same exit at 2:45p.m. At what time will JR
catch up to RJ?
a. 3:25p.m.
b.6:00p.m.
c. 5:30 p.m.
d. he can’t catch up
_____10. If
1
𝑢
1
1
+ 𝑣 = 𝑓 then what is the formula for v?
a.v = u - 2f
𝑓𝑢
𝑢−𝑓
𝑎 3 −𝑏 3 −𝑎 2 𝑏+𝑎𝑏 2 −𝑎+𝑏
factored form of
2𝑎−2𝑏
𝑎 2 +𝑏 2 −1
𝑎 2 +𝑏 2 +1
b.
c.
2𝑎
2
b. v=
_____11. What is the complete
a. (a-b)(a2+b2-1)
𝑓𝑢
𝑢+1
1
c. v=
d. v = 𝑢 +
1
𝑓
?
d. 2a2+2b2-2
_____12. Which of the following lines has an undefined slope?
a.
Vertical b. horizontal
c. skewed to the right d. skewed to the left
_____13. If three vertices of a parallelogram are A(2,0), B(4,4), C(6,0), find the vertex D if D is in the 4th
quadrant.
a. (1,-1)
b.(4,-4)
c.(2,-4)
d.(4,-1)
_____14.The line with equation 2y= - 4x +8 is perpendicular to a line whose one point is (2,-3). What is the
equation of the line?
a.y=
𝑥−8
2
b. y=
𝑥+2
2
c. y = -2x +1
d. y= 2x+1
_____15. For how many different positive integers n is 0<10-√n<1?
a.19
b. 21
c. 23 d. 18
_____16. To solve x2 +8x =-5 by completing the square, what number must be added to both sides of the
equation?
a. 64
b. 8
c. -64
d. 16

203. 𝑥 3 −8
_____17. What is the complete factored form of2𝑥 2 +4𝑥+8?
a. x-2
𝑥−2
2
b.
c. 2 (x-2)
d. not factorable
_____18. For what values of k will kx2 +11x -2 =0 have unequal roots?
a.k >0
1
b. k> 4
c. k <
121
8
d.k >
−121
8
_____19. In the quadratic equation y= x2-8x +3, what is the minimum point?
a.(13,4)
b.(-13,4)
c.(4,-13)
d.(-4,13)
_____20. For what values of x will
a.±1,±2
4𝑥 2 −9
𝑥 4 −5𝑥 2 +4
b. ±1,±3
c.±1,0
_____21. What is the simplified form of
a.
𝑦−5
3𝑦
be meaningless?
𝑦−5
b. 3𝑦 3
2𝑦−14
𝑦 2 −2𝑦−35
𝑦+5
c. 𝑦
÷
d. 0
6𝑦 3
𝑦 2 −25
?
d.
𝑦−5
𝑦
_____22.What is the value of (81/256)-3/4?
64
27
a.
1
b. 4
c.
_____23.If 62(3x-2)=324, what is x?
a.4
b.3
𝑎
𝑏
_____24. If
:
𝑎𝑏 6
: :_______
𝑏
3
24
5
27
d. 64
c.1
a.
63
3
b.
d.0
18
3
c. 2
d.
18
3
3
_____25. If 𝑥 3 𝑦 3 + 𝑥 4 𝑦 6 = 4𝑥𝑦, then xy3 is equal to? a.31
b.63
c.96
d.15
_____26. y varies directly with x such that and y =12 when x=4. What is the equation of variation?
a. xy=k
b. y=-3x/12
c.4x=12y
d. y=3x
_____27. The distance of a body falls from rest is directly proportional to the square of the time it falls. If an
object falls 256 feet in 4 seconds, how far will it fall in 8 seconds?
a.128ft
b.1024ft
c.64ft
d. none among the options given
_____28. What is the general term for the sum of the first 100 whole numbers?
a. 𝑎 𝑛 = 100(1 + 100)
b. 𝑎 𝑛 =
99(0+99)
2
c. 𝑎 𝑛 =
100(1+100)
2
d. 𝑎 𝑛 =
100(0+99)
2
_____29.Find the 11th term of the sequence 25,50,75… a.250
b.200
c.275
d.300
_____30. Suppose a ball always rebounds 1/3 of the height from which it falls and the ball is dropped from a
height of 24 feet. What is the general tem of its sequence whose sequences are the heights from
which the ball falls? a.an = 24(1/3)n
b. an = (8)n
c. an = 24(1/3)n-1 d. an = 8n-1
_____31. Which of the following geometric statements is stated correctly?
a. A polygon is a plane figure formed by two or more non-collinear segments such that each
segment intersects exactly two others, one at each endpoint.
b. Among skew, perpendicular, parallel and intersecting lines, only skew lines are non-coplanar.
c. An angle is formed by rays that have a common endpoint.
d. A segment bisector is a ray that divides a segment into two congruent parts.
e. All statements are stated correctly.
_____32. E is the midpoint of segment FL. If FE = 4x2 –x +12 and EL = 3x2 +x +60, what are the possible
lengths of FL?
a. 260 and 162
b. 144 and 200 c. 520 and 364 d. 8 and -6

204. _____33. <a and <b are both right angles. Which can justify the conclusion that the two right angles, <a and
<b, are congruent?
a. Definition of right angles
b. definition of congruent angles
b. Right angles theorem
c. Transitive property of Equality
_____34.Which among these is a geometric corollary?
a. Law of Substitution
b. Supplement Theorem
c. Supplement Postulate
d. Definition of Linear Pair
_____35. Angles C and A are same-side interior angles. What type of angles are they if m<A=m<C?
a. right b. acute c. obtuse d. can’t be determined due to limited data
_____36. Which of the following is not a triangle congruence postulate?
a. SAS
b.SSS
c. AAA
d. ASA
A
B
_____37.(Refer to the figure at the right) If M is the midpoint of AC and BD, which postulate
M
can be used to prove that the 2 ∆s are congruent?
a. SAS
b. ASA c. AAS
d. AAA
_____38. Which inequality describes an obtuse triangle?
D
C
a. c2 ≠ a2+b2 b. c2 > a2+b2
c. c2 < a2+b2
d. c 2≤ a2+b2
_____39. Which is correct for the angles of a rectangle and square?
a. Two consecutive angles are supplementary
b. Two nonconsecutive angles are congruent
c. One of the four angles is right.
d. all statements
_____40. The consecutive angles of a parallelogram are (3x +4) and (2x+6) degrees. What is the measure
of (3x+4)?
a. 10
b. 106
c.74
d. b or c
_____41. The diagonals of an isosceles trapezoid are denoted by 2x2+3 and x2+28. What is the length of
one diagonal? a.43
b. 53
c.5
d.106
For nos. 42-43, refer to circle E at the right.
J
_____42. What is the measure of <IEB if its 1/8 of a revolution?
O
D
J
a.45
b. 10
c. 170
d. 135
M
E
D
_____43. IF m<IEB=73, what is the measure of <IOB?
J
a.73
b. 143.5
c. 36.5
d. 287
B
_____44. What is the other endpoint of a segment with one endpoint at (3,-7) and the midpoint at (2,0)? J
a. (1,7)
b. (-4, 3)
c. (3, 4)
d. (7,1)
_____45. The line through (-2,-1) with a slope of 3/8 also passes through the point (6,y) What is the
coordinate of y?
a. y=1
b. y = -1
C. y=2
d. y =-2
_____46. Which correspondence is a function?
a. One-to-one b. one-to-many c. many-to-one d. a and b
e. a and c
_____47. If y = x/4, how many sixths of y does 1/12 of x represent?
a. 0
b.1
c.2
d.3

205. _____48. For what values of x is x2 + 5x -14 greater than 0?
a. x< -7; x >2
b. x> -7; x >2
c. x> 7; x >2
d. x> -7; x >-2
_____49. Which polynomial has the integral roots of -1/3 and 1 ± 2?
a. 3x3-5x2-5x-1=0
b. 3x3-5x2-5x+1=0
3+5x2+5x-1=0
b. 3x
d. 3x3+5x2-5x+1=0
_____50. What is the domain of y = 3𝑥 2 + 5 ?
a. x ≥ ±5/3
b. x ≥ ± 5/3
c. x ≥ -5/3
d. the set of reals (R)
7 then what is the value of x?
_____51. If x = log8 8
a. 1
b. 8
c. 7
d. 0
_____52. If x = eln5, then what is the value of x?
a. 0
b. e
c. 1
d. 5
_____53. Which is a coterminal angle of -150 degrees?
a. 30
b. 210
c. 510
d.330
_____54. The second hand of a clock is 10.5cm. What is the linear speed of the tip of this second hand as it
passes around the clock face?
a. 2 cm/sec
b. 3.3 cm/sec c.1.099cm/sec d. 1.315cm/sec
_____55. Which of the following is equal to ( 3/2, 1/2)?
a. [5∏/6, 17∏/6, 29∏/6, 41∏/6]
b. [7∏/6, 19∏/6, 31∏/6, 43∏/6]
b. [11∏/6, 23∏/6, 35∏/6, 47∏/6]
d. [∏/6, 13∏/6, 25∏/6, 37∏/6]
2 x+ sin x = 1; 0≤ x ≤∏/4?
_____56. What is the solution of cos
a. ∏/2
b. 90
c. ∏/2, 7∏/6, 11∏/6
d. no solution
_____57. Two dice are tossed. How many possible outcomes are there?
a. 12
b. 24
c. 36
d. 42
_____58.In how many ways can 4 people be seated in a round table?
a.12
b. 6
c. 24
d. 30
_____59. Which of the following is equal to the median?
a. 5th decile
b. 50th percentile c. 2nd quartile
d. all
_____60.When gathering raw data using a 5-point Likert Scale, what is the appropriate statistical tool to be
used to determine the desired data necessary to interpret results?
a. Standard deviation
b. Variation
c. weighted Mean
d. Frequency count
ANSWER KEY TO MATHEMATICS COMPETENCE TEST
ITEM
NO.
Answer
1
A
ITEM
Answer
NO.
31
B

206. 2
E
32
C
3
A
33
B
4
C
34
B
5
C
35
A
6
B
36
C
7
C
37
A
8
C
38
B
9
B
39
D
10
C
40
B
11
C
41
B
12
A
42
A
13
B
43
C
14
A
44
A
15
D
45
B
16
D
46
E
17
B
47
C
18
D
48
B
19
C
49
A
20
A
50
D
21
B
51
C
22
A
52
D
23
A
53
B

207. 24
C
54
C
25
B
55
D
26
D
56
D
27
B
57
C
28
D
58
B
29
C
59
D
30
C
60
C

208. TEST SPECIFICATIONS FOR MATHEMATICS COMPETENCE TEST
Knowledge
AREA OF
GRADING
MATHEMATICS PERIOD
Comprehension/
Application
Analysis
CONTENT
STANDARDS
Evaluation
Analytical/
Reasoning
Computational
Skills
Skills
E
N
T
A
2ND
%
2
#7
First-degree
Equations
#8
3 1/3%
#4
2
3 1/3%
#5
#3
Algebraic
Expression
and
Inequalities in
One variable
Total
ProblemSolving
Skills
#2
Scientific
Notation
E
E
#1
Measurements
L
M
Real Number
System
Pts
Pts
Conceptual
Skills
1ST
Synthesis/
1
1 2/3%
2
3 1/3%
2
3 1/3%
#6
#9

209. Y
Rational
Algebraic
Expressions
A
Linear
Equations and
R
3RD
G
4TH
B
15
3 1/3%
#11
#12
#13
2
3 1/3%
Systems of
Linear
Equations
#14
2
3 1/3%
#17
#15
2
3 1/3%
#19
2
3 1/3%
#21
2
3 1/3%
and
Inequalities in
Two Variables
R
A
1ST
I
N
Special
Products and
Factors
#16
Quadratic
Equations
T
E
2
Inequalities in
Two Variables
L
E
#10
2ND
Equations
Involving
Rational
#18
#20

210. R
Expressions
M
Expressions
with Rational
Exponents
E
D
3RD
I
A
A
L
G
E
B
R
A
4TH
2
Radical
Expressions
and Equations
#24
#28
#29
2
3 1/3%
#27
#26
Sequences
and Series
3 1/3%
15
#23
Variations
T
E
#22
#25
2
3 1/3%
#30
3
5%

211. 1ST
Geometry of
Shape and
Size
E
1
1 2/3%
1
1 2/3%
#33
2
3 1/3%
#35
1
1 2/3%
#37
2
3 1/3%
Inequalities in
a Triangle
G
#38
1
1 2/3%
Quadrilaterals
#39
1
1 2/3%
2
3 1/3%
O
Geometric
Relations
M
Writing Proofs
#31
E
2ND
T
R
3RD
#34
Perpendicular
Lines and
Parallel Lines
Triangle
Congruence
Y
#32
#36
Similarity
#40
#41
4TH
Circles
#42
15
2
3 1/3%

212. #43
Plane
Coordinate
Geometry
A
1ST
D
A
2
3 1/3%
1
1 2/3%
1
1 2/3%
#45
#46
Linear
Functions
V
#47
Quadratic
Functions
N
C
Relations and
Functions
#44
2ND
E
D
#48
1
1 2/3%
Polynomial
Functions
#49
2
3 1/3%
2
3 1/3%
2
3 1/3%
Exponential
and
Logarithmic
Functions
A
3RD
Circular
#50
#51
#52
#53
#54

213. L
Functions
G
Trigonometric
Identities and
Equations
E
B
R
A
T
R
I
G
O
&
S
T
4TH
#55
Counting
Techniques
and Probability
Measures of
Central
Tendency and
Variability
#56
2
#57
15
3 1/3%
2
3 1/3%
2
3 1/3%
#58
#59
#60

214. A
T
TOTAL
14
16
16
14
PERCENTAGE
23 1/3 %
26 2/3 %
26 2/3%
23 1/3%
60
100%

215. Questionnaire
QUESTIONNAIRE FOR HEADS
(SAC/Dept. Head/Academic Coordinator/Principal)
SAINT LOUIS COLLEGE
City of San Fernando, La Union
GRADUATE SCHOOL
October 11, 2010
Highly Esteemed Educators,
The undersigned is a Master of Arts in Education Major in Mathematics
(MAEd-Math) student of Saint Louis College undertaking the study
entitled, ―Competence of Mathematics Teachers in the Private
Secondary Schools in San Fernando: Basis for a Two-Pronged
Training Program.‖ It is with this cause that your support is sincerely
solicited so that this study can be carried out and may greatly contribute
to the improvement of the teaching-learning process.
Please accomplish then this very objectively and accurately. It may
take much of your precious time but your responses will contribute
much to the success of this study. Please don‘t leave an item
unanswered. Rest assured that all information obtained herein will be
held strictly confidential. Your immediate attention to this request is
highly cherished.
Thank you so much!
Sincerely yours,
Mr. Feljone G. Ragma
Researcher

216. QUESTIONNAIRE FOR HEADS
COMPETENCE OF MATHEMATICS TEACHERS IN THE PRIVATE SECONDARY SCHOOLS IN
SAN FERNANDO CITY, LA UNION: BASIS FOR A TWO-PRONGED TRAINING PROGRAM
PART I. PROFILE OF THE HEADS
Directions: Please fill in the data needed by putting a check mark (√ ) in the option that corresponds to your
answers.
A. Name (Optional): _______________________________________________
B. Institution Connected with:
___BHC
___CICOSAT
___CKC
___DSHJ
___UCC
___FELKRIS
___GLC _
__ LUCI
___LUCNAS
___MBC
___NCST
___SLC
___SLSHS
PART II. LEVEL OF INSTRUCTIONAL COMPETENCY
Directions: Below are behaviors of an effective and efficient Mathematics Teacher. Please feel
free to rate your math teacher by checking the blank in the appropriate column using
the scale below:
Scale
Equivalent Description
5
Outstanding (O)
-refers to performance that is rarely equaled and with
numerical rating within 95-99
4
Very Satisfactory (VS) - refers to performance that clearly exceeds acceptable
standards and with numerical rating within 90-94
3
Satisfactory (S)
- refers to performance that meets acceptable standards
and with numerical rating within 85-89
2
Fair (F)
- refers to performance below acceptable standards and
with numerical rating within 80-84
1
Poor (P)
- refers to performance that is unacceptable and with
numerical rating within 75-79
D. Teaching / Facilitating Skills
7. Substantiality of Teaching
The teacher...
i.
j.
shows confidence and exhibits mastery of the subject matter
shows awareness of the developments of the subject matter as seen in
the utilization of key concepts, relationships, and different perspectives
related to the content area
k. aligns classroom instruction with national standards, school’s visionmission and educational philosophy
5 4 3 2 1

217. l.
focuses on and covers all important aspects of the subject matter
m. connects students’ prior knowledge, life experiences, and interests in
the instructional process
n. provides values clarification and integration considering the
applications of the subject area to the students’ practical life
o. engages students in in-depth and varied experiences that meet the
diverse needs and promote holistic growth
p. relates ideas and information within and across content areas
8. Quality of teacher’s explanation
The teacher …
e. makes abstract concepts clear for students’ understanding
f.
asks students how they got a particular answer
g. encourages students to probe into reactions, answers and responses
h. uses knowledge of students’ development to make learning
experiences meaningful and accessible for every student
9. Receptivity to students’ ideas and contributions
The teacher …
d.
leads students to ask or initiate thought-provoking questions
e.
integrates and elaborates students’ questions and contributions into
the class discussion
demonstrates flexibility and responsiveness in adjusting instruction to
meet students’ needs, ideas and contributions
f.
10. Quality of questioning procedure
The teacher …
g.
poses thought-provoking questions that promote high-order thinking skills
h.
encourages students to explain ideas and ask questions about the content
i.
provides time for student to think, ponder on and express response
j.
poses follow-up questions to clarify initial question when a student is
unable to respond effectively

218. k. emphasizes on essential ideas and problems
l.
ensures that factual information and skills are applied to ideas and problems
11. Selection of teaching methods
The teacher uses teaching methods which are…
f.
determined on behavioral objectives and appropriate to the content area
g. used in expressing ideas and problems (projects, themes, panel
discussion, demonstration, etc)
h. emphasizing on and eliciting students’ inquiry
i.
used to address individual differences and develop multiple intelligences
j.
intended to engage students in learning and supportive of theories of
collaborative and cooperative learning
12. Quality of information and communication technology used
The teacher uses…
f.
computers for designing and printing instructional materials
g. the principles of computer-aided and computer-based instruction
h. multi-media resources, including technologies such as the internet, in
the development and sequencing of instruction
i. computerized grading sheets (without received corrections)
j.
overhead/LCD projector
E. Guidance Skills
3. Quality of Interaction with students
The teacher …
f.
arouses, maintains and sustains students’ interests
g. gives students recognition (praises and reinforcements)
h. regards students’ errors/mistakes as fruitful opportunities for learning
i.
makes use of teaching as guide in helping students improve their work

219. j.
communicates high and realistic expectations from students
4. Quality of students’ activity
The teacher ensures that…
f.
activities are purposeful, relevant and experiential
g. students are developing increased self-reliance and responsibility
h. learning activities are appropriate for students’ developmental tasks
i.
time allocation is flexible to allow continuity of productive activities
j.
resources and facilities are appropriate for the learning activities
F. Management Skills
1. Atmosphere in the Classroom
The teacher …
i. creates and encourages positive social interaction, active engagement
and self-regulation for every student
j. is enthusiastic and maintains a warm friendly atmosphere conducive to
learning
k. establishes, communicates, models, and maintains standards of
responsible student behavior
l. instills mutual respect, order and discipline
m. incorporates creative and constructive discipline techniques rather than
coercive and restrictive discipline techniques
n. develops and implements classroom procedures and routines that
support learning and enforce school policies among students
o. cultivates students’ deep sense of controlling for their direction
p. is organized, punctual and manages class time well ( accomplish the
objectives and procedures set for the time period)
2. Conduct and return of evaluation materials
The teacher …
g. corrects test papers, quizzes, assignments/requirements carefully

220. h. returns corrected test papers, quizzes, requirements promptly
i.
conducts efficiently quizzes/ examinations to avoid cheating
G. Evaluation Skills
4. Quality of Appraisal questions
The teacher is able to…
f.
frame questions to find out students’ understanding
g. ask questions, integrated in varying techniques, that lead to the
synthesis of the salient points of the lesson
h. prepare well-framed questions covering the subject matter taken in class
i.
guide students in goal setting and assessing their own learning
j.
provide students substantive, timely, and constructive feedback for
specific area for improvement (write comments on paper/talk to
students privately)
5. Quality of assignment/ enrichment activities
The teacher provides and considers…
f. varying authentic assessments to gauge the extent of authentic learning
g. assignment/ enrichment activities to supplement the day’s lesson and/or
aligned to classroom instruction
h. subject requirements that are practical and challenging
i. adequate time for students to complete assignments/ requirements
j.
availability of materials in giving assignments and subject requirements
6. Quality of appraising students’ performance
The teacher …
e. observes the standard grading system of the school
f.
grades/ scores students objectively and accurately
g. encourages students’ participation in creating rubrics

221. h. utilizes criteria/ rubrics in checking requirements

222. Questionnaire
QUESTIONNAIRE FOR MATHEMATICS TEACHERS
SAINT LOUIS COLLEGE
City of San Fernando, La Union
GRADUATE SCHOOL
October 11, 2010
Dear Fellow Math Teachers,
The undersigned is a Master of Arts in Education Major in Mathematics
(MAEd-Math) student of Saint Louis College undertaking the study
entitled, ―Competence of Mathematics Teachers in the Private
Secondary Schools in San Fernando: Basis for a Two-Pronged
Training Program.‖ It is with this cause that your support is sincerely
solicited so that this study can be carried out and may greatly contribute
to the improvement of the teaching-learning process.
Please accomplish then this very objectively and accurately. It may
take much of your precious time but your responses will contribute
much to the success of this study. Please don‘t leave an item
unanswered. Rest assured that all information obtained herein will be
held strictly confidential. Your immediate attention to this request is
highly cherished.
Thank you so much!
Sincerely yours,
Mr. Feljone G. Ragma
Researcher

223. QUESTIONNAIRE FOR MATHEMATICS TEACHERS
COMPETENCE OF MATHEMATICS TEACHERS IN THE PRIVATE SECONDARY SCHOOLS IN
SAN FERNANDO CITY, LA UNION: BASIS FOR A TWO-PRONGED TRAINING PROGRAM
PART I. PROFILE OF THE TEACHER-RESPONDENTS
Directions: Please fill in the data needed by putting a check mark (√ ) in the option that corresponds to your
answers.
A. Name (Optional): _______________________________________________
B. Institution Connected with:
___BHC
___CICOSAT
___CKC
___DSHJ
___UCC
___FELKRIS
___GLC _
__LUCI
___LUCNAS
___MBC
___NCST
___SLC
___SLSHS
C. Highest Educational Attainment
___ BSED/BSE/AB/BS graduate (Non-licensed)
___ BSED/BSE/AB/BS graduate (Licensed)
___ BSED/BSE/AB/BS graduate MS/MA units
___ MS/MA graduate
___ with EDd/PHd units
___ EDd/PHd graduate
D. Years of teaching mathematics
___0-5 years
___6-10 years
___11-15 years
___16-20 years ___21-25 years
___26 years and above
E. Mathematics seminars/trainings attended (last two years)
Name of Seminar
School Local Regional National Internat’l
_____________________________ ___
___
___
___
___
_____________________________ ___
___
___
___
___
_____________________________ ___
___
___
___
___
_____________________________ ___
___
___
___
___
PART II. LEVEL OF INSTRUCTIONAL COMPETENCY
Directions: Below are behaviors of an effective and efficient Mathematics Teacher. Please feel
free to rate yourself by checking the blank in the appropriate column using the scale below:
Scale
Equivalent Description
5
Outstanding (O)
-refers to performance that is rarely equaled and with
numerical rating within 95-99
4
Very Satisfactory (VS) - refers to performance that clearly exceeds acceptable
standards and with numerical rating within 90-94
3
Satisfactory (S)
- refers to performance that meets acceptable standards
and with numerical rating within 85-89

224. 2
Fair (F)
1
Poor (P)
- refers to performance below acceptable standards and
with numerical rating within 80-84
- refers to performance that is unacceptable and with
numerical rating within 75-79
A. Teaching / Facilitating Skills
1. Substantiality of Teaching
I...
a. show confidence and exhibit mastery of the subject matter
b. show awareness of the developments of the subject matter as seen in
the utilization of key concepts, relationships, and different perspectives
related to the content area
c. align classroom instruction with national standards, school’s visionmission and educational philosophy
d. focus on and cover all important aspects of the subject matter
e. connect students’ prior knowledge, life experiences, and interests in
the instructional process
f. provide values clarification and integration considering the applications
of the subject area to the students’ practical life
g. engage students in in-depth and varied experiences that meet the
diverse needs and promote holistic growth
h. relate ideas and information within and across content areas
2. Quality of teacher’s explanation
I…
a. make abstract concepts clear for students’ understanding
b. ask students how they got a particular answer
c. encourage students to probe into reactions, answers and responses
d. use knowledge of students’ development to make learning experiences
meaningful and accessible for every student
3. Receptivity to students’ ideas and contributions
I…
a. lead students to ask or initiate thought-provoking questions
5 4 3 2 1

225. b. integrate and elaborate students’ questions and contributions into the
class discussion
c. demonstrate flexibility and responsiveness in adjusting instruction to
meet students’ needs, ideas and contributions
4. Quality of questioning procedure
I…
a. pose thought-provoking questions that promote high-order thinking skills
b. encourage students to explain ideas and ask questions about the content
c. provide time for student to think, ponder on and express response
e.
d. pose follow-up questions to clarify initial question when a student is
unable to respond effectively
emphasize on essential ideas and problems
f.
ensure that factual information and skills are applied to ideas and problems
5. Selection of teaching methods
I use teaching methods which are…
a. determined on behavioral objectives and appropriate to the content area
b. used in expressing ideas and problems (projects, themes, panel
discussion, demonstration, etc)
c. emphasizing on and eliciting students’ inquiry
d. used to address individual differences and develop multiple
intelligences
e. intended to engage students in learning and supportive of theories of
collaborative and cooperative learning
6. Quality of information and communication technology used
I use…
a. computers for designing and printing instructional materials
b. the principles of computer-aided and computer-based instruction
c. multi-media resources, including technologies such as the internet, in
the development and sequencing of instruction

226. d.
computerized grading sheets (without received corrections)
e.
overhead/LCD projector
B. Guidance Skills
1. Quality of Interaction with students
I…
a. arouse, maintain and sustain students’ interests
b. give students recognition (praises and reinforcements)
c. regard students’ errors/mistakes as fruitful opportunities for learning
d. make use of teaching as guide in helping students improve their work
e. communicate high and realistic expectations from students
2. Quality of students’ activity
I ensure that…
a. activities are purposeful, relevant and experiential
b. tudents are developing increased self-reliance and responsibility
c. learning activities are appropriate for students’ developmental tasks
d. time allocation is flexible to allow continuity of productive activities
e. resources and facilities are appropriate for the learning activities
C. Management Skills
5. Atmosphere in the classroom
I…
a. create and encourage positive social interaction, active engagement
and self-regulation for every student
b. am enthusiastic and maintain a warm friendly atmosphere conducive
to learning
c. establish, communicate, model, and maintain standards of responsible
student behavior

227. d.
instill mutual respect, order and discipline
e.
incorporate creative and constructive discipline techniques rather than
coercive and restrictive discipline techniques
f. develop and implement classroom procedures and routines that support
learning and enforce school policies among students
g. cultivate students’ deep sense of controlling for their direction
h. am organized, punctual and manage class time well; accomplish the
objectives and procedures set for the time period
6. Conduct and return of evaluation materials
I…
a. correct test papers, quizzes, assignments/requirements carefully
b. return corrected test papers, quizzes, requirements promptly
c. conduct efficiently quizzes/ examinations to avoid cheating
D. Evaluation Skills
1. Quality of Appraisal questions
I am able to…
a. frame questions to find out students’ understanding
b. ask questions, integrated in varying techniques, that lead to the
synthesis of the salient points of the lesson
c. prepare well-framed questions covering the subject matter taken in class
d. guide students in goal setting and assessing their own learning
e. provide students substantive, timely, and constructive feedback for
specific area for improvement (write comments on paper/talk to
students privately)
2. Quality of assignment/ enrichment activities
I provide and consider…
a. varying authentic assessments to gauge the extent of authentic
learning
b. assignment/ enrichment activities to supplement the day’s lesson
and/or aligned to classroom instruction

228. c. subject requirements that are practical and challenging
d. adequate time for students to complete assignments/ requirements
e. availability of materials in giving assignments and subject requirements
3. Quality of appraising students’ performance
I…
a. observe the standard grading system of the school
b. grade/ score students objectively and accurately
c. encourage students’ participation in creating rubrics
d. utilize criteria/ rubrics in checking requirements

229. Questionnaire
QUESTIONNAIRE FOR STUDENT-RESPONDENTS
SAINT LOUIS COLLEGE
City of San Fernando, La Union
GRADUATE SCHOOL
October 11, 2010
My Dearest students,
The undersigned is a Master of Arts in Education Major in Mathematics
(MAEd-Math) student of Saint Louis College undertaking the study
entitled, ―Competence of Mathematics Teachers in the Private
Secondary Schools in San Fernando: Basis for a Two-Pronged
Training Program.‖ It is with this cause that your support is sincerely
solicited so that this study can be carried out and may greatly contribute
to the improvement of the teaching-learning process.
Please accomplish then this very objectively and accurately. It may
take much of your precious time but your responses will contribute
much to the success of this study. Please don‘t leave an item
unanswered. Rest assured that all information obtained herein will be
held strictly confidential. Your immediate attention to this request is
highly cherished.
Thank you so much!
Sincerely yours,
Mr. Feljone G. Ragma
Researcher

230. QUESTIONNAIRE FOR STUDENT-RESPONDENTS
COMPETENCE OF MATHEMATICS TEACHERS IN THE PRIVATE SECONDARY SCHOOLS IN
SAN FERNANDO CITY, LA UNION: BASIS FOR A TWO-PRONGED TRAINING PROGRAM
PART I. PROFILE OF THE STUDENT-RESPONDENTS
Directions: Please fill in the data needed by putting a check mark (√ ) in the option that corresponds to your
answers.
A. Name (Optional): _______________________________________________
B. School Connected with:
___BHC
___CICOSAT
___CKC
___DSHJ
___UCC
___FELKRIS
___GLC _
__LUCI
___LUCNAS
___MBC
___NCST
___SLC
___SLSHS
PART II. LEVEL OF INSTRUCTIONAL COMPETENCY
Directions: Below are behaviors of an effective and efficient Mathematics Teacher. Please feel
free to rate your math teacher by checking the blank in the appropriate column using
the scale below:
Scale
Equivalent Description
5
Outstanding (O)
-refers to performance that is rarely equaled and with
numerical rating within 95-99
4
Very Satisfactory (VS) - refers to performance that clearly exceeds acceptable
standards and with numerical rating within 90-94
3
Satisfactory (S)
- refers to performance that meets acceptable standards
and with numerical rating within 85-89
2
Fair (F)
- refers to performance below acceptable standards and
with numerical rating within 80-84
1
Poor (P)
- refers to performance that is unacceptable and with
numerical rating within 75-79
A. Teaching / Facilitating Skills
1. Substantiality of Teaching
The teacher...
a. knows very well his lesson
b. is updated with his subject
c. connects teaching to school’s vision-mission, philosophy and national
goals
5 4 3 2 1

231. d. teaches all important areas of the subject matter
e. connects students’ knowledge, life experiences, and interests to the
lesson
f. gives values integration practical to life
g. gives students different activities (puzzles, games, recitation)
h. connects the lesson to other lessons and subjects (ie. English,
Science,AP)
2. Quality of teacher’s explanation
The teacher …
a. makes math concepts clear
b. asks students how they got an answer
c. asks students to agree or disagree with presented answers
d. makes his teaching understandable to all (teacher simplifies lessons)
3. Receptivity to students’ ideas and contributions
The teacher …
a. pushes students to raise very good questions
b.
includes students’ questions into the discussion
c.
fits lessons to students’ level
4. Quality of questioning procedure
The teacher …
a. asks questions that make students think deeply
b. lets students explain answers
c. allows students to think and react
d. rewords questions when a student is unable to answer
e.
emphasizes important ideas (formulas, techniques etc.)

232. f.
makes sure that concepts and skills are learned
5. Selection of teaching methods
The teacher uses teaching methods which are…
a. applicable to the subject
b. used in explaining ideas and problems
c. allowing students to investigate and examine
d. appropriate to every student in the class (no one is left behind)
e. intended to keep students learning
6. Quality of information and communication technology used
The teacher uses…
a. computers for making and printing materials for teaching
b. computers in teaching
c. the internet in teaching
d. computerized grading sheets (without mistakes)
e. overhead/LCD projector
B. Guidance Skills
1. Quality of Interaction with students
The teacher …
a. awakens, keeps and sustains students’ interests
(students are not bored)
b. appreciates students’ correct response (says very good, thank you)
c. doesn’t get angry when a student commits mistakes
d. helps students improve their work

233. e. talks of high but practical expectations from students
2. Quality of students’ activity
The teacher ensures that…
a. activities are practical, focused and applicable
b. students are developing independence and responsibility
c. activities are appropriate for students (not too hard but not too easy)
d. time is flexible for students’ activities
e. materials and facilities are proper for learning
C. Management Skills
1. Atmosphere in the Classroom
The teacher …
a. leads students to correct their misbehavior
b.
maintains a friendly classroom environment
(students don’t fear the teacher)
c. shows good behavior
d.
encourages respect, order and discipline
e.
uses positive discipline procedures
f.
implements school policies among students
g. develops students’ sense of control
h. is organized, punctual and manages class time well
2. Conduct and return of evaluation materials
The teacher …
a. checks test papers, quizzes, assignments/requirements carefully

234. b. returns corrected test papers, quizzes, requirements on time
c. conducts efficiently quizzes/ examinations to avoid cheating
D. Evaluation Skills
1. Quality of Appraisal questions
The teacher is able to…
a. ask questions to find out students’ understanding
b. ask questions that lead to the important points of the lesson
c. prepare very good questions covering the lessons taken in class
d. guide students in evaluating their own learning
(helps a student if he needs improvements or not)
e. provide feedback for specific area for improvement (write comments on
paper/talk to students privately)
2. Quality of assignment/ enrichment activities
The teacher provides and considers…
a. different activities and ways to measure the amount of learning
b. assignment/ enrichment activities that support learning
c. subject requirements that are practical and challenging
d. adequate time for students to complete assignments/ requirements
e. availability of materials in giving assignments and subject requirements
3. Quality of appraising students’ performance
The teacher …
a. uses the standard grading system of the school
b. grades/ scores students with accuracy and fairness
c. encourages students’ participation in creating rubrics

235. d. utilizes criteria/ rubrics in checking requirements

236. QUESTIONNAIRE FOR VALIDATION ON THE
INSTRUCTIONAL COMPETENCE CHECKLIST
NAME:_____________________POSITION:___________________DATE:______
Purpose: To validate questionnaire on instructional competence for
Secondary Mathematics Teachers in the City Division of San
Fernando
Direction: Please put a check (√) in the box that corresponds to your
judgment on validity of the instructional competence
questionnaire for the secondary mathematics teachers.
1-poor
2-slight
3-moderate
CRITERIA
4-high
5-very high
5 4 3 2 1

237. 1.Every sentence is easily understood
2.The sentences are grammatically correct
3.There are no errors in sentence construction
4.The directions are clear and easy to follow
5.The headings/titles of the different items are
Appropriate
6.The scales are suited to what they are supposed to
Measure
7.The questionnaires are representation of what they are
to measure
Other comments:
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________

238. QUESTIONNAIRE TO ESTABLISH CONTENT VALIDITY
OF THE MATHEMATICS COMPETENCE TEST
NAME:________________________________POSITION:__________________
EDUCATIONAL ATTAINMENT:_____________________________________
YEARS IN TEACHING MATHEMATICS:_____________________________
DIRECTION: Please place a check (√) on the appropriate point value to
evaluate the extent of content validity of the test indicate by the factors
below:
1-poor
2-slight
3-moderate 4-high
5-very high
Criteria
5 4 3 2 1
1. Are the items representative of the concepts being
measured?
2. Are the questions free from grammatical error?
3. Are the items perfectly clear and unambiguous? Is the
general frame and reference from which these are
asked, and from which the answers should be given
clear?
4. Are the test items stable, relatively deep-seated, wellconsidered, non-superficial, non-ephemeral, but
something which is typical of the subject area?
5. Do the test item pull? That is, can these be responded
to by a large enough proportion of examinees to permit
validity? Are the test items engaging enough to get
response with some depth and reality?
6. Are the options of reasonable range of variations?
7. Are the test items sufficiently inclusive? Are full scope
and intent of the test items so clearly indicated that
the test takers will not omit parts of the options
through lack of certainty as to what the test items
desired.

239. Other Comments
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
Lifted from the study of Dr. Ramos (2009) on Mathematics Education.

240. QUESTIONNAIRE TO ESTABLISH THE VALIDITY
OF THE TWO-PRONGED TRAINING PROGRAM
NAME:________________________________POSITION:__________________
EDUCATIONAL ATTAINMENT:_____________________________________
DIRECTION: Please place a check (√) on the appropriate point value to
evaluate the extent of validity of the two-pronged training program as
indicated by the factors below:
1-poor
2-slight
3-moderate 4-high
5-very high
Criteria
5 4 3 2
I.
Face
II.
Content
a. Functionality
b. Acceptability
c. Appropriateness
d. Timeliness
e. Implementability
f. Sustainability
Other Comments
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
1

241. CURRICULUM VITAE
PERSONAL DATA
Name:
Feljone Galima Ragma
Date of Birth:
July 31, 1986
Place of Birth:
San Isidro, Candon City, Ilocos Sur
Home Address:
San Isidro, Candon City, Ilocos Sur
e-mail Address:
feljrhone@yahoo.com
Civil status:
single
EDUCATIONAL ATTAINMENT
Pre-Elementary:
Elementary:
Secondary:
Tertiary:
UCCP
Candon City, Ilocos Sur
Graduated 1991
With honors
Candon South Central School
Candon City, Ilocos Sur
Santa Lucia Academy
Santa Lucia, Ilocos Sur
Graduated 1997
With honors
Graduated 2003
With honors
Saint Louis College
San Fernando City, La Union
Bachelor in
Secondary Education
Major in Mathematics
Graduated 2007
Cum Laude
Recognition Award
Graduate Studies: Saint Louis College
San Fernando City, La Union
Master of Arts in Education
Major in Mathematics
Graduated 2011
Cum Laude
Best in Research

242. BOARD EXAMINATION/ CIVIL SERVICE ELIGIBILITY

Licensure Examination for teachers (LET) 2007

P.D. 907 Civil Service Eligible
WORK EXPERIENCE. POSITIONS/SPECIAL ASSIGNMENTS
Saint Christopher Academy
Bangar, La Union
Classroom Teacher, 2007-2008
Christ the King College
San Fernando City, La Union
Classroom Teacher, 2008- present
Subject Area Coordinator, 2010- present
TRAININGS/SEMINAR-WORKSHOPS FACILITATED
Problem-Solving Techniques in Secondary Mathematics
Association of Private Schools
City of San Fernando, La Union
July, 2010
Seminar-Workshop on Creating Gradebooks through MS EXCEL
Christ the King College
City of San Fernando, La Union
2009
Seminar-Workshop on Creating Interactive Slides through MS
PowerPoint
Christ the King College
City of San Fernando, La Union
2009
Seminar-Workshop on Campus Journalism
Saint Christopher Academy
Bangar, La Union
2008

243. How to Love and Like Math
Saint Louis College
City of San Fernando, La Union
2007
CONFERENCES/ SEMINARS PARTICIPATED
Moving Forward with Backward Design: A Deeper look at UBD
Saint Louis University Laboratory Elementary School
January, 2011
Understanding and Planning for the 2010 SEC for Mathematics
Phoenix Hall, Quezon City
November, 2010
Training Program for Mathematics Teachers
University of the Cordilleras
September, 2010
Seminar on Yoga and Relaxation
Christ the King College
August, 2010
Critical Questions to Elicit Critical Thinking
Christ the King College
July, 2010
Seminar-Workshop on Homeroom Guidance and Counseling Techniques
Christ the King College
June, 2010
Utilizing and Interpreting CEM Test Data
University of Baguio
May, 2010
In-Service Training and Workshop on Curriculum Programs and
Teaching Strategies
Christ the King College
November, 2009
Seminar on Innovations in Teaching and Learning Approaches
Christ the King College

244. July, 2009
Understanding and Planning for the SEC
Phoenix Hall, Pangasinan
September, 2009
First Aid Program for Teachers
Christ the King College
June, 2008
PROFESSIONAL ORGANIZATION/ GROUPS
Professional Teachers‘ Organization
Mathematics Teachers‘ Association in Region I (MATARI)