Feljone g. ragma master's thesis

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This paper looked into the profile of math teachers, their content and instructional competence and the relationship existing between and among the profile, content and instructional competence

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Feljone g. ragma master's thesis

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 21. Table 21………………………………………………………… 112 Table 22………………………………………………………… 114 Table 23………………………………………………………… 116 Table 24………………………………………………………… 117-121 Table 25 ……………………………………………………….. 129-130
  22. 22. FIGURE Figure 1 Page The Research Paradigm ………………………………….. 18
  23. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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