1. BSMT-3 CHARLIE
GROUP 3
COMPARATIVE PERFORMANCE OF
BSMT AND BSMAR-E STUDENTS
IN MATH
JOSE P. BATUIGAS
ADVISER
JERRYBELLE G. BUNSAY JR.
RONE RYAN R. DESIERTO
RICHARD D. LUMANOG
MATT RYAN J. AGUIRRE
CRISTER S. HUERVA
JEROME MARIANITO J. GUILLERMO
EDUARDO P. JALLORINA JR.
JOFFER D. OCCIANAS

2. COMPARATIVE PERFORMANCE OF BSMT
AND BSMAR-E STUDENTS IN MATH
----------------------------------------------------------------------
A Research Study
Presented to the faculty of
VMA GLOBAL COLLEGE
------------------------------------------------------------------------
In partial fulfillment
Of the requirements
In Research
Submitted by:
Jerrybelle G. Bunsay Jr.
Rone Ryan R. Desierto
Richard D. Lumanog
Matt Ryan J. Aguirre
Crister S. Huerva
Jerome Marianito J. Guillermo
Eduardo P. Jallorina Jr.
Joffer D. Occianas
October 2011

3. Approval Sheet
This study entitled: “COMPARATIVE PERFORMANCE OF BSMT
AND BSMAR-E STUDENTS IN MATH” prepared and submitted by BSMT III
cadets, in partial fulfillment of the requirements for research subjects, has been
examined and approved for oral examination.
Jose P. Batuigas
Adviser
PANEL OF EXAMINERS
RAUL C. ALVARES, JR., Ed. D.
Chairman
GERARDO T. TAÑADA, Ph. D. EDWIN P. BENITEZ, MBA-HRM
Member Member
Accepted and approved in partial fulfillment of the requirements for the subject of
Research
CHRISTINE P. SALVADOR MAEd GERARDO T. TAÑADA, Ph. D.
Research Instructor Dean of Maritime Studies

4. ACKNOWLEDGEMENT
The researchers are truly grateful to the following personalities who extended
their effort, time and support all throughout the process of making this work a successful
one:
The Almighty God, for his power and blessings who showered upon us to
continue and accomplish what have started.
Our Mom and Dad, for their endless love and caring in every endeavor we
make.
VMA GLOBAL COLLEGE; Ms. Vivien Garasmia and Mrs. Fritzel
Tabaque, for the references we borrowed.
Mr. Jose P. Batuigas, our adviser for professional guidance and support to make
this study a reality.
Ms. Stella Reciado, Assistance Research Officer of VMA GLOBAL COLLEGE,
for being our mentor in this endeavor.
Our jurors in order to validate and correct our survey questionnaire.
Mrs. Christine D. Salvador, our subject instructor for the bodies of knowledge
you have radiated to us.
Thank you very much and God blessed
THE RESREARCHER

5. DEDICATION
This project is dedicated to God and to our Parents who have never failed to give us
financial and moral support, for giving all our need during the research and for
teaching us that even the largest task can be accomplished if it is than one step at a
time. And to our teachers who teach us well to accomplish this Research.
Mr. & Mrs. Bunsay
Mr. & Mrs. Desierto
Mr. & Mrs. Lumanog
Mr. & Mrs. Aguirre
Mr. & Mrs. Huerva
Mr. & Mrs. Guillermo
Mr. & Mrs. Jallorina
Mr. & Mrs. Occianas

6. Chapter 1
Introduction
Every culture on earth has developed some mathematics. In some cases, this
mathematics has spread from one culture to another. Now there is one predominant
international mathematics, and this mathematics has quite a history. It has roots in ancient
Egypt and Babylonia, then grew rapidly in ancient Greece. Mathematics written in ancient Greek
was translated into Arabic. About the same time some mathematics of India was translated into
Arabic. Later some of this mathematics was translated into Latin and became the mathematics
of Western Europe. Over a period of several hundred years, it became the mathematics of the
world.
There are other places in the world that developed significant mathematics, such as
China, southern India, and Japan, and they are interesting to study, but the mathematics of the
other regions have not had much influence on current international mathematics. There is, of
course, much mathematics being done these and other regions, but it is not the traditional math
of the regions, but international mathematics.
By the 20th century the edge of that unknown had receded to where only a few could
see. One was David Hilbert, a leading mathematician of the turn of the century. In 1900 he

7. addressed the By far, the most significant development in mathematics was giving it firm logical
foundations. This took place in ancient Greece in the centuries preceding Euclid. See Euclid’s
Elements. Logical foundations give mathematics more than just certainty they are a tool to
investigate the unknown.
International Congress of Mathematicians in Paris, and described 23 important mathematical
problems.
Mathematics continues to grow at a phenomenal rate. There is no end in sight, and the
application of mathematics to science becomes greater all the time.
Arguably the most famous theorem in all of mathematics, the Pythagorean Theorem has
an interesting history. Known to the Chinese and the Babylonians more than a millennium
before Pythagoras lived, it is a “natural” result that has captivated mankind for 3000 years.
More than 300 proofs are known today.
Exploring the concepts, ideas, and results of mathematics is a fascinating topic. On the
one hand some breakthroughs in mathematical thought we will study came as accidents, and on
the other hand as consequences of attempts to solve some great open problem. For example,
complex numbers arose in the study of the solution of cubic polynomials. At first distrusted and

8. ultimately rejected by their discoverers, Tartaglia and Cardano, complex numbers were
subsequently found to have monumental significance and applications
In this course you will see firsthand many of the results that have made what
mathematics is today and meet the mathematicians that created them. One particularly
interesting attribute of these “builders” of mathematical structure is how clear they were about
what to prove. Their results turn out to be just what is needed to establish other results
sometimes in an unrelated area. What is difficult to understand for the ordinary mathematics
students is just how brilliant these people were and how tenaciously they attacked problems.
The personality of the greatest mathematicians span the gamut from personable and friendly to
arrogant and rude. David E. Joyce (djoyce@clarku.edu)
In December 2009, the district administration reported that 171 pupils or 13.9% of the
district’s pupils received Special Education services.
The District engages in identification procedures to ensure that eligible students receive
an appropriate educational program consisting of special education and related services,
individualized to meet student needs. At no cost to the parents, these services are provided in
compliance with state and federal law; and are reasonably calculated to yield meaningful
educational benefit and student progress. To identify students who may be eligible for special
education, various screening activities are conducted on an ongoing basis. These screening
activities include: review of group-based data (cumulative records, enrollment records, health

9. records, report cards, ability and achievement test scores); hearing, vision, motor, and
speech/language screening; and review by the Instructional Support Team or Student Assistance
Team. When screening results suggest that the student may be eligible, the District seeks
parental consent to conduct a multidisciplinary evaluation. Parents who suspect their child is
eligible may verbally request a multidisciplinary evaluation.
In 2010, the state of Pennsylvania provided $1,026,815,000 for Special Education
services. The funds were distributed to districts based on a state policy which estimates that
16% of the district’s pupils are receiving special education services. This funding is in addition to
the state’s basic education per pupil funding, as well as, all other state and federal funding.
Line Mountain School District received a $723,333 supplement for special education
services in 2010.
The District Administration reported that 44 or 3.51% of its students were gifted in
2009. By law, the district must provide mentally gifted programs at all grade levels. The referral
process for a gifted evaluation can be initiated by teachers or parents by contacting the
student’s building principal and requesting an evaluation. All requests must be made in writing.
To be eligible for mentally gifted programs in Pennsylvania, a student must have a cognitive
ability of a least 130 as measured on a standardized ability test by a certified school
psychologist. Other factors that indicate giftedness will also be considered for eligibility.

10. The mathematics of general relativity are very complex. In Newton’s theories of
motions, and object’s mass and length remain constant as it changes speed, and the rate of
passage of time also remains unchanged. As a result, many problems in Newtonian mechanics
can be solved with algebra alone. In relativity, on the other hand, mass, length, and the passage
of time all change as an object’s speed approaches the speed of light. The additional variables
greatly complicates calculations of an object’s motion. As a result, relativity requires the use of
vectors, tensors, pseudotensors, curvilinear coordinates and many other complex mathematical
concepts.
In 2007, the district employed 91 teachers. The average teacher salary in the district was
$47,418 for 180 days worked. The district’s average teacher salary was the second highest of all
the Northumberland Country school districts in 2007.
The district administrative costs per pupil were $723.52 in 2008. The lowest
administrative cost per pupil in Pennsylvania was $398 per pupil. In 2007 the board approved a
five contract with David Campbell as superintendent. His initial salary was $88,000 plus an
extensive benefits package including life and health insurance. The Pennsylvania School Board
Association tracks salaries for Pennsylvania public school employees. It reports that in 2008 the
average superintendent salary in Pennsylvania was $122,165.

11. The district administration reported that per pupil spending in 2008 was $13,243 which
ranked 159th in the state 501 school districts.
In January 2010, the Pennsylvania Auditor General conducted a performance audit of
the district. Findings were reported to the administration and the school board, including
possible conflicts of interests in the actions of board members.
The district is funded by a combination of: a local occupation assessment tax 430%, a 1%
earned income tax. A property tax, a real estate transfer tax – 0.50%, per capita tax (678) $5, per
capita tax (Act 511) $5, coupled with substantial funding from the Commonwealth of
Pennsylvania and the federal government. Grants can provide an opportunity to supplement
school funding without raising local taxes. In the Commonwealth of Pennsylvania, pension and
Social Security income are exempted from state personal income tax and local earned income
tax regardless of the individuals wealth.
Math, as seen by many school aged children and even some adults, is considered boring
and useless. There are many areas in life where math can help you, I found out the hard way
and figured out that it was the simple stuff I had gotten stuck on and once that was in placee,
everything else came into view. You can see examples of math in use daily with all aspects of
building, finance industry, all areas of management, clerial and other customer facing jobs. Even
if all calculations are done for you wherever you go, you still have to balance a budget, save
money, pay bills no one is exempt from these tasks.

12. It’s common to hear children say things like “I’m” going to be the ‘big boss’ like my Dad,
I don’t need math.| I’d suggest showing that child every example of where math was required
to complete a task or project first at home and then if desired, in work decisions. When mom
planted that garden, there was math involved or when dad submitted that bid for a contract,
math again was heavily involved. Any way you look at it we use math daily. Those in
improverished situations can generally trace the causes back to choices they made. Choosing to
lease the newest car every year despite your company’s shaky situation in the current market
and then being shocked and dismayed when you got laid off, losing your car in the process.
Math as seen by many school aged children and even some aduts, is considered boring
and useless. There are many areas in life where math can help you, I found out the hard way
and figured out that it was the simple stuff I had gotten stuck on and once that was in place,
everything else came into view. You can see examples of math in use daily with all aspects of
building, finance industry, all areas of management, clerical and other customer facing jobs.
Even if all calculations are done for you wherever you go, you still have to balance a budget,
save money, pay bills, no one is exempt from these tasks.
‘Doing the math’ consistently and effectively in regards to your finances is crucial to
your daily life. Those who know this go father, faster, Knowing math and how to use it in daily
life will by no means protect you from all possible pitfalls but it does go a long way in minimizing
them.

13. Different levels of mathematics are staught at different ages and in somewhat different
sequences in different countries. Sometimes a class may be taught at an earlier age than typical
as a special or “honors” class. Elementary mathematics in most countries is taught in a similar
fashion, though there are differences. In the United States fractions are typically taught starting
from 1st grade, whereas in other countries they are usually taught later, since the metric system
does not require young children to be familiar with them. Most countries tend to cover fewer
topics in grater depth that in the United States. In most of the US, algebra, geometry and
analysis (pregreated depth than in the United States. In most of the US, algebra, geometry and
analysis (precalculus and calculus) are taught as separate courses in different years of high
school. Mathematics in most other countries (and in a few US states) is integrated, with topics
from all branches of mathematics studied every year. Students in many countries choose an
options or predefined course of study rather than choosing courses a la carte as in the United
States. Students in science-oriented curricula typically study differential calculus and
trigonometry at age 16-17 and integral calculus, complex numbers, analytic geometry,
exponential and logarithmic functions, and infinite series in their final year of secondary school.
You need math every day.
The Line Mountain School Board has provided the districts antibully policy online. All
Pennsylvania schools are required to have an anti-bullying policy incorporated into their Code of
Student Conduct. The policy must identify disciplinary actions for bullying and designate a
school staff person to receive complaints of bullying. The policy must be available on th schools
website and posted in every classroom. All Pennsylvania public schools must provide a copy of

14. its anti-bullying policy to the Office for Safe Schools every year, and shall review their policy
every three years. Additionally, the district must conduct an annual review of that policy with
students. The Center for Schools and Communities works in partnership with the Pennsylvania
Commission on Crime & Delinquency and the Pennsylvania Department of Education to assist
schools and communities as they research, select and implement bullying prevention programs
and initiatives.
Education standards relating to student safety and antiharassment programs are
described in the 10.3. Safety and Injury prevention in the Pennsylvania Academic Standards for
Health, Safety and Physical Education. Wikipedia, the free encyclopedia.

15. GENERAL OBJECTIVE:
This study seeks to establish the comparative performance in math between BSMT
and BSMAR-E of the VMA GLOBAL COLLEGE this first Semester of Academic
Year 2011-2012.
Specific Objective:
Specifically the study aims to answer the following question.
1. What is the profile of the BSMT and BSMAR-E Students in MATH.
1.a. Age
1.b. High school attainment (private or public)
2. To know the capacity of BSMT and BSMAR-E Students in Math.
2.a. Fraction and Decimal
2.b. Algebra
2.c. Trigometry
3. Is there significant difference in the performance of BSMT and BSMAR-E
in Math?

16. Hypothesis
The opinions of the correspondents do not differ significantly as regards to
the factors that affect enrolment decline in Marine Engineering compared to
Marine Transportation. The effects on these factors in the overall condition of
maritime education and maritime industry in the country are negligible.
THEORITICAL FRAMEWORK
Mathematics relies on both logic and creativity, and it is pursued both for a
variety of practical purposes and for its intrinsic interest. For some people, and not only
professional mathematicians, the essence of mathematics lies in its beauty and its
intellectual challenge. For others, including many scientists and engineers, the chief value
of mathematics is how it applies to their own work. Because mathematics plays such a
central role in modern culture, some basic understanding of the nature of mathematics is
requisite for scientific literacy. To achieve this, students need to perceive mathematics as
part of the scientific endeavor, comprehend the nature of mathematical thinking, and
become familiar with key mathematical ideas and skills.
This chapter focuses on mathematics as part of the scientific endeavor and then on
mathematics as a process, or way of thinking. Recommendations related to mathematical
ideas are presented in Chapter 9, The Mathematical World, and those on mathematical
skills are included in Chapter 12, Habits of Mind.

17. Mathematics is the science of patterns and relationships. As a theoretical discipline,
mathematics explores the possible relationships among abstractions without concern for
whether those abstractions have counterparts in the real world. The abstractions can be
anything from strings of numbers to geometric figures to sets of equations. In addressing,
say, "Does the interval between prime numbers form a pattern?" as a theoretical question,
mathematicians are interested only in finding a pattern or proving that there is none, but
not in what use such knowledge might have. In deriving, for instance, an expression for
the change in the surface area of any regular solid as its volume approaches zero,
mathematicians have no interest in any correspondence between geometric solids and
physical objects in the real world.
A central line of investigation in theoretical mathematics is identifying in each field of
study a small set of basic ideas and rules from which all other interesting ideas and rules
in that field can be logically deduced. Mathematicians, like other scientists, are
particularly pleased when previously unrelated parts of mathematics are found to be
derivable from one another, or from some more general theory. Part of the sense of
beauty that many people have perceived in mathematics lies not in finding the greatest
elaborateness or complexity but on the contrary, in finding the greatest economy and
simplicity of representation and proof. As mathematics has progressed, more and more
relationships have been found between parts of it that have been developed separately—
for example, between the symbolic representations of algebra and the spatial
representations of geometry. These cross-connections enable insights to be developed
into the various parts; together, they strengthen belief in the correctness and underlying
unity of the whole structure.

18. Mathematics is also an applied science. Many mathematicians focus their attention on
solving problems that originate in the world of experience. They too search for patterns
and relationships, and in the process they use techniques that are similar to those used in
doing purely theoretical mathematics. The difference is largely one of intent. In contrast
to theoretical mathematicians, applied mathematicians, in the examples given above,
might study the interval pattern of prime numbers to develop a new system for coding
numerical information, rather than as an abstract problem. Or they might tackle the
area/volume problem as a step in producing a model for the study of crystal behavior.
The results of theoretical and applied mathematics often influence each other. The
discoveries of theoretical mathematicians frequently turn out—sometimes decades
later—to have unanticipated practical value. Studies on the mathematical properties of
random events, for example, led to knowledge that later made it possible to improve the
design of experiments in the social and natural sciences. Conversely, in trying to solve
the problem of billing long-distance telephone users fairly, mathematicians made
fundamental discoveries about the mathematics of complex networks. Theoretical
mathematics, unlike the other sciences, is not constrained by the real world, but in the
long run it contributes to a better understanding of that
world.(http://www.project2061.org/publications/sfaa/online/chap2.htm)
Conceptual Framework
In order to accomplish the objective of this study is to set forth to identify the
following variables. The ideas were established to give the direction or the research in the

19. choices of accumulated data. This conceptual framework has to set guide to identify the
comparative performance of BSMT and BS-Mar E Student’s and each respondents.
Students have widely knowledge in using the different kinds of formula in every
problems they encounter. Each of these variables was guide us to present the following
choices that correspond the respondents.
The research has identify in term of course, section, and year level is interrelated
with their comparative performance in math, on board calculations, conversation and
theoretical knowledge and trainings. Through this, the researchers were set up a
performance level program to identify how these undertaking works to the BSMT and BS
Mar-E of the VMA Global College.

20. Figure 1. Schematic diagram of performance level of BSMT & BSMAR-E in Math.
Students of the VMA Gloabal College
BSMT BSMAR-E
PROFILE:
PERFORMANCE:
1.Age
1.Fraction & Decimal
2.High School
2.Algebraic expression
attainment
3.Trigometry
Performance Level

21. Scope and Limitation
The research study focuses on the comparative performance between the BSMT
and BSMAR-E Students in Math. There are three years level in the BSMT and three year
level in the BSMAR-E Students but the researcher focus on the BSMT 3 and BSMAR-E
3. Which the third year of BSMT 3 and BSMAR-E 3 is divided in sections. There are
four sections in BSMT and three sections BSMAR-E the subjects understudied where the
third year level which encounter many Math problem and navigational calculation which
they use on board ship. But the researcher focus in section Bravo only. The study was
conduct on the first semester of the academic year 2011-2012.
The researcher select the third year level of BSMT and BSMAR-E Students of the
VMA GLOBAL COLLEGE being the nearest and easiest school to address the problem,
the researchers encounter regarding time constrained, financial incapability and distance
of the locality. These have considerably improve the speedy conduct and development of
the study.
Selecting VMA GLOBAL COLLGE as the study ground help the researchers to
minimize the expenses in money, time, and effort.
Definition of terms
The following were defined for the clearer understanding of the study.

22. Comparative. One that compares with another. (Webster third new international
dictionary).
Performance. The act or process carrying something, the execution of an action
(Webster third new international dictionary).
In this study, it is refer to the comparative performance of the BSMT3 and
BSMAR-E3.
Math. The science of expressing and studying the relationship between quantities and
magnitude as represented by numbers and symbols (The new Webster dictionary of the
English language).
In this study, it refers to the academic performance in math.
Profile. This terms is defined as the biographical sketch of the person(Webster universal
dictionary and thesaurus.
In this study refers to the biographical sketch of BSMT3 and BSMAR-E3
cadets who are subject respondent of the study. It include there biographical sketch
is there personal profile term of age, and high school attainment.
Year Level . It is refers to the level of the students (Webster dictionary).
In this study, year level refers to the BSMT3 and BSMAR-E3 cadets
academic performance on the first semester of school year 2011-2012.
Course . It is refers to a prescribe number of lesson, and lecture in educational
curriculum. (Wikipedia, the free encyclopedia).

23. Fraction and Decimal . It refer to the separation or division of number and to a number
express in the scale of tens (Webster third international dictionary.
Volume and Pressure . It is refer to the dealing with or involving large quantities in the
burden of physical or mental distress (The new Webster dictionary of the English
language).
Conversation . It refers to a converting or being convert
In the study refer to the method of teaching and how to solve the problem,
deliver and discuss to compare the performance of BSMT3 and BSMAR-E3
in Math.
Significance of the study
The finding of the study may provide significance information which may be value to
the:
School – that they had implemented further the basic math, conversation, and the
navigational problem and was providing more undertaking to their students concerning
the great importance in math.
Students – That they were be aware on the importance in math especially those who are
engaged in maritime field and would guide them to the practice in math not only in

24. school but also in their everyday life and be able to apply that knowledge in their future
profession.
Researchers – That give information where there the BSMT3 and BSMAR-E3 have the
essential knowledge pertaining to the basic math problem and calculation that are seeing
required and were provide them a between understanding and supplement on how they
can solve nautical seamanship and navigational problem. Thought this study it had been
promote in the Maritime and Allied Industry.
Faculty – That give and examine those student and grade their accordingly on their
performance. Which they are rank the students and they well know what is capacity and
the performance of the student on some particular of the subject.
Curriculum – Development that record and gather those information of what students
can reach and they gather these percentage of those students that good in math and need
more practice for their performance. VMA GLOBAL COLLEGE, that helps the student
to build the future and have a successful life someday, that give a better learning and
trained the student and support those shipping companies a well trained student.
Maritime Industry – That accept intelligent and well trained that has capacity to lead
and become an officer on board the vessel.
Parents – That give as everything we need and being supported in everything we do and
be proud of what their son’s know about what they learned.