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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 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

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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

ultimately rejected by their discoverers, Tartaglia and Cardano, complex numbers were

subsequently found to have monumental significance and applications

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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 ([email protected])

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

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

4

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.

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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.

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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

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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.

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.

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‘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.

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.

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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

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.

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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. Age1.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?

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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.

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Theoretical 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.

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

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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.

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.

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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 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.

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Figure 1. Schematic diagram of performance level of BSMT & BSMAR-E in Math

Students of the VMA Gloabal College

BSMT

PROFILE: 1.Age

2.High School attainment

BSMar-E

PERFORMANCE: 1.Fraction &

Decimal 2.Algebraic

expression 3.Trigometry

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

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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.

Comparative. One that compares with another. (Webster third new international dictionary).

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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).

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.

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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 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.

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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.

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Chapter 2

Review related literature

Foreign literature

College math courses are very different than the ones in high school. They usually meet less

often and move faster, typically covering material at about twice as fast as a high school course.

College professors expect students to keep up. They cannot wait for students that fall behind.

In many cases, it is actually assumed that a few of the students will need to repeat the course.

Remember, it isn't fair to hold back the rest of the class when some students have not kept up or

sought out help when they need it. Students that have kept up have paid to be in the class.

Most college math professors do not grade homework - students are expected to "practice" math

skills and come to class prepared to move on. When a student has questions or problems; they

are expected to get help, often, outside of class. Students are responsible for their learning, not

the college professor. The college math class has tests and quizzes spaced farther apart.

Each "checkpoint" probably tests on a larger amount of material.

Students can expect to spend more time doing homework in a college math class (even when that

homework is not graded). In general, it is expected that a student spend 2 hours of homework for

every hour spent in class - and that might not even be enough time for some. In most cases,

college math classes are designed to prepare students for higher-level math, science, and a

variety of other important courses.

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We all need help at some point - especially in math classes. Because college math classes are so

different from high school classes, many students, especially freshman or return adults, will find

that they need help. PLEASE GET HELP JUST AS SOON AS YOU THINK YOU NEED IT!

Don't wait until you fail a quiz or exam. Instructors appreciate it when students can recognize

problems BEFORE they are behind - it make life easier for everybody. Asking questions is

important - there is no such thing as a "dumb" question, but some questions are more helpful

than others. When working with others, try to ask questions that will allow them to see where

you need help.

"I don't understand this section," is better than no question at all, but it is hard to see where the

problem is. A more meaningful question might be, "I don't see why f(x+h) doesn't equal f(x) +

f(h)." If you ask this question to someone that understands math, for example, they will

immediately see that the problem is a misunderstanding about function notation. When doing

homework, it can help to create a list of questions to ask the professor in class or during office

hours, or to another person.

Creating a study-group for a math class is a great way to meet people, get involved on campus,

and make a math class more meaningful and fun. Classmates, friends, or students in other

sections can often work together to the benefit of all.

Most campuses have "Academic Support" to provide assistance to students that are ready to get

help and take responsibility for doing so. Often, one-on-one tutoring or study groups are

available - on some campuses, at no cost. Take advantage of all the resources available.

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Today, many high-quality resources are online - virtually any math topic is supported online.

Often, there are examples, tutorials, and alternative presentations. They represent a great way to

help and build information and technology literacy skills.

Math is learned by doing problems. Do the homework. The problems help you learn the formulas

and techniques you do need to know, as well as improve your problem-solving prowess.

A word of warning: Each class builds on the previous ones, all semester long. You must keep up

with the Instructor: attend class, read the text, and do homework every day. Falling a day behind

puts you at a disadvantage. Falling a week behind puts you in deep trouble.

A word of encouragement: Each class builds on the previous ones, all semester long. You're

always reviewing previous material as you do new material. Many of the ideas hang together.

Identifying and learning the key concepts means you don't have to memorize as much.

Math is a skill. To develop that skill you must practice. Do your homework in a quiet place,

similar to the classroom if possible. Do not spend "hours" on one problem. If you cannot solve a

problem, look for a similar problem in your notes or your text. If you still cannot solve the

problem, skip it and work on other problems. Try the problem later. Many times you will come

up with an idea after you have done something else for a while. If you still cannot solve the

problem, get some help.

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Local literature

The Institute of Mathematics is the leading institution for mathematics research and

education in the Philippines. Since 1998, it has been recognized by the Philippine Commission

on Higher Education as a Center of Excellence. It is home to the country's best and more

promising researchers in mathematics.

Apart from offering an excellent BS Mathematics program, the Institute also grants the

following graduate degrees: MA Mathematics, Professional Master's in Applied Mathematics,

MS Applied Mathematics, MS Mathematics and PhD Mathematics.

Formerly known as the Department of Mathematics, the Institute is the largest institute in

the University of the Philippines System, with about 100 full-time faculty members supported by

9 administrative and computer staff. It nurtures about 300 undergraduate and 200 graduate

students, and handles all the mathematics courses of some 5000 undergraduate students in the

whole UP Diliman campus.

The Mathematical Society of the Philippines held its 2011 annual convention on 20-21

May 2011 (Fri-Sat). The 2011 Convention was hosted by the University of Santo Tomas, on the

occasion of its quadricentennial anniversary. On this occasion, the MSP celebrated its 38 th year

as the country’s largest professional organization dedicated to the promotion of mathematics and

mathematics education.

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Researchers and educators in all areas of pure and applied mathematics, mathematics

education, computing, statistics and other related areas presented short papers for oral or poster

presentation during the convention. This convention was fully endorsed by the Commission on

Higher Education (CHED).

Plenary talks were given by Elvira de Lara-Tuprio (Ateneo de Manila University),

Manuel Joseph Loquias (University of the Philippines), Frank Morgan (Williams College, MA,

USA), Akihiro Munemasa (Tohoku University, Japan), and Edwin Tecaro (University of

Houston).

April 10, 2008 marks a historic event for Malayan Colleges Laguna (MCL), a wholly-

owned subsidiary of Mapua Institute of Technology; and Philippine Transmarine Carriers, Inc.,

(PTC), one of the country’s largest crew management companies, as they launch the MAPUA-

PTC COLLEGE OF MARITIME EDUCATION AND TRAINING.

The partnership between these two institutions, both leaders in their respective fields,

represents an industry-academic linkage which aims to further develop globally competitive

Filipino maritime professionals, equipped with a solid background in Marine

Transportation and Marine Engineering and quality hands-on training and instruction to meet

industry standards of competence. With Mapua’s long history of excellence in the fields of

Mathematics, Science and Engineering and PTC’s 29 years of experience in crew management

and training, the MAPUA-PTC College of Maritime Education and Training is envisioned to

ensure that the Philippines continues to maintain its position as the leading provider of quality

maritime manpower worldwide. This is especially crucial in light of the worldwide shortage in

marine officers, projected to reach as many as 27,000 in 2015.

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The College aims to provide world-class instruction and training. Aside from a full

Marine Transportation and Marine Engineering curriculum which will be offered at the Malayan

College campus in Cabuyao, Laguna, the students will undergo hands-on training at PTC’s state-

of the-art training facility, PHILCAMSAT, which provides a wide range of training courses

including exposure to bridge, engine and cargo handling simulators, international shipping

environments, and technology-based instruction.

At the formal launching of the Mapua-PTC College of Maritime Education and Training,

MCL was represented by Dr. Reynaldo B. Vea, President of Malayan Colleges Laguna and

Mapua Institute of Technology, and PTC by Mr. Carlos C. Salinas, its Chairman and Chief

Executive Officer. The ceremony took place at the PTC Office in First Maritime Place, Makati

City.

According to Dr. Reynaldo B. Vea, “This linkage between PTC and Mapua, via our

subsidiary Malayan Colleges Laguna, is undoubtedly the most substantial linkage we have

forged with a private company in the country, in the whole history of our institution. This is

going to help a lot of Filipinos attain a higher level of professionalism in their maritime careers,

which translates to greater job opportunities.”

Carlos C. Salinas also lauded the benefits of being allies with Mapua. “We have finally

found an institution that will provide the strong fundamentals in math, science and physics

required for the development of the global Filipino maritime professional. This partnership

allows our company to be associated with the finest engineering school in the country, and

allows us to be a complete crew management and development company, involved with the

molding of quality maritime manpower,” he said.

26

Foreign study

Available data on U.S. student performance in mathematics and science present a mixed picture.

Although data show some overall gains in achievement, most students still perform below levels

considered proficient or advanced by a national panel of experts. Furthermore, sometimes

substantial achievement gaps persist between various U.S. student subpopulations, and U.S.

students continue to do poorly in international comparisons, particularly in the higher grades.

This section describes long-term trends based on curriculum frameworks developed in the late

1960s, recent trends based on frameworks aligned more closely with current standards, and the

performance of U.S. students relative to their peers in other countries.

The National Assessment of Educational Progress (NAEP), also known as "The Nation's Report

Card," has charted U.S. student performance for the past 3 decades (Campbell, Hombo, and

Mazzeo 2000) and is the only nationally representative, continuing assessment of what students

know and can do in a variety of academic subjects, including reading, writing, history, civics,

mathematics, and science. NAEP consists of three separate testing programs. The "long-term

trend" assessment of 9-, 13-, and 17-year-olds has remained substantially the same since it was

first given in mathematics in 1973 and in science in 1969, and it thereby provides a good basis

for analyzing achievement trends. [More detailed explanations of the NAEP long-term trend

study are available in Science and Engineering Indicators — 2002 (National Science Board

2002) and at http://www.nces.ed.gov/naep3/mathematics/trends.asp.] A second testing program,

the "National" or main NAEP, is based on more contemporary standards of what students should

know and be able to do in a subject. It assesses students in grades 4, 8, and 12. A third program,

"state" NAEP, is similar to national NAEP, but involves representative samples of students from

http://www.nsf.gov/statistics/seind04/c1/c1r.htm#nsb2002

http://www.nsf.gov/statistics/seind04/c1/c1r.htm#nsb2002

http://www.nsf.gov/statistics/seind04/c1/c1r.htm#campbell2000


27

participating states. The NAEP data summarized here come from the long-term trend assessment

and the national NAEP. Chapter 8 covers the considerable variation by state.

The most recent NAEP long-term trend assessment took place in 1999. Because the 1999 NAEP

data have already been reported widely (including in the 2002 version of this report), this chapter

only summarizes the main findings. The NAEP trend assessment shows that student performance

in mathematics improved overall from 1973 to 1999 for 9-, 13-, and 17-year-olds, although not at

a consistent rate across the 3 decades (Campbell, Hombo, and Mazzeo 2000) (figure 1-1). In

general, declines occurred in the 1970s, followed by increases in the 1980s and early 1990s and

relative stability since that time. The average performance of 9-year-olds held steady in the

1970s, increased from 1982 to 1990, and showed additional modest increases after that. For 13-

year-olds, average scores improved from 1978 to 1982 with additional improvements in the

1990s. The average performance of 17-year-olds dropped from 1973 to 1982, rose from 1982 to

1992, and has since remained about the same, resulting in an overall gain from 1973 to 1999.

Average student performance in science also improved from the early 1970s to 1999 for 9- and

13-year-olds, although again, not consistently over the 3 decades. Achievement declined in the

1970s and increased in the 1980s and early 1990s, holding relatively stable since that time. By

1999, increases had overcome the declines of the 1970s. In 1999, 9-year-olds' average

performance was higher than in 1970. Among 13-year-olds, average performance in 1999 was

higher than in 1973 and essentially the same as in 1970. By 1999, 17-year-olds had not recouped

decreases in average scores that took place during the 1970s and early 1980s. This resulted in

lower performance in 1999 than in 1969 when NAEP first assessed 17-year-olds in science.

http://www.nsf.gov/statistics/seind04/c1/fig01-01.htm


28

The NCLB Act requires every student, regardless of poverty level, sex, race, ethnicity, disability

status, or English proficiency, to meet challenging standards in mathematics and science.

Patterns in the NAEP long-term trend data can show whether the nation's school systems are

providing similar learning outcomes for all students and whether performance gaps between

different groups of students have narrowed, remained steady, or grown.

Thus far, this section has presented NAEP results based on the long-term trend

assessments, which use the same items each time. The next analysis uses data from the national

NAEP program, which updates instruments to measure the performance of students based on

more current standards. These assessments are based on frameworks developed through a

national consensus process involving educators, policymakers, assessment and curriculum

experts, and representatives of the public, then approved by the National Assessment Governing

Board (NAGB).

NAEP first developed a mathematics framework in 1990, then refined it in 1996 (NCES

2001c). It contains five broad content strands (number sense, properties, and operations;

measurement; geometry and spatial sense; data analysis, statistics, and probability; and algebra

and functions). The assessment also tests mathematics abilities (conceptual understanding,

procedural knowledge, and problem solving) and mathematical power (reasoning, connections,

and communication). Along with multiple-choice questions, assessments include constructed-

response questions that require students to provide answers to computation problems or describe

solutions in sentence form.

NAEP developed the science framework in 1991 and used it in the 1996 and 2000

assessments (NCES 2003c). It includes a content dimension divided into three major fields of

29

science (earth, life, and physical) and a cognitive dimension covering conceptual understanding,

scientific investigation, and practical reasoning. The science assessment also relies on both

multiple-choice and constructed-response test questions. A subsample of students in each school

also conducts a hands-on task and answer questions related to that task.

Student performance on the national NAEP is classified according to three achievement

levels developed by NAGB that are based on judgments about what students should know and be

able to do. The basic level represents partial mastery of the knowledge and skills needed to

perform proficient work at each grade level. The proficient level represents solid academic

performance at grade level and the advanced level signifies superior performance. Disagreement

exists as to whether NAEP has appropriately defined these levels, but they do provide a useful

benchmark for examining recent changes in achievement.

Local study

Filipinos in general have never been noted for mathematical ability. International

surveys (including the Trends in Mathematics and Science Study, TIMSS 2004) have placed the

country near the bottom; and local studies similarly reflect such performance - by students and

teachers alike. In 2004 the Department of Education (DepEd) launched a bridge program to

address basic deficiencies in elementary math, among others (less than 10% of elementary

graduates scored 75%). Several years ago, the Mathematics Teachers Association of the

Philippines (MTAP) tested pre-service teachers in arithmetic, algebra, and geometry, and

discovered that the overall mean for high school teachers was 16 out of 50 (questions), while that

for their elementary school counterpart was only 10 (Lee, 1993).

30

The Philippines is a country of paradox. We are vibrant part of Asia, yet our sensibilities

have been heavily influenced by the West, especially the US. We pride ourselves on being the

only predominantly Catholic country in the continent, and on speaking English well enough to

give us an edge in overseas professional employment (many teachers and nurses in the West are

Filipino). Our pro-West stance is usually thought to be due to lengthy colonization by Spain and

the US, and archival documents reveal this to be quite likely in the case of education.

At the of the 19th century, the revolutionary Filomeno Bautista noted that Filipinos were

conquered "not by American guns, but by American schools" and that "boxes of books were the

real peace makers" (Gates, 1973, p. 277). Certainly these boxes contained various math primers,

and in 1906, the most prolific textbook writer in the US, George Wentworth, authored A First

Book in Arithmetic for the Philippine Islands. When native-born authors started producing their

own books in the 1920s, they were hugely influenced by their US counterparts. In 1925, a

committee of educators headed by Prof. Paul Monroe of Columbia University tested 32, 000

children, interviewed teachers, and observed classrooms. They reported that primary arithmetic

teaching was done well, and that Filipino students performed at par with their US peers. (Only

when the English language became more difficult to understand in higher texts did Filipinos lag

behind.) Monroe also late reported that of the many countries he had visited, the advances he saw

in the Philippines were the most impressive (Pecson & Racelis, 1959).

However, even with a US-style education system still in place, at the start of this

millennium, Filipinos seem to have lost their edge. In the TIMSS, even though the US has mid-

range scores, other Asian countries such as Singapore and Chinese Taipei occupy the top ranks.

Much research has been conducted concerning the factors behind our poor performance, such as

31

society (Abasolo-Ababa, 2002), teacher education (Ibe, 1995), learning styles (Arellano, 1997),

curriculum (Ulep, 2000), and ways of remediation.

In recent decades, several groups in the Philippines have aimed to develop in the youth a

balance between foundational understanding and higher-level creativity. Established in 1989 at

the Ateneo de Manila University under the leadership of Dr. Jose A. Marasigan, PEM primarily

trains gifted students for the most prestigious fest - the International Mathematical Olympiad

(IMO). PEM invites to be co-trainers, and screens potential IMO participants from all over the

country. Patterned after Germany, the two-pronged screening process divides participants from

the National Capital Region (NCR) from those from the rest of the country.

For the NCR, at the start of each school year in June, challenging questions are

formulated and distributed through the DepEd network. Solutions are submitted by September,

and PEM invites the top 30 scorers for each level to undergo a training program from - October

till July of the following year. Members of the Philippine team to the IMO are selected from the

participants, who are rigorously exposed to number theory, combinatorics, functions, solid

geometry, advanced algebra - all beyond the scope of the average Filipino secondary math

curriculum, which centers on elementary algebra, geometry, trigonometry, and statistics. Since

1988, approximately 20 Filipino students have garnered silver/bronze medals, or honorable

mention in various IMOs, and most of the winners have taken advantage of scholarship offers by

universities abroad. For students in the 15 other regions of the country, the route to the IMO is

just as challenging.

They have to be winners in the premier local math competition: the PMO. Under Prof.

Josefina Fonacier of the University of the Philippines, Diliman, the first PMO was conducted in

32

1984, and since then it is held every two years, with the Department of Science and Technology

as major sponsor.

The PMO also promotes professional growth of teachers, with expert coaches from the

NCR conducting free seminars of teachers, with expert coaches from the NCR conducting free

seminars for teachers in other areas. These sessions, which have become very popular, deal with

specific problem-solving skills and content.

Advanced classes in problem solving for the tertiary level are not known, so in the

summer session of April to May 2001, we decided to teach high-level non-routine problem

solving to selected college science majors, with the help of Paul Zeitz' The Art and Craft of

Problem Solving (1999).

Encouraged by the positive response of the students (as shown by class participation and

reflection papers), we decided to continue the course. We authored a case study, providing

concrete data regarding factors and effects surrounding structured problem solving (Nebres &

Lee-Chua, 2001). Year level, gender, course major, and high school background do not

significantly affect subsequent problem solving performance but beliefs and attitudes do.

According to the students, the techniques and mind set acquired are perceived to be useful in

other classes and in real life. They also feel a sense of satisfaction, especially after having solved

problems they had grappled with for so long; and learn to appreciate the beauty of math,

especially the elegance of proofs and the connectedness of seemingly disparate ideas. They also

feel that learning under master teachers enables them to fully understand the abstract concepts

involved.

33

After taking this course, some college volunteers train gifted grade school and high

school students themselves, in an attempt to develop the problem-solving culture early on. The

ability and knowledge they acquire are showcased in the Ateneo Math Olympiad, now on its

third year.

34

Chapter 3

METHODOLOGY

In this chapter, the researcher present the research method used, the respondents of the

study, the date gathering instruments and statistical tools for date analysis.

Research Design

This study aimed to determined the performance level BSMT 3 and BSMAR-E 3

students math of VMA Global College this 1st semester of A.Y. 2011-2012.

To meet the objective of this study the descriptive research design will be used to

describe the nature of situation or a given state of affairs in terms of specified aspects or factors

or characteristic of individual or group or physical environment or conditions (David 2002).

With this study the researcher want to know if there is a significant difference to the performance

level between the BSMT 3 to BSMAR-E 3 students in math of the VMA Global College for the

first semester of 2011-2012. Likewise the study would give an insights to the faculty in the

administration to deliver quality education.

Subject /Respondents

The respondents of the study are the third year students of the VMA Global College that

will be given self-administered questionnaires.

35

The surveyed total population is 400. However, the respondents are selected in terms of

section. The total number of section of which is 7 (as the present School Year 2011-2012) the

respondent for section are selected randomly to present their section as a group; the researcher

will have to survey the respondents.

Total Population - 400

Total number of section - 7

No. of Male = 400

Using the Lynch formula, the researcher got the number of sample subject to present to

population on which is based on any statement about the population from which it is drawn.

n=NZ 2 p(1-p)

Ne2 +Z2p(1-p)

Where:

n = Of sample subject

N = Total number of section

e = Margin Error (5% or 0.05%)

z = Confidence level value

P = Largest possible portion, usually 50% or 0.5

36

Validity of Research Instrument

To test the validity of the instruments, content validity will be used. The instrument will

be shown to 3 jurors for them to go over the items to job the appropriateness and to make

accommodation in order to improve the research instrument. Each jurors was requested to

analyze and rate the questionnaire based on criteria presented by Carter V. Good and Douglas B.

Scates. Validation for questionnaire rated 3.7 which interpreted “Very Good”.

Reliability of Research Instrument

To test the reliability of the questionnaire, the Z – test method will be used. The

procedure involves two values (odd items and even items) scoring of the 1st half and then the 2nd

half in the instrument separately each person and then calculating a correlation coefficient for the

two sets of score. The questionnaire will be given to 20 respondents with similar characteristics

to the actual respondents of the study.

After calculating the test on desired date, the retest will soon be conducted after the week.

Data Gathering Procedure

The researcher conducted an interview schedule where the interviewer prepared two sets

off questionnaire, and carefully prepared information from the respondents of the study.

37

Statistical Tools and Analytical Scheme

In accordance with the objectives of the study and the statement of the problem, the data

that the researcher will gather will be subjected to tabulation, statistical analysis and

interpretation. The data that will be obtain will be computed and analyze using the statistical

tools to answer the problem of the study.

For problem no. 1 we use percentage to determine the level of performance of the BSMT and

BSMAR-E in basic math of the VMA GLOBAL COLLGE in terms of their age, and last high

school attainment (public school or private school). For problem no. 2 we use the main to know

the capacity of BSMT and BSMAR-E in basic math.

For problem no. 3 is to determine if there is significant deference between the academic

performance of BSMT and BSMAR-E in basic math we used.

r=∑ xy−¿¿¿

∑ = mean

r = roman r

x = score

y = statistic score

38

BIBLIOGRAPHY

A. BOOKS

Ardales, Venacio B. ( 2001 ). Basic Concepts and Methods

VMA Global College Library

David, Fely (2002) Understanding and Doing Research Work:

a handbook for beginners.

VMA Global College Library.

Oxford Popular School Dictionary. Oxford University Press.

Angeles , Ma. Felisa D. (2005) Simplified Approach to Statistics

VMA Global College Library.

William L. Hart (1964) College algebra 4th Edition

39

B. Webliography

www.yahoo.com

www.google.com

www. Teaching college math.com

www.clubtnt.org/my_collegian/college_math.htm

www.math society phil.org

www.ptc .com.ph

www.nsf .gov/statistics

www.fuse.org.ph

http://www.math.upd.edu.ph/

http://www.ptc.com.ph/news_display2.php?articleid=27

http://www.nsf.gov/statistics/seind04/c1/c1s1.htm

http://www.mathsocietyphil.org/

http://www.mathsocietyphil.org/

http://www.nsf.gov/statistics/seind04/c1/c1s1.htm

http://www.ptc.com.ph/news_display2.php?articleid=27

http://www.math.upd.edu.ph/

http://www.fuse.org.ph/

http://www.math/

http://www.clubtnt.org/my_collegian/college_math.htm

http://www.google.com/

http://www.yahoo.com/

40

Appendix A Data Gathering Instrument

QUESTIONNAIRE ON COMPARATIVE PERFORMACE OF

BSMT AND BSmar-E IN BASIC MATH

We, the Graduation students of the VMA Global College are currently conducting a

research on “COMPARATIVE PERFORMANCE OF BSMT AND BSMAR-E MATH” as

a part of our requirements in the research subject rest assured that your opinions and

response on this questionnaire will be treated with almost confidentially.

Part 1 (Respondents Profile)

Course: ________ BSMT ________ BSMar-E

Age: ________

Part 2 (Fraction to Decimal)

Instruction: Convert the following fraction into decimal form. Encircle the latter of the

correct answer.

1.) 23

a) 0.667 b) 1.541 c) 1.00 d) 1.11

2) 138

a) 1.411 b) 1.040 c) 1.380 d.) 1.0375

41

3) 1339

a) 0.4 b) 0.333 c) 0.34 d) 0.413

4)357

a) 7.35 b) 5.37 c) 5 d) 3.75

5) 1 23

+2 16

a) 3.333 b) 3.88 c) 4 d) 3.833

6) 23

+ 12

a) 1.167 b) 1.611 c) 1.600 d) 1.566

7) 38

+12

a) 0.578 b) 0.785 c) 0.758 d) 0.875

8) 23

100

a) 23 b) 0.23 c) 2.3 d) 0.023

91003.25

a) 13 b) 15 c) 14 d) 16

42

10. 13617

a) 8 b) 9 c) 6 d) 10

PART 3 (Algebraic Expression)

Instruction: Find the value of X. Encircle the letter of the correct answer.

1) 8x – 24 = 0

a. 3 b. 4 c. 2 d. 5

2)24x – 8x = 4

a. 32

b. 14

c. 12

d. 513

3)2x-25= -8x

a. 42

b. 62

c. 52

d. 32

4) (-2x) – 38 (-5x) = 11

a. 453

b. 643

c. 463

d. 493

5)40 + 10 = 5x

a. 8 b. 9 c. 10 d. 5

43

6) -30 -6x = 60

a. -3 b. -15 c. -12 d. - 5

7) (3x) (10) = 70

a. 73

b. 4 c. 2 d. 5

8) 10x + y = 40 + y

a. 3 b. 4 c. 2 d. 5

9) 34

X + 10 = 13

a. 3 b 4 c. 2 d 5

10)12

x + 20 = 50

a. 60 b 40 c 2 d. 5

PART 4 (TRIGOMETRY)

Instruction: Identify the following. Encircle the letter of the correct answer.

1.________is a form by rotating a ray around its end point?

a. sides c. vertex

b. angle d. line

44

2. An angle measuring more than 90 degrees but less than 180 degrees?

a. acute angle c. right angle

b. scalene d. obtuse angle

3. An angle exactly 180 degrees?

a. vertex c. right angle

b. straight line d. scalene

4. 1 degrees is equal to?

a. 60mins. c. 90mins.

b. 30mins. d. 180mins.

5. what is the unit use in measuring angle?

a. minutes c. second

b. degree d. hour

6. a complete rotation of a ray result in an angle measuring?

a. 180 degrees c. 90 degrees

b. 360 degrees d. 45 degrees

7. what is a formula of a circle?

a. 4s c. πr2

b. 2Lx2w d. Lxw

8. does vertical angle have equal measure?

a. true c. sometimes

b. false d. never

9. does parallel line intersect with each other?

a. true c. sometimes

b. false d. never

10. what is the measure of right angle?

45

a. 90 degrees c. 360 degrees

b. 180 degrees d. 30

Appendix B

VALIDATION OF INDEPENDENT OBSERVER’S QUESTIONNAIRECOMPARATIVE PERFORMANCE OF BSMT AND

BSMAR-E IN BASIC MATH

Juror:________________________

Using the criteria developed for evaluating survey questionnaire by Carter V. Good and Douglas B. Scates, a jury of experts evaluated the self-made questionnaire instruments specifically for this study.

Rating: 5-Excellent 4-Very Good 3-Good 2-Fair 1-Poor

Area Criteria Jury 1 Jury 2 Jury31 The questionnaire is short enough that the respondents

respect it and it would not drain much precious time.4 4 4

2 . The questionnaire is interesting and has a fair appeal such the respondents will be induced to respond to it and accomplish it fully.

4 3 4

3 The questionnaire can obtain some depth to the responses and avoid superficial answer.

3 3 4

4 The items/questions and their alternative responses are neither too suggestive nor unstimulating.

4 2 5

5 The questionnaire can elicit responses, which are definite but not mechanically forced.

4 3 5

6 Questions/items are stated in such a way that the responses will not be embarrassing to the person/persons concerned.

4 3 5

7 Question/items are formed in a manner to avoid suspicion on the part of the respondents concerning hidden responses in the questionnaire.

4 4 4

8 The questionnaire is not too narrow nor restricted or limited in philosophy.

3 3 4

9 The responses to the questionnaire when taken as a whole could answer the basic purpose for which the questionnaire is designed and therefore considered valid.

3 4 4

Total 3.6 3.2 4.3

46

Rating 3.7Interpretation Very Good

Source: Good, Carter V and Scates, Douglas B, Methods of Research, Philippines Copyright, Appleton-Century-Grofts, Inc. 1972.Pp 615-616

Appendix C Vertical Interpretation for Validity

Rating Scale Verbal Interpretation

4.21-5.00 Excellent

3.41-4.20 Very Good

2.61-3.40 Good

1.81-2.60 Fair

47

1.00-1.80 Poor

48

49

50

51

CURRICULUM VITAE

Name: Jerome Marianito J. Guillermo

Home address: Brgy. Miranda, Pontevedra

Telephone/Mobile No.: 09466208500

Email address: [email protected]

Personal Background

Date of Birth: December 2, 1991

Place of birth: Bacolod City

Age: 19

Citizenship: Filipino

Gender: Male

Status: Single

Educational background

Elementary: Calvary Learning Center

High School: Calvary Learning Center

College: VMA Global College

Course: Bachelor of Science in Marine Transportation

52

CURRICULUM VITAE

Name: Rone Ryan R. Desierto

Home address: Brgy. Mandalagan Bacolod City

Telephone/Mobile No. 09094656360


Personal Background

Date of Birth: December 5, 1992

Place of birth: Bacolod City

Age: 19


Gender: Male

Status: Single


Elementary: Abkasa Elementary school

High School: Maranatha Christian College



53

CURRICULUM VITAE

Name: Crister S. Huerva

Home address: Brgy. Malingin Bago City Negros Occ.



Personal Background

Date of Birth: February 17, 1993

Place of birth: Bago City

Age: 18


Gender: Male

Status: Single


Elementary: Jalsis Elementary School

High School: Ramon Torres Malingin National High School



54

CURRICULUM VITAE

Name: Matt Ryan J. Aguirre

Home address: Balangigay Pontevedra Neg. Occ.



Personal Background

Date of Birth: August 18,1988

Place of birth: Pontevedra

Age: 20


Gender: Male

Status: Single


Elementary: Miranda Elementary School

High School: Pontevedra National High School



55

CURRICULUM VITAE

Name: Richard D. Lumanog

Home address: Brgy. Look, Calatrava Neg. Occ.



Personal Background


Place of birth: Calatrava Neg. Occ.

Age: 21


Gender: Male

Status: Single


Elementary: Calatrava 2 Central School

High School: Calatrava National High School



56

CURRICULUM VITAE

Name: Jerrybelle G. Bunsay Jr.

Home address: 18th Aguinaldo Street Bacolod City



Personal Background

Date of Birth: February 20,1992

Place of birth: Bacolod city

Age: 19


Gender: Male

Status: Single


Elementary: Andress Bonifacio Elementary School

High School: Bata National High School



57

CURRICULUM VITAE

Name: Eduardo P. Jallorina Jr.

Home address: Brgy.Tuburan E.B. Magalona Neg. Occ.



Personal Background


Place of birth: Brgy. Tuburan

Age: 19


Gender: Male

Status: Single


Elementary: St.Joseph Academy of Savaria Inc

High School: St.Joseph Academy of Savaria Inc.



1

Technology

results of mathematics

significant mathematics

mathematics of india

theapplication of mathematics

ordinary mathematics

mathematics of western

special education services

screening results