1 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
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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.
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
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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
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
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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
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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
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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?
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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
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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