1

Chapter I

The Problem and Its Background

Introduction

Each year thousands of high school, vocational, and college graduates are being

added to the list of jobless people, each of them hoping to be employed first before the

others. Many of them will not be employed due to certain circumstances but one of the

reasons for sure is what the skills they have and what they have not. According to an

article published by Feature Magazine this March 2010, even in the presence of

opportunities, graduates remain unemployed nowadays because they either fall short of

the employability skills they are supposed to have acquired in school or their education

proves irrelevant when applied to the context of the employment in their country. This is

the same observation that local firms have found among the new graduates. They have a

difficulty finding graduates with the skills needed to make their business grow.

It sends a message that despite of ten or more years of schooling, the graduates

are short-handed in terms of concepts and skills they needed. As a result, many of them

will resort to unemployment, underemployment, and some will lost their job.

According to Carnevale, et al. (1989), the most important skills for any employee

are the academic triumvirate: reading, writing, and computation (p.8).SCANS (Secretary

of Commission on Achieving Necessary Skills, 1991) include speaking and listening

(p.17). But these skills are broad in themselves. One can be adept to writing, speaking,

and computation and still fall short of effectiveness in the workplace. What really are the

specific skills and concepts needed in order to survive the economically?

2

Since it is a very broad study to cover in only one deal, let us just have a portion

of it as a focus of study. The study focused on mathematical side of the problem.

Mathematics is one of the foundation subjects in education. Consciously or

unconsciously we are using mathematics in our everyday living. In fact, in almost every

aspect of our life, we cannot help but to use skills that involves computations.

Math, in the words of Kathryn Tyler of HR Magazine, it is the word that strikes

tear deep in the souls of many otherwise well-educated professionals; most of whom

probably hoped that graduation day meant never having to solve another numbers

problem. But, as it turns out, high school teachers are right – we do use math in everyday

life.

If students will describe Algebra, Geometry, Trigonometry and Calculus in one

word that would be “hard”. Had they been songs, nobody will sing. Had they been

movies, it will be flop. Had they been foods, it is exotic. Had they been teachers, they

terrors. Had they not been subjects, then all is well.

The afore-mentioned subjects are generally known as mathematics. Mathematics

is one of the most significant subjects in education. It is a group of science that includes

arithmetic, algebra, geometry, trigonometry etc. It uses numbers and symbols, deals with

measurement, properties, quantities, magnitudes and forms and the relationships and

attributes of these. It is a science that develops skills while it is in itself is a skill.

Learning Mathematics forces one to learn how to think logically and to solve problems

using acquired skills. It also teaches one to be precise in thoughts and words.

Those who do not appreciate math are those who do not understand what math is

all about. That is why the nature of math desperately needs to be explained. Simply put,

math is all about solving problems. Ever since there was human existence, there have

3

been problems to solve. Whether the problems were basic requirements like sustaining

sufficient amounts of food or major accomplishments like constructing multifunctional

homes, problems such as these remain with us today. The strange thing about problems is

that they all have similar properties. These problems have to be dealt with the same

approach. A problem solver has to know the details surrounding the problems, and then

will eventually examine the details. Afterwards he will then make choices or decisions,

which is the beginning step of strategy. Then when actual solution is obtained, it must be

tested whether it is effective or not. It is a step-by-step process. Every math problems that

we encountered forces us to use many, if not all, of the detailed method of problem

solving. Each problem becomes a small yet important lesson for solving problems in

general. Traditionally, math is learned by doing many smaller problems and then these

small problems if put together, can solve bigger problems. One example is that, to solve

an algebraic equation, there must be knowledge of basic addition, subtraction,

multiplication, and division. This is a reality that concretized the significance of math in

our daily life and therefore must be given ample amount of consideration and treatment.

However, no matter how much emphasis have been given on the importance of this

subject, majority of student hates mathematics.

While it is true that some students may like math more than the others, all is

capable of learning math. Mathematics is not just for the elite but for the common

workers also. Math is common in the factory as it is common in the office.( Kathryn

Tyler). Jobs that pay a living need employees with strong mathematical problem solving

and reasoning skills.

However, a study made by Riam Kay Sumajit of the University of the Philippines

showed that the labor sector is not equipped with the skills required by the local

4

industries. If the skills are inadequate to carry out specific tasks, that means they are

unable to meet the requirements and standards their job demands, there is therefore a

mismatch. Due to skills mismatch, there is a tendency for workers to become inflexible

since they will find it difficult to adapt to the system.

One of the primary concerns is that many students try to avoid math that’s why

they are taking courses that they are resistant of solving it. Many factors affect to this

resistance and some are the behavior toward the subject, the teaching style and maybe the

broadness of the scope of the subject. There are so many topics that have nothing to do

with the field that they will go through. Educators spend much time discussing theories,

sharing knowledge, experimenting and searching with concept that has significance to the

students. We can say that methodologies and styles of teachings might affect as proven

but one of the neglected factors is the selection of the concept and skills that should have

given more emphasis. If only students are given just what they needed the most, their

skills will be maximized and will be equipped of right skills in the work place.

Algebra is one of the mathematics subjects that should be included in the

consideration since it is commonly integrated with other concept of the branches of

mathematics. It is a system of calculation in which certain operations are generalized by

the used of letters and symbols to stand for numbers. Yet Algebra is a broad subject as a

whole. Obviously, not all the concepts and skills in Algebra will be needed in the

workplace. Under the subjects are topics and subtopics not a few.

During high school days, Algebra is traditionally a subject to be taken by every

student. This is the very end reason of this study, to enrich our high school curriculum.

This is the most crucial part of learning Algebra whether one will continue on college or

will take a job after graduation.

5

As said, there are only some skills and concepts that educators are to work onto.

The main goal of this study is to determine the most commonly used mathematical skills

and concepts in Algebra in two selected companies at Laguna Techno park. Findings may

vary depending on the position or the nature of work of the employee. Eventually, this

study might be a basis for high school curriculum enrichment.

This study might lead and help the administrators to come up to some curriculum

enrichment and will give a hint to our teachers to focus on the skills and concepts most

needed in the companies.

6

Conceptual Framework

Input Process Output

FEEDBACK

Figure 1

Figure 1 shows the conceptual framework of the study presents by the researcher

in order to give view of concepts of what and how the study will be done.

The framework consists of inputs which will be used by the research. It also

includes the process on how the researchers conduct the study. The output of the study

will also be presented.

Profile of the respondents in terms of position

Mathematical skills and concepts used in the production of companies

Construction of questionnaire

Distribution of questionnaire

Retrieval of questionnaire

Tallying of the result of the survey

Commonly used mathematical skills and concepts by the employees

7

Statement of the Problem

1. What is the profile of the respondents in terms of their position in the company?

2. What mathematical concepts and skills in Elementary Algebra are most used in

different positions?

3. What are the most commonly used mathematical concepts in Elementary

Algebra?

4. What are the least used mathematical concepts in Elementary Algebra?

5. How are those mathematical concepts and skills encountered or used?

6. Is there a significant difference between the mathematical concepts and skills in

Elementary Algebra used by the employees when they are grouped according to

their positions?

Hypothesis

There is no significant difference between the mathematical concepts and skills in

Elementary Algebra used by the employees when they are grouped according to their

positions.

8

Significance of the Study

This study is conducted hoping that the findings would be more useful to the

following:

High school teacher who are handling mathematics subjects. The findings of

this study may help those assists the needs of their students for their future work.

Through emphasizing on teaching the commonly used mathematical skills and

concepts needed in the industry. Teachers may also provide the necessary

activities and programs for the students to further enhance the skills needed in

their future work.

High school students who are ready to work in a company after graduation.

The findings of this study will give them ideas about the necessary skills they

need to acquire as a preparation for the future job.

Educational Administrators who are responsible for designing the

curriculum. The result of the study may provide administrators ideas in

modifying curriculum that will fit to the needs of the students considering the

future of the students.

School Administrators who are responsible for designing the school activities

and programs. They may provide seminars to inform students and provide

training about the skills and concepts in Elementary Algebra needed in student’s

future work.

Future researchers who will conduct researches related to this study. The

findings of the study may help other researches who will pursue the same nature

9

of study because this can provide them information about the commonly used

mathematical skills and concepts in Elementary Algebra.

Scope and Delimitation of the Study

This study looked into the mathematical skills and concepts used by employees in their

operations. The number of respondents from each selected companies were limited by using the

Slovin’s Formula.

The scope of this study is delimited to two companies leading electronics. The chosen

companies were Toshiba and Hitachi, which hire employees that are at least high school graduate.

The position of employees was classified according to the nature of work. Workers are classified

as operator and engineer.

The mathematics covered in this study is the mathematical concepts and skills in

Elementary Algebra.

10

Definition of Terms

Competency Level – the results where an employee possesses skills or abilities to be

hired and productive in a certain job.

Employee – includes only the paid workers in a certain company from the lowest

position the highest position.

Engineering Staff – are employees not necessarily engineers or professionals but are

in higher position than operators.

Engineer – position being performed or occupied by professional engineers

performing related work or specialization.

Least Used – skills and concepts with lowest frequency of usage.

Mathematical Concepts – are knowledge which includes formulas, solutions, topics,

ideas, and processes in mathematics.

Mathematical Skills – mathematical abilities or proficiency to perform a notion or a

mathematical concept.

Most Commonly Used – are skills and concepts with highest rank as to average.

Operator – position being occupied by mostly high school graduates and does not

require a college diploma.

Orally – concepts and skills are encountered in verbal mode.

Position – designation of worker as to the nature of work.

Tool Aided – concepts and skills are encountered with the used of instruments or

tools.

11

Workforce – the collective force of the entire numbers of employee of the company.

Written – concepts and skills are encountered as written

Chapter II

Review of Related Literature and Studies

This chapter presents a review of literature that were gathered from books,

journals, and studies that are related to this research in order to give a view and support

the claims of this study.

Ferndale in Preparing Students for life and work states that the reason behind

creating new high school graduation requirements for the class of 2008 and beyond is

pretty simple: the world is much tougher and competitive place than it used to be, and our

children have to be much better prepared than we were when left high school. High

school is the last education opportunity that lays the significant foundation which is

requisite to enter college. Its purpose is to do the best it can to provide all the foundation

necessary to further prepare for adult life.1 High school graduates would have better

chances of getting employed than those who do not possess the minimum requirement in

most jobs available, which is a high school diploma. In the Philippines, children who are

able to finish at least high school can be considered luckier than the rest of youth

population who either fail to complete secondary or elementary school or has never

attended any schooling at all.2 However, there are reports written that there has been

insufficient focus on the types of high school training and learning that meets the needs

1 http://www.ferndale.wednet.edu/fhs/facts/GraduationRequirementsHandbook.pdf2 “Beyond Access: Prospect for Relevant and Responsive Education in the Philippines”, Feature, 26 March 2010

12

of students who decide not to go to college or who leave soon after enrolling – and on

education that meets the needs of potential employers.3 Students must have a fundamental

set of skills when they leave high school. The most or majority of jobs now require some

kind of training or education after high school. And too many of our students are skill

struggling with just the basics. To succeed in life, whether it’s buying a house, choosing a

doctor, or applying for and keeping a job, people must be able to think critically and

creatively solve problems. We can no longer afford to let some students “fall through the

cracks” of our education system, and leave high school without the skills they need to

succeed in life.4

Today, however, most of the technical people are trained either at the area

vocational, high school or through a two-year program at a community college. Math

skills are called for throughout the company, and yet, according to Speeding Managers,

many of its entry level employees are deficient in math (and communication) skills. But

industry’s demands for reading and math skills have outstripped overall educational

achievement.5

High school graduates should enter the workplace with the academic and

vocational skills that afford employment and sustain this longevity as productive

members in today’s complex work environment.6 However, secondary education for

workplace readiness, and the opportunities in secondary education are in dire straits.

Educators spend much time discussing theories, sharing knowledge, experimenting and

searching for concepts, while employers who hire students who graduated from our

3 Lucy N. Friedman, The After-School Corporation (TASC), July 20074 http://www.ferndale.wednet.edu/fhs/facts/GraduationRequirementsHandbook.pdf5 Brenda H. Scott, Robert J. Quinn, and C. J. Daane, “Are we teaching the Mathematics Skills Students will Need for Work in the Twenty First century?” Heldref Publications, 19966 John E. De Leon/ Ralph E. Borchers, High School Graduate Employment Trends and The Skills Graduates need to Enter Texas Manufacturing Industry, 10 December 2009

13

educational system want to see results and want their employees to be able to do

something with their knowledge. Educational system’s lack of adequate instructional

content (curricula, instruction and support values).7 It was reported that business leaders

can’t find qualified applicants who can read operating manuals, write coherent memos

and compute sales prices.8 On top of this, education system seems to be confused as the

economy as to what kind of education should they give to the children to prepare them

for employment. Even in the presence of opportunities, graduates remain unemployed

because they fail short of the employability skills they are supposed to have acquired in

school or, their education proves irrelevant when applied to the context of employment in

their community. Such is one of the major problems facing the Philippines education

system today.9

The common complaint among graduates every year in the Philippines is that

there is no job available to them. The truth of the matter, however, is aside from the

scarcity of jobs in the country, employers find many, if not most, of the graduates ill-

prepares for the workplace. Employers raise issue of minimum levels of competencies

and communication skills, which they usually find absent in most of the graduates.10

Palatino once said that unemployment problem is rooted in country’s educational

system wherein degree holders do not have the skills and knowledge required to qualify

for the job they aspire for “Raw training underwent by new graduates make them

unqualified for in demand jobs, so most of them are forced to resort to

underemployment” he explained. He then urged the government and the education

7 Koffel, “Teaching Workplace Skills”, 19948 http://www.ferndale.wednet.edu/fhs/facts/GraduationRequirementsHandbook.pdf9 “Beyond Access: Prospect for Relevant and Responsive Education in the Philippines”, Feature 26 March 201010 “Beyond Access: Prospect for Relevant and Responsive Education in the Philippines”, Feature 26 March 2010

14

department to restructure the education curriculum in the context of national

industrialization that would generate mass employment and will provide adequate income

for the family of Filipino workers.11

In relation to these, according to an article written by Tina Arceo – Dumlao, local

firms whine all the time about the difficulty of finding graduates with the skills needed to

make their business grow. Human resource experts say that most of the new entrants to

the labor force either know too much of what companies don’t really need in their

operations, or too little of the important study required by businesses to stay ahead of the

competition.12

In the same tone, skills mismatch blamed for Southern Philippines

unemployment. The lack of coordination among government various academic

institutions, and the business sector has continuously resulted to a skill mismatch in

Southern Mindanao. Globalization, liberalization and deregulation policies are forcing

local industries to make some adjustments in terms of infrastructure, technology and

labor requirements. However, a study made by Riam Kay Sumajit of the University of the

Philippines in Mindanao showed that Region XI’s labor sector is not equipped with the

skills required by these changes. Despite the technological advancements, she said, the

country has not improved its educational quality to get in line with other countries that

have already made advances in their educational curriculum decades ago. Thus, the

Philippines lagged behind. “If the society desires to maximize the effects of education on

the development, it has to systematize its educational system to hit the manpower

requirement of the economy”, she said. The skills acquired by each individual depends on

11 Carl Marc Ramota, Bulatlat Vol. V, No. 7, March 20-26, 2005 12 Tina Arceo – Dumlao ,Philippines Daily Inquirer 21 May 2008

15

the quality of education they learned from a certain institution that has invested and

upgraded its teaching quality from time to time depending on the socio – economic

changes. If the skills are inadequate to carry out specific tasks, it means that they are

unable to meet the requirements and standards their job demands, there is then a

mismatch. Mismatch is thus the gap between the skills in terms of type of quality

supplied by the education sector and the skills in terms of type and quality demanded by

the employers. The study found out that skills mismatch makes it more difficult for

employers to adapt new technology that will make their employees more productive and

competitive in the global market place. Due to skills mismatch, there is a tendency for

workers to become inflexible since they will find it difficult to adapt to the changes

within the system. As a result, they become bored, and unhappy with their work, which

leads to poor performance level or incompetence.13 Labor mismatch slows Philippines

economic growth according to ADB Schools in the Philippines are producing the wrong

kind of skills for its labor market needs, which is hurting economic growth, according to

an Asian Development Bank (ADB) study, ADB economist Hyun H. Son further

emphasized that the current education sector does not supply the right kind of skills that

are demanded by the labor market. Accelerating economic growth would require

government action in addressing the labor mismatch, he added.14 This is exactly what Edu

H. Lopez wrote in 2001 about new graduates facing industry skills mismatch in his

article. There is a big mismatch between the needs of industry and the manufacturing

sector and the skills gained by the new graduates. Although this problem has been known

13 Riam Kay Sumajit, Asia Pulse News May 20, 200314 Agence France-Presse, ADB (Asian Development Bank) September 9, 2008

16

for a long time, nothing substantial has been accomplished on the educational institution,

said Donald Dee, President of the Employers Confederation of the Philippines (ECOP).15

Philippines is not the only nation facing skills mismatch and deficiency. De Leon

in his study entitled High School Graduate Employment Trends and The Skills Graduates

Need to Enter Texas Manufacturing Industry said that, experts predicts that due to the

influx of new technologies in the workplace, high school graduates will need to possess

better academic and vocational skills as compared to their predecessors.16

Australia’s shortage of skilled laborer will worsen as the economy improves,

according to a survey by the Australian Institute of Management. Sixty-six percent of the

executives said their organizations had a workforce skills gap. “The skill gap identified in

our survey will escalate and that means an increasing number of Australian organizations

face the risk of under-performing”, the chief executive of AIM in Victoria and Tasmania,

Susan Heron, said.17

According to a National Association of Manufacturers Survey of 4500

manufacturers, 60 percent of workers lacked even the most basic skills. In a survey of

300 executives conducted by the National Institute for Literacy, a federal institute in

Washington, D.C, 47 percent of the respondents said they think the workers in their

companies need math training.18

The number of individuals who lacked marketable skills fueled the growth of the

rehabilitative and vocational training industry. Firms in this industry were formed as a

result of the lack of training available to individuals without a college degree.19

15 Edu H. Lopez, Manila Bulletin, 1 April 200116 John E. De Leon/ Ralph E. Borchers, High School Graduate Employment Trends and The Skills Graduates need to Enter Texas Manufacturing Industry, December 10, 200917 Susan Heron, “Australia’s Workplace Skills Crisis”, December 15, 200918 Kathryn Tyler, “Not just solving for 'x': help employees master their fear of math by creating support for math skills training - Training & Development Agenda”,HR Magazine, August,200319 http://www.answers.com/topic/job-trainingandvocationalrehabilitationservice

17

The Integrated University Program of Hitachi GST Philippines is a knowledge

and skills enhancement initiative being done by the company through collaboration with

the key universities in the country. Under the program, recipients or beneficiaries of

scholarship and research grants as well as OJT program are chosen every year based on

the different universities’ schedules. Grants and scholarship focus on academic

disciplines in engineering (Mechanical, Electrical, Chemical and Industrial), the sciences

(Chemistry, Physics, Materials and Computer Science) and statistics. The six beneficiary

universities include Ateneo de Manila Universitiy (AdMU), De LaSalle Universities

(DLSU), Magna Institute if Technology (MIT), Polytechnic University of the Philippines

(PUP), University of the Philippines (UP) and University of Sto. Tomas (UST).20 Hitachi

has always been expanding every year, which is good, for it will create more opportunity

especially in Sta. Rosa and Biñan. Another giant company, the Toshiba Information

Equipment Philippines Inc. is investing an additional P110 million to expand its

operations in the country. The new investment will translate to more jobs in the

electronics industry. The expansion will employ 618 people.21

Yet, youth unemployment is at alarming rate of 28.26% (for the population

between 15 and 25 years of age) and that means our young people including our

graduates are not finding enough jobs.22 Most of them are not armed with right skills

required by the companies. They are the ones affected by educational system since most

of the older employees will be retained and trained by the companies. It is therefore

imperative to go beyond universal coverage in education of the right kind of skills.

20 Manila Bulletin, 27 August 200821 Ma. Elisa P. Osorio, The Philippine Star 20 February 2009 22 Ma. Lourdes A. Sereno, Manila Times 19 July 2009

18

Through the above discussion, is very that our individual must be equipped with

the correct knowledge and skills they need find or stay longer in a job. Training program

may be helpful but it benefit those who already in job. We find it necessary the student

should be prepared before applying for a job through high school training. The

researchers found out that having mathematical skills and abilities is one of the

fundamental skills needed in working in companies. The researcher found it significant to

know the commonly used mathematical skills and concepts in Algebra in the production

of companies to be helpful to high school students.

19

Chapter III

Methodology

This chapter presents the methods and procedures used by the researchers to come

up with this study. This includes the research methods used, research environment,

research subjects, sampling procedures, research instruments, data gathering,

categorization of the variables and statistical treatments.

Research Method

The research method used by the researchers in this study is the descriptive

method. This method is used because the researchers gather and tabulate data regarding

present conditions.

Research Environment

Laguna Technopark is widely acknowledged as the Philippines’ premiere

industrial park. Among the attractions of locating in the Technopark is its accessibility to

key centers including Makati, the airports and seaports. The locators in the Technopark

are progressive companies, mostly foreign, and engaged in a wide range of enterprises

including precision or leading edge electronics including integrated circuit assembly and

20

packaging and hard drive manufacture, and assembly of automobiles and related parts. It

is host to leading international companies such as Honda, Hitachi, Toshiba and

Matsushita, as well as major local manufacturers including Pure Foods and Integrated

Microelectronics.

Research Subjects

The two selected companies at Laguna Technopark are Hitachi and Toshiba. The

researchers chose Hitachi and Toshiba as the subjects of the study since both are one of

the leading international companies in the world and one of the bigggest electronics

companies at Laguna Technopark. There are approximately one thousand (1,000)

engineers and six thousand (6,000) operators working in Hitachi while in Toshiba, there

are approximately three thousand (3,000) engineers and six thousand seven hundred fifty

(6,750) operators.

To determine the sample size of population for each company, the researchers

used the Slovin’s formula. From approximately 7,000 workers operating at Hitachi, the

researchers got 99 respondents, 85 from operators and 14 from engineers. And for

Toshiba, 99 respondents were selected, 64 from operators and 30 from engineers.

Sampling Design

21

The researchers used the Slovin’s Formula to determine the sample size of the

population.

The Slovin’s formula is given below

where:

n = sample size

N = population size

e = desired margin of error.

Sampling Strategy

The researchers used the proportional allocation technique wherein they got the

sample population from the sub- group of the population.

The distribution of the sample is given as follows:

HITACHI TOSHIBATOTAL

Operator Engineer Operator Engineer

Population 6,000 1,000 6,750 3,000 16,750

Sample 85 14 69 30 198

Development of the Research Instruments

22

The researchers used survey questionnaire as their instrument in this research. The

lists of mathematical skills and competencies were gathered from the Department of

Education. The researchers modified the lists of math skills and competencies without

eliminating any concept to fit in the need of this research. The researchers asked the

professor to check and edit some questions if necessary.

The questionnaire consists of two parts. The first part sought to get the

information about the profile of the respondents in terms of gender, educational

background and position in the company. In the second part, the researchers used a

checklist to determine the most commonly used math skills and concepts in Elementary

Algebra considering the given scale. And to know how are those mathematical sills and

concepts encountered or used, the researchers provided another column for orally,

written, and tool-aided. The questions are divided into 6 different concepts in Elementary

Algebra.

To determine how frequent each math skills and concepts used, the researchers

used the scale:

5 – Always

4 – More Often

3 – Sometimes

2 – Rarely

1 – Never

Data Gathering Procedure

23

In this study, the researchers find it hard to gather data since the respondents did

not have so much time to entertain such kind of survey questionnaire.

The researchers’ first step was to send letters to the administration of Hitachi and

Toshiba asking for permission to conduct a survey. The researchers started to conduct the

survey after getting the approval of the said companies.

The researchers oriented the respondents about the purpose of the study and

instructed them on how to answer the questionnaire.

The distribution of the instrument to the respondents took so much time because

the researchers had to wait for the respondents’ vacant time or perfect time to answer the

survey questionnaire. After retrieving all the needed data, the researchers tabulate the

data for statistical treatment and analysis.

Statistical Treatment

In order to get the frequency distribution of the respondents profile, the

researchers used:

P = (F/N) x 100

where:

P = Percentage

F = Frequency

N = Total number of respondents

In order to determine the weighted mean of each mathematical concept, the

researchers used:

24

where:

= Weighted mean

x = Measurement or value

w = Weight factor

Σxw = Summation of the product of measurement and weighted factor

n = Number of observations

In order to determine the significant difference between the mathematics used by

the employees when they are grouped according to their positions, the researchers used t-

test at 0.05 level of significance.

where:

= Mean of sample A

= Mean of sample B

= Number of subjects in sample A

= Number of subjects in sample B

= Variance of sample A

25

= Variance of sample B

Chapter IV

Presentation, Analysis and Interpretation of Data

This chapter presents the data gathered, the analysis of this data and the

interpretation of the result using the statistical tools indicated in the previous chapter. The

presentation of this data follow the order in the statement of the problem indicated in

Chapter I.

Table 1

Frequency Table Showing the Distribution of the Respondents

in Terms of their Position in the Company

PositionNumber of Respondents

Total Percentage (%)Hitachi Toshiba

Operator 85 69 154 77.78

Engineer 14 30 44 22.22

Total 99 99 198 100

Table 1 shows the frequency distribution of the respondents in terms of their

position in the company. The respondents came from selected companies at Laguna

Technopark, the Toshiba and Hitachi. The respondents were grouped according to their

position. From the table, 77.78% of the respondents are operators and 22.22% are

26

engineers. Therefore, there is greater number of respondents from operators than

engineers.

Table 2

Frequency of How Often Each Mathematical Concepts and Skills in Elementary

Algebra were Used in Different Positions

Mathematical Concepts in Elementary

Algebra

Weighted

Mean for

Operators

Rank

Weighted

Mean for

Engineers

Rank

A. Measurement 2.01 1 3.25 1

B. Real Number System 1.73 3 2.77 2

C. Algebraic Expression 1.41 6 2.47 5

D. First Degree Equation 1.66 4 2.72 3

E. Linear Equation in Two Variables 1.91 2 2.62 4

F. Special Products and Factoring 1.46 5 2.28 6

Table 2 shows the frequency of how often each mathematical concepts and skills

in Elementary Algebra were used in different positions. From the table, the first two

concepts in ranking for the mathematical concepts used by the operators are

Measurement and Linear Equation in two variables, while the first two in ranking for the

mathematical concepts used by the engineers are Measurement and Real Number System.

Therefore, the concepts of Measurement and Linear Equation in two variables are most

27

used by the operators in their work, while the concept of Measurement and Real Number

System are most used by engineer in their operations.

The skills under the concept of measurement are illustrating the development of

measurement from the primitive to the present international system of units; measuring of

length, weight, volume, temperature, time, angle; expressing relationship between two

quantities using ratios; converting measurements from one unit to another; and solving

problems involving measurements.

Table 3

Overall Frequency of How Often Each Mathematical Concepts in

Elementary Algebra were Encountered or Used

Mathematical Concepts in Elementary

Algebra

Mean Rank

A. Measurement 2.63 1

B. Real Number System 2.25 3

C. Algebraic Expression 1.94 5

D. First Degree Equation 2.19 4

E. Linear Equations in Two Variables 2.27 2

F. Special Products and Factoring 1.87 6

28

Table 3 shows the overall frequency of how often each Mathematical concept in

Elementary Algebra were encountered or used. From the table, the concept of

Measurement is first in ranking, followed by Linear Equations in two variables while the

concept of Algebraic Expression is fifth in ranking followed by the last in ranking which

is Special Products and Factoring.

Therefore, the most commonly used mathematical concepts in Elementary

Algebra are Measurement and Linear Equations in two variables. Some skills under these

concepts are measuring of length, weight, volume, temperature, time, and angle;

expressing relationship between two quantities using ratios; converting measurements

from one unit to another; and solving problems involving measurements; plotting of

points on the coordinate plane; constructing table of values for x and y given a linear

equation in two variables; and determining the slope, intercept, domain, range, and trend

of linear equation.

However, the least used mathematical concepts in Elementary Algebra are

Algebraic Expression and Special Products and Factoring. Some skills under these

concepts are simplifying numerical expression involving exponents and grouping

symbols; evaluation of mathematical expressions for given values of the variable(s)

involve; simplifying algebraic expressions using the laws of exponent; finding special

product given the factors; and factorization of polynomial completely.

29

Table 4

Percentage on How the Used Mathematical Concepts and Skills in

Elementary Algebra were Encountered or Used

Mathematical Concepts in Elementary

Algebra

Orally

(%)

Written

(%)

Tool-

Aided (%)

A. Measurement 50.25 61.59 70.83

B. Real Number System 49.51 69.46 69.28

C. Algebraic Expression 42.91 60.13 41.33

D. First Degree Equation 69.12 70.76 55.28

E. Linear Equation in Two Variables 48.97 53.18 45.65

F. Special Products and Factoring 79.73 80 78.89

Table 4 shows the percentage on how the used mathematical concepts and skills

in Elementary Algebra were encountered or used. The mathematical concepts and skills

in Elementary Algebra were encountered or used by the respondents either orally,

written, or with the aid of tools. From the table, 50.25% of the used skills in

Measurement were encountered or used orally, while 61.59% of the used skills in

Measurement were encountered or used in written form, and 70.83% of the used skills in

measurement were used with the aid of tools. In the concept of Special Products and

30

Factoring, 79.73% of the used skills were encountered or used orally while 80% of the

used skills were encountered in written form and 78.89% of the used skills were

encountered with the aids of tools.

The table shows that there is greater percentage of the used skills that were

encountered as written in almost all concepts.

Table 5

Difference between the Mathematical Concepts and Skills in

Elementary Algebra Used by the Employees When they are Grouped according to

Their Position

Position Mean S2 t-value Decision

Operator 1.70 0.06 -5.96 < -2.57

-5.96 > 2.57Reject

Engineer 2.69 0.11

Using the t-distribution, the critical values are t < -2.57 and t > 2.57.

The researchers worked for the computed value of t in order to find the significant

difference between the mathematical concepts and skills used by the employees when

they are grouped according to their position. The computed value of t is -5.96378, is less

than -2.57. It means that the null hypothesis will be rejected. Therefore, there is

significant difference between the mathematical concepts and skills in Elementary

Algebra used by operators and engineers.

31

Chapter V

Summary, Findings, Conclusion and Recommendation

This chapter presents the summary and conclusions of all the findings from the

data gathered. This chapter also contains the recommendations of the researchers for

respective persons.

Summary

This research was conducted at Laguna Technopark Inc. It attempted to know the

most commonly used mathematical skills and concept in Elementary Algebra in two

selected companies at Laguna Technopark. The researchers used questionnaire that

include the profile of the respondents and the checklist of the mathematical concepts and

skills in Elementary Algebra.

The researchers also determined how are those mathematical concepts and skills

were encountered or used and if there a significant difference between the mathematical

concepts and skills in Elementary Algebra used by the employees when they are grouped

according to their position.

The researchers used statistical treatment such as percentage, weighted mean, and

t-test as a guide in analyzing and interpreting the data gathered.

32

The following are the findings of this study:

1. Almost 78% of the respondents are operators and 22% are engineers.

2. The most commonly used mathematical skills and concepts in Elementary

Algebra in different position is Measurement with a number 1 ranked on both

operators and engineers.

3. Measurement has a mean of 2.63 and was ranked number 1 and being interpreted

as the most commonly used mathematical concept. It was followed by Linear

equations in two variables with a mean of 2.27.

4. The least used mathematical concepts in Elementary Algebra are Algebraic

Expression with a mean of 1.41 and Special Products and Factoring which has a

mean of 1.46.

5. The most commonly used skills are those under the most commonly used

concepts such as: (1) Illustrating the development of measurement from the

primitive to the present international system of units; (2) Measuring of length,

weight, volume, temperature, time, angle; (3) Expressing relationship between

two quantities using ratios; (4) Converting measurements from one unit to

another; (5) Solving problems involving measurements; (6) Presenting the

location of point in the coordinate plane by giving coordinates; (7) Plotting of

points in the coordinate plane; (8) Determining the quadrant of a point; (9)

constructing a table for the values of x and y, given a linear equation in two

variables; (10) Illustrating the graph of Ax + By = C based on the table of values

for x and y; determining the slopes, intercepts, domain, range, and trend of linear

equation; (11) Illustrating the graph of a linear equation in two variables described

33

by our equation using the intercepts; any two-points and slope and a given point;

and (12) Solving problems using linear equations in two variables.

6. The least used mathematical skills in Elementary Algebra are the skills under the

least used mathematical concepts such as: (1) Simplifying numerical expression

involving exponents and grouping symbols; (2) translating verbal phrases to

mathematical expressions and vice versa; (3) Evaluating the mathematical

expressions with given values for the variable(s) involve; (4) Simplifying

algebraic expressions using the laws of exponents; (5) Expressing numbers in

scientific notation; (6) Adding and subtracting polynomials; (7) Multiplying

polynomials by another polynomials; (8) Dividing a polynomial by a monomial;

(9) Dividing a polynomial by a polynomial; (10) Solving problems involving

polynomials; (11) Finding special product given the factors; (12) Factoring the

polynomials completely.

7. The skills in measurement are being encountered orally, tool-aided or written.

Almost 61.59% of the skills in measurement are encountered as written, almost

50.25% is being encountered orally and 70.83% of the skills are encountered with

the aid of tools.

8. There is a significant difference between the mathematical skills and concepts in

Elementary Algebra used by the operators and engineers.

34

Conclusions

1. The number of operators is more than thrice the number of engineers.

2. The most commonly used mathematical concept and skills in Elementary Algebra

in different positions is Measurement and the skills under Measurement.

3. The most commonly used concepts in Elementary Algebra are Measurement and

Linear Equations in Two Variables.

4. The least used mathematical concepts in Elementary Algebra are Algebraic

Expression and Special Products and Factoring.

5. The most commonly used skills in Elementary Algebra are the skills under the

concepts of Measurement and Linear Equations in Two Variables.

6. The least used skills in Elementary Algebra are the skills under the concepts of

Algebraic Expression and Special Product and Factoring.

7. Most of the most commonly used mathematical concepts and skills are being

encountered in written mode.

8. Engineers use more mathematical concepts and skills in Elementary Algebra in

their operations in the company than operators.

35

Recommendations

1. The High School teachers who are teaching Elementary Algebra may assist the

needs of their students who are preparing for future work after graduation through

emphasizing on teaching the most commonly used mathematical skills and

concepts in Elementary Algebra needed in the industry.

2. The High School teachers should provide more activities that use tools and

equipments in Measurement and written activities in Linear Equation, First

Degree Equation, Algebraic Expression, Real Number System and Special

Product and Factoring.

3. Future researchers may study the most commonly used mathematical skills and

concepts in Intermediate Algebra, Geometry, Physics and Trigonometry in the

production of companies.

4. Curriculum Planner may modify the construction of our present curriculum as to

the number of time allotted to each topic. They may allot more time to the concept

and skills in Elementary Algebra that are mostly used in the production of

companies for the students to have the mastery in those concepts and skills. They

may also lessen the time allotted to the mathematical skills and concepts in

Elementary Algebra that are least used in the production of companies. The

following concepts were arranged according to the length of time to be allotted to

each. The number 1 being the longest time and number 6 being the shortest time

allotted.

36

1. Measurement

2. Linear Equation

3. Real Number System

4. First Degree Equation

5. Algebraic Expression

6. Special Product and Factoring

5. School administrators may provide seminars to inform students and provide

training about the skills and concepts in Elementary Algebra that are needed for

future work.

37

BIBLIOGRAPHY

Scott , et. al. “Are we teaching the Mathematics Skills Students will Need for

Work in the Twenty First century?” .Heldref Publications. 1996

Tyler, Kathryn. “Not just solving for 'x': Help Employees Master their Fear of

Math by Creating Support for Math Skills Training - Training & Development

Agenda”. HR Magazine. August 2003

De Leon, John E. and Borchers, Ralph E. ”High School Graduate Employment

Trends and The Skills Graduates need to Enter Texas Manufacturing Industry” 10

December 2009

Heron, Susan. “Australia’s Workplace Skills Crisis”. 15 December2009

Dumlao,Tina. Philippines Daily Inquirer 21 May 2008

Koffel. “Teaching Workplace Skills”. 1994

Lopez, Edu H. Manila Bulletin, 1 April 2001

Osorio, Ma. Elisa P. The Philippine Star 20 February 2009

Ramota, Carl Marc. Bulatlat Vol. V, No. 7, March 20-26, 2005

Sereno, Ma. Lourdes A. Manila Times 19 July 2009

Sumajit, Riam Kay. Asia Pulse News 20 May 2003

“Beyond Access: Prospect for Relevant and Responsive Education in the

Philippines”, Feature 26 March 2010

France-Presse,Agence. ADB (Asian Development Bank) September 9, 2008

Friedman, Lucy N. The After-School Corporation (TASC) July 2007

http://www.answers.com/topic/job-trainingandvocationalrehabilitationservice

38

http://www.ferndale.wednet.edu/fhs/facts/GraduationRequirementsHandbook.pdf