i

READINESS OF STUDENTS IN COLLEGE ALGEBRA

An Institutional Research

Presented to

the Research Management Office

Saint Louis College

City of San Fernando, La Union

by:

Ragma, Feljone G.

Manalang, Edwina M.

Rodriguez, Mary Joy J.

Hoggang, Gerardo

Fernandez, Mark Edison

Oredina, Nora A.

Parayno, Dionisio Jr.

Hailes, Imelda Lyn R.

Coloma, Roghene A.

February 26, 2014

ii

TABLE OF CONTENTS

Page

TITLE PAGE………………………………………………………………… i

TABLE OF CONTENTS………………………………………………….. ii

LIST OF TABLES…………………………………………………………. v

LIST OF FIGURES……………………………………………………….. vi

CHAPTER

I INTRODUCTION……………………………………………… 1

Background of the Study.……......………….......... 1

Theoretical Framework……………………………..... 4

Conceptual Framework……………………………….. 6

Statement of the Problem…………........................ 9

Hypotheses……………………………………........... 9

Importance of the Study……………...................... 9

Definition of Terms…………………………………..... 11

II METHOD AND PROCEDURES…………………………… 14

Research Design……………………………………… 14

Sources of Data………………………………………. 14

Locale and Population of the Study……………... 14

Instrumentation and Data Collection ..……….... 16

Validity and Reliability of the

Questionnaire……………………………………..

16

iii

Page

Data Analysis ………………………………………….

Data Categorization……………………………….....

16

19

Parts of the Learning Activity Sheets..….……………………………………………….

21

Ethical Considerations…………………………...... 22

III RESULTS AND DISCUSSION…………………………….. 23

Profile of the College Students……………………..

Level of Readiness of Students in College

Algebra……………………………………………..

23

25

Correlation between Profile and Level of

Readiness…………………………………………..

27

Comparison on the Level of Readiness of the

three respondent groups……………………….. 29

Strengths and Weaknesses of Students in College Algebra…………………………………..

31

Learning Activity Sheets………..……………………

33

IV

SUMMARY, CONCLUSIONS AND RECOMMEN- DATIONS………………………………………………..

96

Summary………………………………………………. 96

Findings………………………………………………… 96

Conclusions…………………………………………… 98

Recommendations…………………………………… 99

BIBLIOGRAPHY……………………………………………… 101

iv

APPENDICES………………………………………………… 95

v

LIST OF TABLES

Table Page

1 Distribution of Respondents………………………….

2 Profile of Respondents ………………………………. 24

3 Level of Readiness of Students in College

Algebra ………………………………………………….

26

4

Correlation between Profile and Level of Readiness……………………………………………….

28

5

Difference in the Level of Readiness among the respondent groups……………………………….

30

6 Strengths and Weaknesses of Students in

College Algebra ……………………………………

32

7 Level of Validity of the Learning Activity

Sheets…………………………………………………

vi

LIST OF FIGURES

Figure Page

1 The Research Paradigm ……………………………………….. 8

1

CHAPTER I

INTRODUCTION

Background of the Study

Quantitative Literacy, as defined by the Mathematical Association

of America (MAA), is the ability to apply the minimum computational

competency or fluency to solve problems in the real world

(http://www.maa.org/college-algebra). It is implicit that when a person

is quantitatively literate, he is able to use his mathematical skills in

dealing with situations in his life, whether it is in the complex line of

business, economics, and politics or in the simple context of time

reading, scheduling, and many others. Indeed, Mathematics is

necessary.

One mathematics subject that is necessary to person’s life is

College Algebra. Packer (2004) explains that College Algebra is the

introductory mathematics subject to any university or community

college. He added that College Algebra is the starting course for students

to be trained logically as they would deal with algebraic expressions,

axioms of equations, functions and the like. Furher, Leeyn (2009)

exemplifies that College Algebra is a critical element to 21st century jobs

and citizenship. Gateschools staff (2013) also asserts that it is the

gatekeeper subject. It is so because it is used by professionals ranging

from electricians to architects to computer scientists. Robert Moses

2

(2009), founder of the Algebra Project, says that learning College Algebra

is no less than a civil right. As such, College Algebra is really very

important.

However, no matter how important College Algebra is, it is still

considered by most students as a non-helpful subject. According to a

paper presented in the Mathematics Association of America (MAA)

conference in the year 2009 which revealed that College Algebra is the

last mathematics course many students take. A majority entered the

classroom having already decided that it would be their final

mathematics course. Data, contained in the same conference report,

indicated that only one in ten College Algebra students go on to take

other higher math subjects. Many would skip College Algebra if they did

not have to pass it to get the degree they need to enter their chosen

career field. In addition, enrollment in this subject tends to fall

dramatically when colleges make quantitative reasoning or intermediate

algebra the requirement. It was also reported that, a few years after

finishing the course, the students cannot recall anything they learned.

All of these pinpoint to the fact that college algebra seemed hard for most

students (http://www.maa.org/college-algebra). As a result, readiness,

evident in their performances, declines. According to the New York

Times, in the last fall of 2013, results from national math exams stirred

3

up a tempest in a standardized test. It turned out that math scores

declined more quickly. It was also mentioned that math scores haven’t

improved since 2007 (http://www.nytimes.com/). In addition, Shepherd

(2005) revealed that most students do not excel in their Algebra course.

Most of them cannot perform indicated operations, especially when

fronted with word problems. Students find it hard to solve problems in

Algebra. Some just do not answer at all. These situations reflect poor

understanding of and performance in the course (The Journal of

Language, Technology & Entrepreneurship in Africa, Vol. 2, No.1,

2010).Moreover, Kuiyuan (2009) also mentioned that in University of

Florida, the student’s success rate in College Algebra is more than the

desired level. Kuiyan (2009) stressed that with this trend in dismal

performance, the readiness of students in such subject is very low.

In the Philippines, College Algebra is a pre-requisite subject in all

course curricula. CHED Memorandum Order 59 series of 1996 mandates

the inclusion of College Algebra as a basic subject in all courses. The

country is not exempted from the predicaments on College Algebra

performance. A recent study of on the readiness graduating high school

students of Marian Schools in College Algebra revealed that their

readiness is only at the moderate level. This means that the students did

4

not yet fully attain the desired competence to be able to hurdle the

demands of College Algebra.

In the provincial scene, the recent study of Ragma (2014) revealed

that the students have only poor performance in College Algebra. In

Saint Louis College, the study of Oredina (2009) revealed that the

students had only moderate performances. Additionally, the mathematics

instructors, the researchers of the study, observed that most students

enrolled in College Algebra are not yet ready for the subject. This is

shown in their quizzes, exams and grades. In fact, in a class of 50, more

than 40% have failing grades in their prelim grades. The state of dismal

performances in this subject point out to the fact that the students are

not ready to take up College Algebra.

The foregoing situations encouraged the math instructors to

embark on assessing the level of readiness of SLC students in College

Algebra for school year 2013-2014 as basis for formulating learning

activity sheets.

Theoretical Framework

E. Thorndike (1978) proposed the law of readiness. The readiness

theory states that a learner’s satisfaction is determined by the extent of

5

his preparatory set. It implies the need of acquisition of necessary pre-

requisite skills so that learners will be ready to tackle the succeeding

lessons and at the same time, they can anchor the new lessons to the

previous ones. This theory serves as the main foundation of the proposed

study since it looked into the level of readiness of students in College

Algebra.

Central to the theory of readiness are the concepts where the

theory is founded. According to the theory, there are several factors

affecting readiness. These include maturation, experience, relevance of

materials and methods of instruction, emotional attitude and personal

adjustment. In addition, the same theory proposes several strategies in

building readiness skills. These strategies include the analysis of skills

using diagnosis or pre-assessment and the design of an instructional

intervention programmed to match the individual’s level of readiness.

This central concept of the readiness theory provided the justification of

formulating a College Algebra readiness test as a form of diagnostic

assessment among students.

Moreover, Jeane Piaget (1964), a Swiss psychologist and biologist

formulated one of the most widely used theories of cognitive

development. Piaget’s theory stresses that the potentials of formal

operational thought develop during the middle school years. These

6

potentials can be actualized by ages 14, 15, or 16 years. Apparently,

learning mathematics involves formal operational thought. The research

of Piaget shows that individuals are formal operational thinkers by ages

15 or 16, the usual ages of college freshmen in the Philippines. In this

connection, this study utilizes this Piaget’s theory to investigate whether

a group of college freshmen performs at the expected level of formal

thought, in other words, if they are ready to take up collegiate courses in

Mathematics.

The law of readiness and its central concept laid the concepts in

structuring the research. The cognitive development theory, on the other

hand, gave additional foundations in formulating the learning activity

sheets.

The learning activity sheets are worksheets that contain the topic,

its objectives, activities with the teacher and activities for group and

independent learning.

Conceptual Framework

Teaching and learning mathematics becomes more meaningful and

directed when the teachers know the level of the learners’ preparation

and when the learners are ready to grasp concepts presented in the

teaching-learning process. In this manner, the teachers know where to

7

start, how to start and what concepts need to be more emphasized;

students, on the other hand, know when to study more and where to

focus on.

As part and parcel of improving performance, instructional

materials such as worktext, activity books and activity sheets are

inevitable. The learning activity sheets are instructional support

materials that provide supplements to classroom instruction and give

opportunities for students to study on their own and deal with some

more additional exercises. These materials provide avenue for the

students to enhance more their competencies required in each topic by

providing relevant activities pertinent to the full understanding of the

topic. Students can even have advanced studies and make study work

using the learning activity sheets.

It is in this light that this study is formulated and thought of. The

research paradigm in figure 1 highlights the relationship of the indicated

variables. The input incorporates the profile of the respondents along

sex, high school graduated from and the mathematics high school final

grade. It also includes the level of readiness of the students along

elementary topics, special products, factoring, rational expressions,

linear equations, systems of linear eqautions and radicals and

exponents.

8

The process includes the interpretation and analysis of the profile,

the level of readiness of the students, the strengths and weaknesses

based on the level of readiness, the correlation between the profile

variables and the level of readiness, and the difference among the level of

readiness among the three colleges: ASTE-IT-CRIM, CCSA, CEA.

The output, therefore, are validated learning activity sheets in

College Agebra.

9

Process Output Input

Validated

Learning

Activity Sheets

in College

Algebra for

Saint Louis

College

I. Analysis and

Interpretation of:

a. Profile

b. Level of Readiness

II. Correlational

Analysis of Profile and

Level of Readiness

III. Difference on the

level of readiness

among ASTE-IT-

CRIM, CCSA, CEA

IV. Analysis and

Interpretation of the

Strengths and

Weaknesses of the

Students in College

Algebra

III.

I. Profile of the Students

in College Algebra

along:

a. gender

b. type of high school

graduated from

c. HS Math IV grade

II. Level of Readiness of

the students in

College Algebra along:

a. Elementary Topics

b. Special Products

and Patterns

c. Factoring

d. Rational

Expressions

e. Linear Equations

in One Variable

f. Systems of Linear

Equations in Two

Variables

g. Exponents and

Radicals

Figure 1. The Research Paradigm

10

Statement of the Problem

This study aimed primarily to determine the level of readiness of

frsehmen in College Algebra in Saint Louis College for the first semester,

school year 2013-2014. Specifically, it aimed to answer the following

questions:

1. What is the profile of the students in College Algebra along:

a. Gender;

b. High School Math IV Final Grade; and

c. Type of High School Graduated from?

2. What is the level of readiness of the students along the following

topics in College Algebra:

a. Elementary Topics;

b. Special Products and Patterns;

c. Factoring;

d. Rational Expressions;

e. Linera Equations in One Variable;

f. Systems of Linear Equations in Two Variables; and

g. Exponents and Radicals?

3. Is there a significant relationship between profile and the level of

readiness of the students?

11

4. Is there a significant difference between the level of readiness of

a. ASTE-IT-CRIM and CCSA;

b. ASTE-IT-CRIM and CEA; and

c. CCSA and CEA?

5. What are the major strengths and weakness of the students along

the specified topics in College Algebra?

6. Based on the results, what learning activity sheets can be

proposed?

Hypotheses

The researchers were guided with the following hypothesis:

1. There is no significant relaionship between profile and the level of

readiness of the students in College Algebra

2. There is no significant difference among the level of readiness

among ASTE-IT-CRIM, CCSA, CEA.

Importance of the Study

The researchers considered this endeavor vital not only to them as

mathematics instructors, but also to the school community specifically

the administrators, students as well as future researchers.

The SLC Administrators. The results of this study can serve as

one of the bases for curricular evaluation and planning. It will also guide

12

the administrators in their conscious effort to undergo planned changes

in drawing up systematic scheme of evaluating students’ performance.

The Mathematics Instructors. The knowledge of the level of

readiness including the specific areas of deficiencies of their students will

lead them to a conscientious and periodic evaluation of the courses of

study. They will be led in formulating instructional strategies and

interventions that suit their students’ level of readiness.

The students. The output of this study can enhance the students’

readiness level; thus, increasing their competence level in College

Algebra.

The future researchers. The future researchers can make use of

this study in formulating researches in other disciplines.

Definition of Terms

The following terms are operationally defined to further understand

this study:

College Algebra. This is a requisite subject in college. The topics in

this subject include elementary topics, special product patterns,

factoring patterns, rational expressions, linear equations in one

unknown, systems of linear equations in two unknowns and exponents

and radicals.

13

Elementary Topics. These topics include concepts on sets,

real number system and operations, and polynomials.

Factoring patterns. These include the topics in factoring

given a polynomial. These include common monomial factor, perfect

square trinomial, general trinomial, factoring by grouping and factoring

completely.

Linear Equations in One Unkown. This includes topics on

equations with one variable such as 2x- 4 = 10 and 5x - 2x=36. The main

thrust of this topic is for an unkown variable to be solved in an equation.

Rational Expressions. These are expressions involving two

algebraic expressions, whose denominator must not be equal to zero.

This includes topics on simplifying and operating on rational

expressions.

Special Product Patterns. These topics include the patterns

in multiplying polynomials easily. These patterns include sum and

difference of two identical terms, square of a binomial, product of two

binomials, cube of a binomial and square of a trinomial.

Systems of Linear Equations in Two Unknowns. This topic

discusses how the solution set of a given system is solved. The methods

that are used in this certain topics include graphical, substitution and

elimination methods.

14

Readiness Level. This is the degree of preparation of the students

along the specified topics in College Algebra. This is categorized into:

highly ready, ready, slightly ready and not ready.

Strengths. An area under readiness level is considered strength

when it has a decriptive equivalent of highly ready and above.

Validated Learning Activity Sheets. This is the output of the

study. It consists of the rationale, the learning objectives and the varied

activities that address the needs of the students based on the identified

level of readiness.

Weaknesses. An area under readiness level is considered a

weakness when it has a decriptive equivalent of ready and below.

15

CHAPTER II

METHOD AND PROCEDURES

This chapter presents the research design, the sources of data,

data analysis and ethical considerations.

Research Design

The descriptive method of investigation was used in the study.

Calmorin (2005) describes descriptive design as a method that involves

the collection of data to test hypothesis or to answer questions regarding

the present status of a certain study. This design is apt for the study

since the study is aimed at describing the level of readiness of students

in College Algebra.

Further, since the comparisons on the level of readiness among the

three departments and the relationship of profile and the level of

readiness were established, the descriptive-comparative and the

descriptive-correlational methods were employed, respectively.

Sources of Data

Locale and Population of the Study

16

The total population of 1,349 students enrolled in College Algebra

for the first semester, school year 2013-2014 was surveyed. Since the

population reached 500, random sampling was conducted. The sample

population of the study was computed using the Slovin’s Formula. The

formula is: n =

where:

n = the sample population

N = the population

1 = constant

e = level of significance @ 0.05

Thus, the sample population is 309 students distributed according

to the three departments: 72 for CASTE-IT-CRIM, 155 for CCSA and 82

for CEA.

Table 1 shows the distribution of the number of specified

respondents.

Table 1. Distribution of Respondents

Department N n

CASTE-IT-CRIM 316 72

CCSA 675 155

17

CEA 358 82

Total 1349 309

Instrumentation

Documentary analysis was used to get the needed data for profile,

specifically for gender, high school Math IV final grade and type of

high school graduated from.

To gather the data pertinent to the level of readiness, a researcher-

made test was made. The researcher-made test is 50-point item test

covering all the topics in College Algebra. (Please see appended table of

specifications)

The readiness test was administered by all the Mathematics

instructors during the 2nd week of June in their respective classes. A

one-hour period was allotted to each student. The instructors

guaranteed that calculators were not utilized in taking the readiness

test.

Data Analysis

18

The data which were gathered, collated and tabulated were

subjected for analysis and interpretation using the appropriate statistical

tools. The raw data were tallied and presented in tables for easier

understanding.

For problem 1, frequency counts and rates were used to determine

the status of the profile of the respondents along gender, high school

Math IV final grade and the type of high school graduated from. The

rates were obtained by using the formula below:

R = n x 100 N

where: R - rate

n - number of frequencies gathered in each item

N - the total number of cases

100 – constant

For problem 2, mean and rates were utilized to determine the level

of readiness in College Algebra. The formula for mean is as follows

(Ybanez, 2002):

M = ∑x

N

Where: M – mean

x – sum of all the score of the students

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N – number of students

For problem 3, the Pearson-r moment of correlation was used to

determine the significance of relationship between profile and the level of

readiness in College Algebra. The formula according to Ybanez (2002) is:

where: X – observed data for the independent variable

Y – observed data for the dependent variable

N – size of sample

r – degree of relationship between X and Y

The computed correlation coefficients were subjected to

significance; thus the formula used

(http://faculty.vassar.edu/lowry/ch4apx.html) was:

where: r – computed correlation coefficient

n-2 – degree of freedom

t – degree of significance for r

For problem 4, t-test independent (t-test between means), taken

two at a time was used to determine the difference in the perceptions of

20

the respondents. The formula for t-test for means

(http://en.wikipedia.org/wiki/Student%27s_t-test) is:

where:

= estimator of the common standard deviation of the two

samples

n = number of participants, 1 = group one, 2 = group two.

n – 1 = number of degrees of freedom for either group

n1 + n2 – 2 = the total number of degrees of freedom, which is used

in significance testing.

t = degree of difference

For problem 5, the major strengths and weaknesses were deduced

based on the findings, particularly on the level of readiness in College

Algebra through statistical ranking. An area was considered strength

when it received a descriptive rating of highly ready; otherwise, the area

was considered a weakness.

21

The MS Excel Data Analysis Tool was employed in treating the

data.

Data Categorization

For the profile of the students along high school grade in Math IV,

the scale system was used:

Grade range Descriptive Equivalent

92.6-97.00 Outstanding Performance

88.2-91.59 Very Satisfactory Performance

83.8-88.19 Satisfactory Performance

79.4-83.79 Fair Performance

75-79.39 Poor Performance

For the level of readiness in each topic in College Algebra, the Scale

System was utilized.

Elementary Topics/ Factoring

Score Range Level of Readiness/ DER

7.20-9.00 very highly ready

5.40-7.19 highly ready

3.60-5.39 fairly ready

1.8-3.59 slightly ready

0.00-1.79 not ready

22

Special Products and Patterns/ Systems of Linear Equations

Score Range Level of Readiness/ DER

5.60-7.00 very highly ready

4.20-5.59 highly ready

2.80-4.19 fairly ready

1.40-2.79 slightly ready

0.00-1.39 not ready

Rational Expressions/ Linear Equations in One Variable

Score Range Level of Readiness/ DER

6.40-8.00 very highly ready

4.80-6.39 highly ready

3.20-4.79 fairly ready

1.60-3.19 slightly ready

0.00-1.59 not ready

Exponents and Radicals

Score Range Level of Readiness/ DER

1.60-2.00 very highly ready

1.20-1.59 highly ready

0.80-1.19 ready

0.40-0.79 slightly ready

0.00-0.39 not ready

23

For the general level of readiness, the scale below was used:

40.00-50.00 80%-100% very highly ready

30.00-39.99 60%-79.99% highly ready

20.00-29.99 40-59.99% fairly ready

10.00-19.99 20-39.99% slightly ready

0.00-9.99 0-19.99% not ready

For the strengths and weaknesses, an area was considered

strength if it got descriptive equivalent rating of highly ready and above;

otherwise, it was considered a weakness.

Parts of the Learning Activity Sheets

The learning activity sheets comprise of the rationale, the learning

objectives, the subject matter, the learning activities and sheets.

The learning activities are either with the help of the teacher or are

designed for independent learning.

Ethical Considerations

To establish and safeguard ethics in conducting this research, the

researchers strictly followed and obeyed the following:

The respondents’ names were not mentioned in any part of this

research. The respondents were not coerced just to answer the test.

24

Proper document sourcing or referencing of materials was done to

ensure copyright.

A communication letter was presented to the registrar’s office to

ask authority to get the needed data on profile.

25

CHAPTER III

RESULTS AND DISCUSSION

This chapter presents the data analysis and interpretation of the

gathered data.

Profile of the Students

The first problem of the study is on the profile of the students in

College Algebra.

Table 2 presents the profile of the students along sex, type of high

school graduated from and their high school final math grade. It shows

that out of 309 students, 161 or 52.10% are males while 148 or 47.90%

are females. This means that there are more male respondents than the

females. This is easy to understand since the courses which include

college algebra in their curriculum for the first semester are along

engineering, architecture, business administration and criminology.

Massey (2011) highlights that male students are more inclined to

enrolling to a course aligned to mathematics, engineering, architecture,

business management and criminal education. Registrar records as of

July 2013 also indicated that there were really more males than females.

26

Further, out of 309 students, 125 or 40.45% graduated from

public schools while 184 or 59.55% graduated from private schools. This

means that majority of the students came from private schools in and

Table 2. Profile of Students

Profile variables Frequency Rate

A. Sex

Male

Female

161

148

52.10%

47.90%

B. Type of High School Graduated from

309 100%

Public

Private

125

184

40.45%

59.55%

C. HS Final Math Grade

309 100%

75-78

79-84

39

106

12.62%

34.30%

27

85-88

89-93

94-97

92

64

8

309

29.77%

20.71

2.59%

100%

outside of La Union. This is because majority of the students came from

families that can afford education offered in the private schools. A

testament to this is their enrolment in SLC, a private HEI.

Lastly, it also shows the grade range of the students in their high

school mathematics subject. It reveals that 39 or 12.62% have grades

ranging from 75-78%, interpreted as poor performance, 106 or 34.30%

have grades ranging from 79-84%, interpreted as fair performance, 92 or

29.77% have grades ranging from 85-88%, interpreted as satisfactory

performance, 64 or 20.71% have grades ranging from 89-93%,

interpreted as very satisfactory performance and only 8 or 2. 59% have

grades ranging from 94-97, interpreted as outstanding performance. It

means that majority of the students had fair-satisfactory performance in

their high school mathematics. This points out to the fact that the

students had not fully mastered the desired learning competencies of

28

Mathematics IV. The finding of the study jibes with Oredina (2011)

stating that students in College Algebra had not fully mastered the

competencies.

Level of Readiness in College Algebra

The second problem of the study is on the level of readiness of the

students in College Algebra.

Table 3 shows the level of readiness of students in College Algebra.

It is shown that the students have a mean score of 2.87 or 31.88% in

elementary topics, 3.70 or 52. 86% in special product patterns, 3.6 or

40% in factoring, 3.84 or 48% in rational expressions, 3.36 or 42% in

linear equations in one variable, 2.8 or 40% in systems of linear

Table 3. Readiness in College Algebra

TOPIC Mean Score Rate Descriptive

Equivalent

Elementary Concepts 2.87 31.88% Slightly ready

Special Product Patterns

3.70

52.86%

Fairly Ready

Factoring

3.6

40%

Fairly Ready

29

Rational Expressions 3.84 48% Fairly Ready

Linear Equation in One

Variable

3.36

42%

Fairly Ready

Systems of Linear Equations in

Two Variables

2.8

40%

Fairly Ready

Exponents and Radicals

1.13

56.50%

Fairly Ready

TOTAL 21.3 42.60% Fairly Ready

equations and 1.13 or 56.50% in exponents and radicals. Thus, the

students were slightly ready in elementary concepts while ready in the

other remaining topics which include special products and factoring,

rational expressions, linear equations, systems of linear equations and

exponents and radicals. This means that the students were not so much

prepared to hurdle topics on sets, number line, operations on integers,

algebraic expressions and polynomials. Further, this means that the

students were prepared to apply special product and factoring patterns,

manipulate rational expressions, solve linear equations and systems and

deal with expressions involving exponents and radicals. However, since

30

the rates of the mean scores are only between 30-57%, the students still

lack the necessary mastery to be able to hurdle the challenges of the

specified topics in College Algebra.

Generally, the students’ mean score is 21.3, equivalent to 42.60%,

interpreted as ready. Thus, students are generally ready for the course

content of College Algebra. They are familiar with the course contents

since majority of the contents of the course are just a review of high

school mathematics. However, it can be construed that students have

not really mastered well the competencies required in each topic.

Testament to this is the fair-poor performance of the students based on

their high school math grades.

This finding of the study corroborate with Kuiyuan (2009) stating

that the level of readiness of the students in College Algebra is at the

moderate level only. It was mentioned that students did not possess the

needed pre-requisite skills.

Correlation between Profile and Level of Readiness

The third problem of the study is on the significant relationship

between the profile and the level of readiness of the students.

Table 4 shows the relationship between profile and the level of

readiness of the students. It shows that the correlation coefficient

between sex and the level of readiness is 0.18, interpreted as negligible

31

Table 4. Correlation between profile and level of readiness

Profile Variables Level of

Readiness

t-

critical

@ 0.05

Interpretation

Sex 0.18

Negligible

0.112 Significant

Type of HS graduated

from

0.12

Negligible

0.112 Significant

HS math final grade 0.63

marked

0.112 Significant

correlation. This negligible correlation is significant at 0.05 level of

significance. This signifies that sex does not significantly affect the level

of readiness and vice versa. Thus, sex does not determine the level of

readiness in college algebra.

Further, it also shows that the correlation coefficient between type

of high school graduated from and the level of readiness is 0.05. This

negligible correlation is significant at 0.05 level of significance. This

denotes that the type of high school graduated from does not

significantly affect the level of readiness and vice versa. Thus, the type of

32

high school graduated from does not necessarily determine the level of

readiness. This is true since schools, regardless of type, offer the same

curriculum provided by the Department of Education, hence, the

students still learned the same content in their secondary schools.

Moreover, it also divulges that the correlation coefficient between

high school math grade and level of readiness in College Algebra is 0.63.

This marked correlation is significant at 0.05 level of significance. This

means that high school math grades significantly affect the level of

readiness. This means that the high school mathematics performance of

students affect their level of readiness in College. This is easy to

understand since the high school mathematics subjects provide solid

foundation for students to hurdle the course contents of College Algebra,

especially so that the contents of the course are review of the high school

topics. This finding of the study corroborates with the study of Kuiyuan

(2009) stating that high school GPA strongly correlates to college

readiness.

This finding run parallel to the study of Kuiyuan (2009) revealing

that high school and college GPA had strong correlation with the

students’ level of readiness in College Algebra, while the other factors

such as national exam scores, type of school graduated from had weak

correlations.

33

Comparison on the Level of Readiness of the Students in the

Three Colleges

The fourth problem of the study is the significant difference

between the level of readiness of the students in the three colleges,

CASTE-IT-CRIM, CCSA, and CEA.

Table 5. Comparison on the Level of Readiness

Departments Mean

Difference

Computed t-

value

p-value Interpretation

ASTE-IT-

CRIM and

CCSA

2.173 1.80 0.0729 Not

Significant

ASTE-IT-

CRIM and

CEA

3.82 3.09 0.0023 Significant

CCSA and

CEA

1.64 1.43 0.1531 Not

Significant

Table 5 reveals the comparison of the level of readiness of students

in the three (3) departments of SLC, the CASTE-IT-CRIM, the CCSA, and

34

the CEA. It shows that the comparison on the level of readiness of

students from CASTE-IT-CRIM and CCSA has a computed t-value of

1.80. This is not significant at 0.05 level of significance since the p-value

is larger than 0.05. Thus, it can be inferred that the mean difference of

2.173 is not significant. This denotes that there is no significant

difference in the performance of the students in the CASTE-IT-CRIM and

the CCSA. Thus, it is safe to construe that students in CASTE-IT-CRIM

are not better than CCSA students, and vice versa. This finding runs

parallel to the hypothesis of the study that there is no significant

difference in the performance of the students in the two identified

departments.

Further, it shows that the comparison on the level of readiness of

students from CASTE-IT-CRIM and CEA has a computed t-value of 3.09.

This is significant at 0.05 level of significance since the p-value is smaller

than 0.05. Thus, it can be inferred that the mean difference of 3.82 is

significant. This denotes that there is a significant difference in the

performance of the students in the CASTE-IT-CRIM and the CEA. This

finding does not run parallel to the hypothesis of the study that there is

no significant difference in the performance of the students in the two

identified departments. Thus, students in CEA are better in College

Algebra than the students in CASTE-IT-CRIM. This is easy to understand

35

since students enrolled in engineering and architecture courses are

inclined to mathematics.

It also shows that the comparison on the level of readiness of

students from CCSA and CEA has a computed t-value of 1.43. This is not

significant at 0.05 level of significance since the p-value is larger than

0.05. Thus, it can be inferred that the mean difference of 1.64 is not

significant. This denotes that there is no significant difference in the

performance of the students in the CCSA and the CEA. This means that

students CSA are not better in College Algebra than students in the CEA,

and vice versa. This finding runs parallel to the hypothesis of the study

that there is no significant difference in the performance of the students

in the two identified departments.

Strengths and Weaknesses in the Level of Readiness in College Algebra

The fifth problem of the study is the strengths and weaknesses in

the level of readiness of the college students.

Table 6 shows the strengths and weaknesses of the students in

College Algebra as culled out from their level of readiness. It can be seen

from the table that all the content areas under College Algebra are

considered as weaknesses of the students. This means that the students

are not that prepared in taking the subject. This implies that they did not

36

possess yet the needed skills needed to hurdle the demands of the

course.

This finding of the study harmonizes with the study of Leongson

(2001) that students’ performance in College Algebra is alarming. It was

mentioned that the students were at the poor-fair levels only.

This finding also corroborates with the study of Ragma (2014)

revealing that all content areas in College Algebra are found to be

constraints. He explained that the students were not able to successfully

imbibe the skills in algebraic concepts and manipulations.

Table 6. Strengths and Weaknesses in College Algebra

TOPIC Mean Score Rate Classification

Elementary Concepts 2.87 31.88% Weakness Special Product Patterns

3.70

52.86%

Weakness

Factoring

3.6

40%

Weakness

Rational Expressions

3.84

48%

Weakness

Linear Equation in One Variable

3.36

42%

Weakness

Systems of Linear Equations in Two Variables

2.8

40%

Weakness

Exponents and Radicals

1.13

56.50%

Weakness

37

CHAPTER IV

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

This chapter incorporates the summary, findings, conclusions and

recommendations of the study.

Summary

The study aimed to determine the level of readiness of frsehmen in

College Algebra in Saint Louis College for the first semester, school year

2013-2014. It specifically looked into the profile of the students, their

level of readiness along the specified topics, the significant relationship

between profile and the level of readiness, the significant difference

betweeen the level of readiness of the students in the three departments

of the college, the strengths and weaknesses based on the level of

readiness and the proposed learning activity package.

The study is descriptive with a validated researcher-made

readiness test as the main data-gathering tool.

Findings

The findings of the study are:

1. a. There were 161 males and 148 females;

b. Out of 309 students, 125 came from public schools while 184 came

from private schools.

38

c. 237 students had a high school math grade ranging from 75-88%;

while 72 had grades ranging from 89-97%.

2. The students were slightly ready in elementary topics while fairly

ready in the remaining topics which include special product and

factoring patterns, rational expressions, linear equations, systems of

linear equations and exponents and radicals. Generally, they were failry

ready in College Algebra.

3. a. There was a negligible correlation between sex and level of

readiness.

b. There was a negligible correlation coefficient between type of high

school graduated from and level of readiness.

c. There was a marked correlation between high school final math

grade and level of readiness.

4. a. There was no significant difference between the level of readiness of

students from the CASTE-IT-CRIM and CCSA.

b. There was a significant difference between the level of readiness of

students from the CASTE-IT-CRIM and CEA.

c. There was no significant difference between the level of readiness of

students from the CCSA and CEA.

5. All the topics were found to be weaknesses.

39

Conclusions

In the light of the above-cited findings, the following conclusions

are drawn:

1. a. Majority of the students were males.

b. Majority of the students were graduates of private high schools.

c. Majority of the students had fair-poor performance in their high

school mathematics.

2. The students were not able to acquire sufficient pre-requisite skills to

be able to hurdle the demands of College Algebra.

3. a. Sex did not significantly affect level of readiness and vice versa.

b. Type of high school graduated from did not significantly affect the

level of readiness.

c. High school final math grades significantly affected the level of

readiness.

4. a. The level of readiness of students from the CASTE-IT-CRIM and

CCSA was the same. CASTE-IT- CRIM students were not better than

CCSA students and vice versa.

b. The level of readiness of students from the CASTE-IT-CRIM and

CEA was not the same. CEA students were better than CASTE-IT-CRIM

students.

40

c. The level of readiness of students from the CCSA and CEA was the

same. CCSA students were not better than CEA students and vice versa.

5. Students were really not that ready to take College Algebra course.

Recommendations

Based on the conclusions of the study, the researcher recommends

the following:

1. The learning activity sheets should be adopted by mathematics

instructors.

2. The readiness test used in this research should be utilized as a

diagnostic tool by all College Algebra instructors before starting the

formal lessons every start of the school year.

3. Students who wish to enroll in mathematically-inclined subjects

should be really good in mathematics.

4. A future study looking into the effectiveness of the learning activity

should should be conducted.

41

BIBLIOGRAPHY

A. Books

Becker, Jon (2004). Flash review for college algebra. U.S.A.: Pearson

Education, Inc.

Barnett, Raymond (2008). College algebra with trigonometry. Boston: McGraw Hill.

Bautista, Leodegario, et al. (2007). College algebra. Quezon City: C & E

Publishing, Inc.

Calmorin, L. (2005). Methods of research and thesis writing. Manila: Rex Bookstore, Inc.

Cayabyab, Sheila P., et al. (2009). College algebra for filipino students.

Quezon City: C & E Publishing, Inc.

Covar, Melanie M., and Rita May L. Fetalvero (2010). Real world mathematics, intermediate algebra. Quezon City: C & E Publishing Inc.

Ee, Teck. (2011). Maths gym. Singapore: SAP Group Pte Ltd.

Huettenmueller, Rhonda (2003), Algebra demystified. New York: McGraw-Hill Companies Inc.

Lial, Margaret (2001). College algebra. Boston: Addison-Weley, Inc.

Oredina, Nora (2011). College algebra. Manila: Mindshapers Co., Inc.

Parreno, Elizabeth (2001). College Algebra. Mandaluyong City: Books atbp.

Petilos, Gabion (2004). Simplified college algebra. Quezon City: Trinitas

Publishing, Inc. Rider, Paul (2009). College algebra. New York: Macmillan Co. Inc.

42

Sta. Maria, Antonia C. et al, (2008). College mathematics: modern approach. Mandaluyong City: National Bookstore.

B. E-journals and Online Sources

http://www.emergo.ca/RecentCourses-Disorder_201111-

Celebrating_Women,_Understanding_Men_Introduction.htm (retrieved July 23, 2013)

http://www.maa.org/college-algebra (retrieved February 21, 2014)

Leeyn, Shiela http://www.enablemathcollege.com/enablemath/algebra.jsp (retrieved February 21, 2014)

http://www.greatschools.org/students/academic-skills/354-why-

algebra.gs (retrieved January 20, 2013) Moses, Robert (2009). The Algebra Project; http://answers. ask. com/

science/ mathematics/ why_is_algebra_important (retrieved February 20, 2014)

http://www.nytimes.com/ (retrieved February 10, 2014)

The Journal of Language, Technology & Entrepreneurship in Africa, Vol. 2, No.1, 2010

Kuiyuan, L. P. (2007). “A study of college readiness in college algebra.” The e-Journal of Mathematical Sciences and Mathematics Education

Retrieved July 29, 2013 from http://www.uwf. edu/mathstat/Technical%20Reports/Assestment2%202010-1-6.pdf

Leongson, J. A. (2001). Assessing the mathematics achievement of college

freshmen using Piaget’s logical operations. Bataan, Philippines. Retrived August 11, 2013 from www.cimt. plymouth.ac.uk/

journal/limjap.pdf

43

http://www.mariancatholichs.org/download.axd?file=ba3db97c-eee0-475b-a77b-7182c50b7ad9&dnldType=Resource (retrieved

February 21, 2014) http://www.google.com.ph/url?sa=t&rct=j&q=worskheets%20in%20sign

ed%20numbers%20.doc&source=web&cd=1&cad=rja&ved=0CCcQ

FjAA&url=http%3A%2F%2Fwww.yti.edu%2Flrc%2Fimages%2FMat

h_Integers.doc&ei=kqkJU8qRLaidiAfEmYHYBw&usg=AFQjCNFJPdi

Bq4UQGqn-1fLtkbypEI9_gQ (retrieved February 21, 2014)

http://www.google.com.ph/url?sa=t&rct=j&q=activities%20in%20polyno

mials.doc&source=web&cd=2&cad=rja&ved=0CCwQFjAB&url=http

%3A%2F%2Fwww.wsfcs.k12.nc.us%2Fcms%2Flib%2FNC0100139

5%2FCentricity%2FDomain%2F822%2FPolynomials%2520Handou

t.doc&ei=TawJU730IISZiQevhoCYBw&usg=AFQjCNE0gj5KIHWOqs

oUHmeEQAqWGJfN0A (retrieved January 15, 2014)

http://www.google.com.ph/url?sa=t&rct=j&q=worksheets%20in%20facto

ring%20patterns.doc&source=web&cd=10&cad=rja&ved=0CFYQFj

AJ&url=https%3A%2F%2Fwww.santarosa.k12.fl.us%2Flessonplan

s%2FHigh%2FPreviousYear%2FWorrell%2520Lesson%2520Plan.do

c&ei=2LQJU6WcJunkiAf6jYHwBw&usg=AFQjCNFp4nwVpTc9VIyfR

5L7fkSPuF0W_g&bvm=bv.61725948,d.aGc (retrieved February 21,

2014)

C. Unpublished Researches

Oredina, Nora A. (2010). “A validated worktext in college algebra.” Institutional Research. Saint Louis College, City of San Fernando,

La Union. Ragma, Feljone G. (2014). “Error Analysis in College Algebra in the Higher

Education Institutions of La Union.” Unpublished Dissertation. Saint Louis College, City of San Fernando, La Union.

44

APPENDIX

Saint Louis College

City of San Fernando, La Union

READINESS TEST IN COLLEGE ALGEBRA

Name:_________________________________Yr & Course:________________Score:______

I. MULTIPLE-CHOICE TYPE: Write the letter of the correct/best answer on the answer matrix given. WRITE

CAPITAL LETTERS ONLY. (50 pts.)

1. If U is the set of integers and set A is the set of counting numbers, what is A’?

a. 0 c. the union of whole and negative numbers

b. whole numbers d. 0 and the negative numbers

2. In a survey of a group of college freshmen, it was found out that 800 love Mathematics, 750 love English

and 450 love both subjects. How many students were surveyed?

a. 1,100 b. 1,250 c. 1,550 d. 2,000

3. Which of the following statements is always true?

a. Decimals are rational numbers. c. Integers are fractions.

b. Zero is counting. D. Zero is whole.

4. Which property is being illustrated by (2x+y) + 4 = 4 + (2x + y)?

a. distributive b. associative c. commutative d. identity

5. What is the answer in 22+3•4-12+8-(2-4)3+8÷(-2+4)?

a. 0 b. 12 c. 24 d. -1

6. Which has a degree of 15?

a. 2x9y5z b. 12x13y2 c. 15x15 d. all of the options

7. What is the result when –{-[-4(-x)-(3x-(x+2))]} is simplified?

a. 7x-2 b. -2x +2 c. -2 d. 2x+2

8. What is the simplified form of [(4x3y5)/ (2x4y3)]2 ?

a. 4x2y4 b. (4y4)/x2 c. 2y2/x4 d. 22x4y2

9. Which is equal to {12,500 x3]0 – (5x/5)?

a. 1-x b. -1 c. 5-x d. 1+x

10. What is the product of (2x-y)(x-y+z)?

a. 2x +y-z b. 2x2-3xy+2xz+y2-yz c. 2x2-y2-yz d. 2x2+x-y+2z

11. The volume of a rectangular solid is expressed as 4x3+6x2+4x+2. If its base area is expressed as

4x2+2x+2, what is the solid’s

height? a. 4x + 4 b. 4x2 + 4 c. x+1 d. x-1

12. Which is the product of (2x-4)(2x+4)? a. (2x-4)2 b. 4x2-16 c.4x2+8 d.

4x2+16

13. Which is the square of the binomial (2x+3y)? a. 4x+9y b. 4x2+9y2 c. 4x2+6xy+9y2

d. 4x2+12xy+9y2

14. Which is the expanded form of (x+2)3? a. x3+23 b. x3+6x2+12x+8 c. x3-6x2-12x+8

d. x3+6x2+12x+6

45

15. Which is the expanded form of (x+y+3)2?

a. x2+y2+9+2xy+6x+6y c. x2-y2+6+2xy+6x+6y

b. x2-y2+9+2xy-6x+6y d. x2+y2+6+2xy+6x+6y

16. What is the area of a square if its side measures (2x-12) cm?

a. 4x- 48 cm2 b. 4x2-24x+144 cm2 c. 4x2-48x+144 cm2 d. 4x2 +144 cm2

17. Which is the common monomial factor of the expression 2x5y + 10x3y7 – 6x4y3?

a. 2xy b. 2x5y7 c. x3y d. 2x3y

18. Which is the factored form of x2n + x n+2?

a. xn (xn+x2) b. x2 (xn+x2) c. x2 (xn+x) d. cannot be factored

19. Which is the factored form of 16x2-36y4?

a. (4x+6y2) (4x-6y2) c. (4x-6y2) (4x-6y2)

b. (8x+18y2) (8x-18y2) d. (4x+6y) (4x-6y)

20. Which of the following is a perfect square trinomial?

a. 4x2-20xy+25y2 b. x2+2xy + y2 c. x2-10x+25 d. all options

21. Which is the factored form of x2-6x+8?

a. (x-8)(x+1) b. (x-4)(x+2) c. (x-8)(x-1) d. (x-4)(x-2)

22. Which is not factorable?

a. x2+1 b. x2-1 c. 2x+4xy d. 100-x2

23. Which is the factored form of x2-2xy+y2-x+y?

a. (x+y)(x-y-1) b. (x-y)(2y) c. (x-y)(y-1) d. unfactorable

24. Which must be placed on the blank (m8-n8) = (m4+n4)(m2+n2) (____) (m-n) to make a correct factoring

process?

a. m-n b. m2-n2 c. m+n d. n2

25. The area of a square is expressed as 16x2+24xy+9y2, what is the measure of a side of the square?

a. 4x-3y b. 4x +3y c. 16x + 9y d. 16x- 9y

26. Which is the simplified form of 6x8/8x6?

a. ¾ b. 3x/4 c. 3x2/4 d. 3/4x

27. Which is the answer when (5t/8) is multiplied to (4/3t2)?

a. 5/6t b. 5/6 c. 5/t d. 6t

28. Which is the quotient of (2x/3) and (x/9)?

a. 2 b. 3x c. 6x d. 6

29. Which is the sum of (5/4x2) and (7/6x)?

a. 19x/12x2 b. 19/12x2 c. (15+14x)/12x2 d. (15+4x)/12

30. Which is not a rational expression?

a. 5x/x b. (2x-1)/(x-1) c. 2x/ x d. none

31.Which is the simplest form of (2x-4)/ (x2-4)?

a. ½ b. 2/(x+2) c. 2/(x-2) d. 2x-4

32. Which is the sum of 1/3 and 1/5?

a. 2/8 b. ¼ c.8/15 d. cannot be added

46

33. Which is the simplified form of the complex fraction, ?

a. ½ b. 7/10 c. ¼ d. 1/5

34. Which is the value of x in 2x+5x+3 = -11?

a. 2 b. 14 c. -2 d. -14

35. One number is greater than the other by 13. If their sum is 41, what are the 2 numbers?

a. 12, 29 b. 40, 1 c. 27, 14 d. 16, 25

36. If a rectangle has a length of 3 cm less than four times its width and its perimeter is 19 cm, what are the

dimensions of the rectangle? a. 3 and 7 b. 5.25 and 10 c. 2.5 and 7 d. 8 and

11

37. Lorna is 20 years older than her daughter, Rudylyn. In ten years, she will be twice as old as her

daughter, how old are they now?

a. 25, 35 b. 10, 20 c. 15, 25 d. 20,30

38. Two buses leave the station at the same time but in different directions. Bus A drives at a distance of 24

km while Bus B at a distance of 28 km. If they arrive at their destinations at the same time, what are their

average rates if Bus A’s average rate is 12 km/hr less than Bus B’s? a.72 kph, 84 kph b. 7 kph,

12 kph c. 2 kph, 8 kph d. 70 kph, 80 kph

39. An encoder can finish a file of documents in 4 hours. Another encode can do the same job in 3 hours.

How long will it take for the job to be done if the 2 encoders help each other?

a. 1 hr 13 mins and 13.21 secs c. 1hr 42 mins and 51.43 secs

b. 2 hr 12mins and 12.23 secs d. 2 hr 2mins and 12.23 secs

40. Feljone has 56 bills consisting of 10-peso and 5-peso bills, If he has a total of 440 pesos, how many 10-

peso bills does he have?

a. 32 b. 18 c. 24 d. 48

41. Three consecutive even integers have a sum of 138. What is the largest among the three numbers?

a. 40 b. 42 c. 44 d. 48

42. In what quadrant can (-2, 4) be located? a. QI b. QII c. QIII

d. QIV

43. What is the slope of 2x- 3y = 4? a. 2/3 b. -4/3 c. -2/3

d. 4/3

44. Which has an undefined slope? a. diagonal line b. horizontal line c. vertical line

d. all lines

45. Which equation has an x- intercept of 8 and y-intercept of -16?

a. y = 2x-16 b. y = -2x -16 c. y = -2x +16 d. y = 2x +16

46. Which is the solution of the system x- y =5 ?

X+2y=2

a. (0,-5) b. (4,-1) c. (3,1) d. (1,1)

47. Which of the following have infinitely many solutions?

a. parallel lines b. skew lines c. intersecting lines d. perpendicular lines

47

48. The sum of two numbers is 315. Their difference is 119. What are the two numbers?

a. 115, 200 b. 15, 300 c. 150, 165 d. 98, 217

49. Which is equal to (81)-3/4?

a. ½ b. 1/36 c. 1/27 d. 2/5

50. Which will make the equation correct?

a. 12 b. 16 c. 18 d. 24