CHAPTER I

Background of the Study

Literature has shown that problem solving is increasingly being used in

classroom activities to enhance students’ mathematical learning (Barlow, 2006; English,

1997, 1998). It has now become an important component of mathematics teaching and

learning.

The shift in learning theory from behaviourism to constructivism has had an

enormous impact on the teaching and learning of mathematics (Hatfield, Edwards,

Bitter, & Morrow, 2003). According to von Glasersfeld (1989) students acquire

knowledge by constructing and restructuring it over time which is similar to the

experiential learning theory by Dewey (1938/1997).

School mathematics of the twenty first century is viewed by educators to be that

which should engage a learner in problem solving and reasoning. It should also foster

deep understanding and develop the learner’s critical and analytical thinking. Instruction

should not be limited to plain mastery of algorithms or the development of certain

mathematical skills. It should involve learners in investigation through “exploring,

conjecturing, examining and testing” (NCTM, 1990, p.95). Willoughby (1990) believes

that the abundant books, pamphlets and courses on critical thinking and problem

solving that have been propagated in the 1980s cannot be of help unless certain

pedagogical misconceptions are clarified. This includes prescribed rules such as finding

1
key words in a problem to decide the appropriate operations on the values given in the

problem, or applying arithmetic algorithm to any word problem. Developing critical and

analytical thinking through problem solving takes time and a lot of teacher’s commitment

and dedication. (Willoughby, 1990; Barb and Quinn, 1997).

In the variety of definitions of attitudes towards Mathematics (ATM) proposed in

research studies, two main categories can be identified. Using a simple definition, ATM

is just a positive or negative emotional disposition towards Mathematics (Mc Leod,

1994). This positive or negative feeling is of moderate intensity and reasonable

stability; sometimes it is especially resistant to change. According to Merriam Webster

attitude is the way you think and feel about something. In other words it is the response

towards something. Ma & Kishor (1997) propose a wider definition; they conceive ATM

as “an aggregated measure of a liking or disliking of Mathematics, a tendency to

engage in or avoid mathematical activities, a belief that one is good or bad at

Mathematics, and a belief that Mathematics is useful or useless” (p. 27).

Review of Related Literature

In a study by Maria Nicolaidou and George Philippou entitled Attitudes Towards

Mathematics, Self-Efficacy And Achievement In Problem-Solving, this study aims to

explore the relationship between students’ attitudes towards Mathematics, self-efficacy

beliefs in problem-solving and achievement. Where the possibility of attitudes and self-

efficacy to predict problem-solving performance was also examined. Attitude and

efficacy scales were completed by 238 fifth-grade pupils. The researchers used a

2
specially prepare test, including simple and multi-steps problems. According to the

analysis the shows that a high proportion of students hold positive ATM. Their answers

on the linear scale indicated that 50% adore Mathematics, while 21.8% consider the

subject as one of their favourite lessons. 18.1% declare neutral, choosing the middle of

the scale, and only 10.1% express negative attitudes, hate and disgust. The same

pattern of responses also emerges from students’ feelings analysis, based on the five

pictures of the ATM instrument. Results also revealed significant correlations among

ATM, SE and performance. It is remarkable, however, that correlation between SE and

performance is stronger than correlation between ATM and performance. This is in

agreement to earlier research findings (Hacket & Betz, 1989· Pajares, 1996· Ma &

Kishor, 1997· Middleton & Spanias, 1999). Consequently, it seems that students with

positive ATM have high SE beliefs at a specific domain and achieve better. Similarly,

ATM and SE are predictors of performance, and, consistently with previous findings, the

predictive power of SE was found to be stronger than the corresponding power of ATM

(Hacket & Betz, 1989; Pajares & Graham, 1999· Pintrich, 1999; Zimmermann, 2000).

In a study by Frank Pajares and M. David Miller path analysis was utilized by the

researchers to test the predictive and mediational role of self-efficacy beliefs in

mathematical problem solving. According to the results the math self-efficacy has a

greater power to predict problem solving than was math self-concept, perceived

usefulness of mathematics, or gender (N=350). Gender and prior experience influenced

self-concept, perceived usefulness, and problem solving largely through the mediational

role of self-efficacy. Men had higher performance, self-efficacy, and self-concept and

3
lower anxiety, but these differences were due largely to the influence of self-efficacy, for

gender had a direct effect only on self-efficacy and a prior experience variable.

According to the results of the researchers it shows that self has greater direct effect on

the performance than any of the variables presented in the study. The finding of the

researchers’ findings strengthen Bandura's (1986) claim that self-efficacy beliefs are key

arbiters of human agency and also lend support to researchers who contend that

student motivation may be better explained by these beliefs than by other cognitive or

affective processes (see Schunk, 1989, 1991).

CONCEPTUAL FRAMEWORK

Figure 1 presents the framework of the study. It seeks to find the relationship

between the students’ problem solving skills (dependent variable) and students’

attitudes towards mathematics (independent variable), and students’ problem solving

skills (dependent variable) and students’ self-concept (independent variable),. The data

were taken from first year BSED Mathematics Major Students of Leyte Normal

University, through employing twelve item problem solving involving Sets, Algebra,

Trigonometry, and Geometry, standardized tests of Attitude Towards Mathematics and

Students Self-concept.

4
 Figure 1: Conceptual Framework

Self-Concept

Attitude
Towards Problem Sex
Mathematics Solving
Skills

Statement of the Problem

5
 This study aims to identify the factors related to problem solving skills in

mathematics of BSED first year mathematics major students in Leyte Normal University.

Specifically this seeks to answer the following questions:

1. What is the profile of the students in terms of the following factors?

1.1 Sex

1.2 Attitude towards mathematics

1.3 Self-concept

1.4 Problem Solving Skills

2. Is there a significant relationship between the problem solving skills in

mathematics and the following personal factors:

2.1 Sex

2.2 Attitude towards Math

2.3 Self-concept

Moreover, the following alternative and null hypothesis were formulated:

H a : There is a significant relationship between problem solving skills in math of the first

year mathematics majors and each of the following personal factors:

a. Sex

b. Attitude towards math

6
 c. Self-concept

H o : There is no significant relationship between problem solving skills in mathematics of

the first year mathematics majors and each of the following personal factors:

a. Sex

b. Attitude towards math

c. Self-concept

Chapter II

METHODOLOGY

The study investigated the factors that relate to problem solving skills of first year

mathematics major students in Leyte Normal University. The identified factors in the

study were personal factors. This chapter presents the variables, respondents of the

study, data gathering procedure, instrumentation and statistical tool.

Variables

The following are the variables used in the study:

1. Problem Solving Skills in Mathematics

This is the students’ complex thinking processes that includes

understanding the problem, planning a strategy, carrying out the solution

and looking back at the solution (NCTM, 1989, 1991, 1995, 2000).

7
 2. Students’ Attitude Towards Mathematics

This is an opinion or general feeling of the students about Mathematics.

3. Students’ Self-Concept

This tries to elicit information on the individuals’ report of what he felt and

thought he was.

4. Sex

This will indicate the gender of the respondents who will participate in the

study.

Respondents

The respondents of this study are the selected first year Bachelor of Secondary

Education major in Mathematics students of Leyte Normal University, Tacloban City of

the School-Year 2018-2019. Each respondent answer the three instruments (Problem

Solving, Scale to Measure Attitude towards Mathematics, and Measuring Instrument for

Self-Concept.) A total of 50 students participated in this study.

Data Gathering Procedure

The researchers conducted a survey on May 3, 2019 to first year mathematics

major students of Leyte Normal University. The following questions served as the guide

of the researchers to get the information that is needed in the study or research.

8
Statistical Tool

The following null hypotheses was tested at .05 level of significance.

1. There is no significant relationship between the problem solving skills in mathematics

and the following personal factors:

1.1 Sex

1.2 Attitude towards mathematics

1.3 Self-concept

To analyse the data gathered, the descriptive statistical tool was used. These

were the frequency counts, means, standard deviation and percentages. Spearman’s

rho, Pearson’s r and ANOVA table and Eta were used in determining relationship.

Instruments

The instruments for student of this study were a collection of those developed,

validated, and utilized to fit the objectives of the study.

i. Problem Solving

This is a test consisting of twelve problems involving Sets, Algebra,

Trigonometry, and Geometry. Each problem is evaluated through the analytic

9
 scoring scale from Charles, R. Lester, F.,and O’Daffer, P. (1987). The conceptual

scoring rubric was adapted from Charles, et al. to assess the respondents’ levels

of success in solving problems. Malloy and Jones (1998) have categorized

students as successful if their total scores were 65% or above and unsuccessful

if the scores were below 65%.

LEYTE NORMAL UNIVERSITY

Tacloban City

Name(Optional):__________________________________ Sex: ______

Directions: Solve the following problems completely and neatly.

10
1. There are 40 students in a class. 20 take Chemistry and 25 take French. 8

students take both.

1. Find how many students take none.

2. How many are there in at least one classes?

2. 100 students were interviewed: 28 took chemistry, 32 took Biology, 40 took

Physics, 9 took Chemistry and Biology, 10 took Chemistry and Physics, 8 took

Biology and Physics and 4 took all three.

1. How many students took none of the three subjects?

2. How many students took Chemistry and Biology but not Physics?

3. In a class of 60 students, 40 students like math, 36 like science, 24 like both the

subjects. Find the number of students who like (i) Math only, (ii) Science only (iii)

Either Math or Science (iv) Neither Math nor science.

4. From the top of a cliff 7 meters high, the angle of depression to a boat is 10̊. How

far is the boat from the base of the cliff?

5. A 6 meter ladder just reaches the sill of a window that is 5 meters above the

ground level. What measure of angle does the ladder have to the wall?

6. A tower 5 meter high is located 44 meters from a tall tree. From the top of the

tower, the angle of elevation to the top of the tree is 8̊. How tall is the tree?

7. Jess is painting a giant arrow on a playground. Find the area of the giant arrow. If

one can of paint covers 100 square feet, how many cans should Jess buy?

11
8. The length of a rectangle is 8 more than the width. Its area is 240 ft sq. Write an

equation for its area letting w be width. Then solve the equation for w and also

find the length of each side.

9. A rectangular swimming pool is twice as long as it is wide. A small concrete

walkway surrounds the pool. The walkway is a constant 2 feet wide and has an

area of 196 square feet. Find the dimensions of the pool.

10. A group of 5 boys goes to the theatre for an evening show. The total cost of ticket

is 55 pesos and popcorn is 25 pesos. What is the cost per person?

11. The present age of Jacob’s father is three times that of Jacob. After 5 years, sum

of their ages would be 70 years. Find their present ages.

12. What’s the total number of passenger in the first 7 carriages?

Carriages 1st 2nd 3rd … 7th First 7

carriages

Number of 125 150 175 … ? S7

passenger

12
 ii. Scale to Measure Attitude Towards Any Subject

This is the standardized instrument used in measuring attitude, arranged

at random expressing affective opinions about the subject. Each statement has a

scale value ranging from 0.6 for the most unfavorable opinion and 8.3 for the

most favorable opinion. A blank space under Column I agree was provided for

the acceptance or rejection of the opinion expressed by the corresponding

number. The method of scoring the test was the median score accomplished by

arranging the endorsed items with their equivalent score from highest to lowest

scale. The middle most score was the respondents’ score.

The instrument was based on the book of Shaw and Wright, tested for its

reliability by Ricafort (1970), clarity and relevancy by Pelingon (2019) and Ortega

(2019).

I. A Scale to Measure Attitude Towards Mathematics

Directions: Indicate whether you agree or disagree to the following statements

about the attitudes towards mathematics as they apply to you. If you agree, put a check

mark ( ⁄ ) on the blank under the column AGREE, if not, check on the blank under the

column DISAGREE.

AGREE DISAGREE

1. I really enjoy this subject.

2. This subject is studied by people all over the world.

3. The minds of the students are not kept active in the

subject.

13
4. I have seen not value in this subject.

5. This subject has a very strong attraction for me.

6. This subject teaches me to be accurate.

7. This subject is O.K.

8. I don’t believe this subject will do anybody any harm.

9. Average student never succeed in this subject, so it

should be eliminated from the school.

10. I have no desire for this subject.

11. This subject is of great value.

12. All lessons and all methods used in this subject are

clear and definite.

13. This subject is a good hobby.

14. I could do very well without this subject.

15. This subject is “Much Effort About Nothing”.

16. This is a punishment for anybody to take this subject.

17. I love to study this subject.

18. This subject is very practical.

19. This subject is one which every educated person

must know.

20. This subject is not tiresome.

21. My parents never had this subject so I see no gain in

it.

22. This subject is very dry.

14
 23. This subject is a waste of time.

24. I hate this subject.

25. I would rather study this subject that eat.

26. This subject develops good reasoning leaders.

27. Great leaders studied this subject.

28. This subject will benefit only the brighter students.

29. This subject does not teach you to think.

30. This subject is based on confused ideas.

31. No matter what happens this subject is always the

best.

32. This subject is profitable to everybody who takes it.

33. This subject is a good subject.

34. This subject is not receiving its proper attention by

high school students.

35. I am not interested in this subject.

36. I would not advise anyone to take this subject.

37. I despise this subject.

iii. Self-Concept Inventory Sheet

This instrument was used by Abanador after Yago. This tried to elicit

information on the individuals’ report of what he felt and thought he was. There

were 38 items answerable by YES or NO. The respondents put a check mark

15
 under the column YES if the statement most clearly described himself, and NO if

otherwise. A score of 33-36 denoted a high self-concept, 27-32 as average, and

26 and below as low self-concept. This instrument was established as highly

reliable according to Buban as cited by Yago but was under revision for it was

tested for its clarity and relevancy by Pelingon and Ortega.

II. Measuring Instrument for First Year Mathematics Major Students (Self –

Concept)

Directions: This Inventory asks you what you honestly feel or think about your own

self. There is no right or wrong answer. If you think or feel that the statement most

clearly describes you own self, put a check on the blank under the column YES, if not,

check on the blank under the column NO.

There are thirty-eight statements. Answer all of them. If in DOUBT, choose the

answer which comes closer to your own feeling about yourself at this moment.

YES NO

1. I am a useful person to have around.

2. When failing, I try twice as hard to succeed.

3. I am capable of creating some new things.

4. I can keep my friends.

5. I do not have much interest in events.

6. I feel I can reach the high grades that I set for myself.

7. I am easily discouraged by failure.

8. I try to break old bad habits and build new ones.

16
9. I accept good suggestions from good people.

10. I can do something well.

11. I like boys and girls of my own age.

12. If anything bad ever happens to me, many people would be

happy.

13. I strive in excellence in whatever I do.

14. I can see myself as a successful person.

15. I can laugh at a good joke on myself from my friend.

16. I am afraid to recite in class orally.

17. I feel that I am a useless person.

18. I feel that I am good, on an equal place with many boys and

girls.

19. I accept new and difficult assignments.

20. I make responsible decisions for myself.

21. I think that I can finish college someday.

22. I have some good personal qualities.

23. I have much self – control.

24. I often have to tell lies to impress others.

25. I do not want that I was someone else.

26. I feel that I can trust some people.

27. I want to feel that I am improving my skill every day.

28. I feel that some people trust me.

29. I want to live up to the highest expectation of my family.

17
 30. I do not want to depend on others without losing my temper.

31. I can argue with others without losing my temper.

32. In a group discussion I can contribute worthwhile ideas.

33. I feel that each new day brings new and happy experiences for

me.

34. I consider it very important, the right to express my own ideas.

35. I can obey older people and still feel free to act on my own.

36. I find myself trembling and sweating when I take the test.

iv. Sex

This will indicate the gender of the respondents who will participate in the

study. The following codes will be used:

Description Code

Male 1

Female 0

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 Chapter III

PRESENTATION, DISCUSSION AND FINDINGS

This chapter presents the results and findings of the gathered data. The

discussion starts with the profile of the students. This will be followed by discussions on

the relationship between problem solving skills and its related factors. The last part

discusses conclusions of the study.

Results and Findings

Table 1. Profile of Students

Factors N %

Sex

Male 19 38%

Female 31 62%

Attitude towards mathematics

Highly Favorable 11 22%

Favorable 37 74%

Not Favorable 2 4%

Self-Concept

High 5 10%

Average 40 80%

Low 5 10%

19
 Table 1 presents the profile of the students in terms of their sex, attitude towards

math, and self-concept.

There were more female than male students in the study.

As gleaned from the table, 22% has a highly favorable attitude towards math,

74% favorable and 4% not favorable. Students who scored 7.7 to 8.3 were considered

to show highly favorable attitude towards mathematics. While students who got a score

of 6 to 7.6 possess favorable attitude. A score of 2.3 to 5.9 indicated that students had

unfavorable attitude towards mathematics, this only means that 96% of the students

included in the study like the subject.

In the terms of self-concept, most of the students had average self-concept.

There were three categories for this variable. It was shown in the table that 5 students

had a score from 33-36, which denoted a high self-concept. But those students who

scored 27-32 were described as average. Students who scored 26 and below had low

self-concept. From the data, it was evident that 40 of the sample or 80% of the students

had average self-concept.

Table 2. Problem Solving Skills of First Year Mathematics Majors

Problem Solving Skills N %

Successful 6 12%

Unsuccessful 44 88%

20
 The results showed only 6 or 12% of the respondents got a score of 46.8 and

above out of 72 items. While the 88% of the respondents got a score below 46.8.

Correlation between Problem Solving Skills and its Related Factors

The correlation coefficient and the corresponding p-value of the variables were

presented in table 3.

Table 3. Correlation between Problem Solving Skills and its Related Factors

Correlations

Problem Attitude Self- Sex

Solving Towards Concept

skill Math

Spearman's Correlation
1.000 .184 -.072 .104
rho Coefficient
Problem Solving

skill Sig. (2-tailed) . .201 .621 .471

N 50 50 50 50

Correlation
.184 1.000 .227 -.198
Coefficient
Attitude Towards

Math Sig. (2-tailed) .201 . .113 .168

N 50 50 50 50

Self-Concept Correlation -.072 .227 1.000 -.183

Coefficient

21
 Sig. (2-tailed) .621 .113 . .204

N 50 50 50 50

Correlation
.104 -.198 -.183 1.000
Coefficient
Sex
Sig. (2-tailed) .471 .168 .204 .

N 50 50 50 50

Table 3 shows the Spearman’s rho Correlation of Students’ Problem Solving Skills

and Students’ Attitude towards Mathematics. Based on the SPSS output, the associate

p-value (2-tailed) is .201, which is greater than α (α = 0.5). This implies that the

researchers failed to reject the null hypothesis.

It also showed that the relationship between problem solving skills and self-

concept is not significant since the level of significance is greater than the α . This

implies that regardless of having low or high self-concept, this will not affect the problem

solving skills of the respondents.

The result also showed that there is no significant relationship between problem

solving skills of first year mathematics major students and their sex.

Discussion

22
 Problem Solving Skills N %

Successful 6 12%

Unsuccessful 44 88%

Out of 50 respondents, there were only 6 which is 12% of the samples,

successfully solved the problems. The average of the problem solving skills of first year

mathematics major students is 26.18.

Factors N %

Sex

Male 19 38%

Female 31 62%

Attitude towards mathematics

Highly Favorable 11 22%

Favorable 37 74%

Not Favorable 2 4%

Self-Concept

High 5 10%

Average 40 80%

Low 5 10%

There were more female respondents (31) than male respondents (19) in this

study. Most of the respondents has favourable attitude towards mathematics. Though

23
the respondents are all math major students, there are still some who has not

favourable attitude towards mathematics.

With regards to the personal factors, it was found out that there is no significant

relationship between problem solving skills of the first year mathematics major students

and personal factors in terms of sex, attitude towards math, and self- concept.

Conclusion

Based on the data gathered in this study, the following conclusions were drawn:

1. There is no significant relationship between problem solving skills in mathematics

and attitude towards mathematics of first year mathematics major students.

2. There is no significant relationship between problem solving skills in mathematics

and self-concept of first year mathematics major students.

3. There is no significant relationship between problem solving skills in mathematics

of first year mathematics major students and their sex. This implies that sex will

not affect their problem solving skills.

24
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