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## TABLE OF CONTENTS

ACKNOWLEDGMENT

DEDICATION

ABSTRACT

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

Chapter I

INTRODUCTION

BACKGROUND OF THE STUDY

CONCEPTUAL FRAMEWORK

RESEARCH PARADIGM

STATEMENT OF THE PROBLEM

HYPOTHESES

SIGNIFICANCE OF THE STUDY

SCOPE AND LIMITATION

DEFINITION OF TERMS

Chapter II

REVIEW OF RELATED LITERATURE AND STUDIES

RELATED LITERATURE

PROBLEM SOLVING ABILITIES

RELATED STUDIES

Chapter III

RESEARCH METHODOLOGY

RESEARCH DESIGN

RESPONDENTS OF THE STUDY

RESEARCH INSTRUMENT

RESEARCH PROCEDURE

STATISTICAL TREATMENT

CHAPTER IV

PRESENTATION, ANALYSIS AND INTERPRETATION OF DATA

CHAPTER V

SUMMARY OF FINDINGS, CONCLUSION AND RECOMMENDATION

Conclusions

Recommendations

BIBLIOGRAPHY

## ACKNOWLEDGEMENT

The researcher would like to express his profound gratitude and thanks to the people who served as his inspiration in making this task a reality. Allow him to thank you all for your invaluable assistance, outmost cooperation and endless support towards the successful completion of this study.

Dr, Ricardo A. Wagan, for his valuable suggestions and constructive comments;

Dr. Eden C. Callo, research adviser, who has been very supportive since the beginning and generously gave her time and ideas throughout the preparation of this study;

Dr. Eva F. Puyo, for her assistance, shared knowledge and encouragement to finished this study;

Professor Marilyn P. Santos, for her motivation and valuable suggestions needed in this manuscript as subject specialist;

Professor Lorna C. Daniel, a language consultant, for sharing her expertise in editing this manuscript and enhancing my English proficiency;

Mrs. Virginia P. Balmes, AITE- VP for Academic, for the moral support, encouragement and permission to pursue this study;

Mr. Nilo S. Gret, AITE- President and researcher’s employer, for his moral and financial support to materialized this study;

AITE students, faculty and staff, for their untiring support and cooperation;

Commission on Higher Education (CHED) and Laguna State Polytechnic University, San Pablo City Campus (LSPU-SPC) Librarian, for allowing to used the facilities in gathering information to support this study;

My loving wife, Sierra Maureen D. Valencia and my daughter, Francine Althea who became my inspiration to pursue this study. Thank you for the time, effort and understanding that they have exerted;

My adored parents, and parent-in-laws, for their untiring moral, social and spiritual supports; my brothers and sister-in- law, who always give encouragement to finish this study on time;

And finally, thanks and gratitude are due to ALMIGHTY GOD whose constant love and Holy presence gave his health, strength, wisdom and courage to face the problems, obstacles and trials while undergoing this study.

The Researcher

## DEDICATION

This piece of work is whole heartedly dedicated to my dearest parents, Eleovino D. Valencia and Teresita A. Valencia; adored parent-in-laws, Virgilio R. Deras and Myrna G. Deras; brothers, Elmer and Elvin; sister-in- law, Donna Mae; and Most specially to my dearly loved wife, **Sierra Maureen** and daughter, **Francine Althea**.

Whose words of encouragement and trust have always been my source of inspiration......

## ABSTRACT

This study sought to find out the correlates of mathematics performance and problem solving abilities of freshmen students of Asian Institute of Technology and Education for the first semester, S.Y. 2009-2010. The specific problems which the research paper sought to answer the following: What are the person-related factors of the respondents in terms of the following: Age; Gender; Course; Socio-economic status (Parents’ Educational Attainment, Parents’ Monthly Income and Source of Family Income); and Type of school last attended?; What is the level of mathematics performance of the students in algebra?; How do the respondents perceive the following problem solving abilities in terms of: Verbal; Spatial-visualization; and Quantitative/ numerical?; What is the level of performance of the students in the assessment test with regards to : Verbal; Spatial; and numerical?: Is the Mathematics Performance is significantly related to the perceived problem solving abilities in terms of : Verbal; Spatial; and numerical?; and Does the mathematics performance significantly relate the level of performance in the assessment test?

The descriptive type of research as the data gathering techniques was used to find out the correlates of mathematics performance and problem solving abilities of freshmen students. The subjects of this study were one hundred twenty-two (122) freshmen students from different courses like Computer Hardware Servicing, Computer Programming, Computer Education with E-Commerce and Bachelor of Science in Information Technology.

## Summary of findings:

The findings of this study are as follows:

1. Findings revealed that 86% of the respondents were 16 to 19 years of age, the distribution of gender was almost equal, majority of the respondents took up computer programming course, they were came from the family with a monthly income of P3,000.00 to P5,999.00, and salaries and farming were the source of their family income. The highest number of respondents declared that their fathers and mothers were graduated in high school with 36.89 % and 34.43% of the 122 respondents, respectively. It also find out that 84.43% or 103 respondents out of 122 total number of respondents were graduated from public secondary school.

2. Sixty-eight (68) or 55.74% of the respondents were belonged to the average ranges 80 to 84. It implies that majority of the respondents’ level of mathematics performance were good.

3. This study shows that the respondents’ perceptions on problem solving abilities in terms of verbal, spatial, and numerical were good with an overall mean of 3.05, 2.92 and 2.86.

4. Findings in the level of performance in assessment test are as follows:

a. The mean verbal ability test of the respondents was found to be fair with a computed mean of 12.98 and standard deviation of 3.11.

b. The mean spatial ability test of the respondents was described to be very good with computed mean of 25.10 and standard deviation of 5.96.

c. The respondents earned the mean score of 17.30 indicating good level of performance in numerical ability test.

5. Result of this study shown that the students’ perceptions in problem solving abilities in terms of verbal and spatial- visualization were both negligible with the r- value of 0.02 and 0.14 when correlated to their mathematics performance, while numerical ability denotes low correlation as revealed by r- value of 0.22. It reveals that perceiving good in their mathematical abilities in terms of verbal and special-visualization abilities do not agree with having good mathematics performance in Algebra subject when correlated. Highly worded mathematical problems that involve critical analysis and abstraction couldn’t be easily understood by the students.

6. This study revealed that the verbal ability test with r-value of 0.30, and numerical ability test with r-value of 0.27 were found to be low positive correlation when correlated to their mathematics performance while spatial ability tests with r-values of 0.43 indicating a substantial relationship. These findings implied that the mathematical performance of the students is significantly related to the level of performance in the assessment test in terms of verbal, spatial and numerical.

## Conclusions

In the light of these findings, the following conclusions are drawn:

1. There is no significant relationship between mathematics performance of the students and their perceptions on problem solving abilities in terms of verbal; and spatial- visualization. However, there is a significant relationship between mathematics performance of the students and their perceptions on numerical ability.

Thus, the first hypothesis of this study is accepted and confirmed in terms of verbal and spatial-visualization while it is rejected in terms of numerical ability.

2. There is a significant relationship between students’ performance in mathematics and assessment test in verbal; spatial; and numerical ability test.

So, the second hypothesis is rejected.

## Recommendation

Based on the findings and conclusions drawn, the following are recommended:

1. Students are encouraged to test their problem solving abilities, so that they will know their weaknesses and strengths that need improvement or enrichment.

2. There is a need to improve the level of performance of the students in mathematics, from the level of good to very good, if not higher. It may be obtain through the evaluation of some related factors.

3. More problem solving strategies could do with the teachers or instructors to enhance the abilities of the learners in terms of verbal, spatial and numerical.

4. Further studies be conducted in other schools or educational institution for more comprehensive findings.

## LIST OF FIGURES

Figure 1: Research Paradigm of the Study

Figure 2: Distribution of the Respondents According to Age

Figure 3: Distribution of the Respondents According to Gender

Figure 4: Distribution of the Respondents According to Course

Figure 5: Distribution of the Respondents According to Parents’ Monthly Income

Figure 6: Distribution of the Respondents According to Source of Family Income

Figure 7: Distribution of the Respondents According to Type of School Last Attended

## LIST OF TABLES

Table 1: Distribution of the Respondents to Parents’ Educational Attainment

Table 2: Distribution of the Respondents as to their Mathematics Performance

Table 3: Students’ Perceptions on Problem Solving in terms of Verbal Ability

Table 4: Students’ Perceptions on Problem Solving in terms of Spatial Ability

Table 5: Students’ Perceptions on Problem Solving in terms of Numerical Ability

Table 6: Students’ Performance in the Verbal Ability Test

Table 7: Students’ Performance in the Spatial Ability Test

Table 8: Students’ Performance in the Numerical Ability Test

Table 9: Correlates between Students’ Perceptions in Problem Solving Abilities and Mathematics Performance

Table 10: Correlates between Students’ Performances in the Assessment Test and Mathematics

## Chapter I

## THE PROBLEM AND ITS BACKGROUND

### INTRODUCTION

The world of work continuously changes which includes an increasing demand for technical and scientific skills thus resulting in the offering of different technical courses in the various institutions of the country. Asian Institute of Technology and Education (AITE) in Tiaong, Quezon is one of those institutions that offer technology courses like Computer Hardware Servicing, Computer Programming, Computer Education with E-Commerce, and Bachelor of Science in Information Technology.

Many students find it hard when it comes to problem solving most especially when the problems are in words. Based from some studies, difficulties of the students were the product of lack of diagnosing the problem solving process. Gender differences are also contributing factors to the difficulties because of the misbeliefs of students that if they are females, they can’t perform very well in mathematics. Likewise in the study of Leder (1992) as cited by Zheng Zhu (2007), the achievement of girls in mathematics across range of different contexts was lower than that of the boys, and this was attributed to a variety of reasons including affective factor. In addition to this, the 1996 and 2000 results of the Third International Mathematics and Science Study (TIMSS) were that male performed very well than female.

Problem solving is a process by which the learner discovers a combination of previously learned rules that he/she can apply to achieve a solution for a novel problem situations (Gagne, 1970 as cited by Belen, 2008). As individuals, they have their own abilities to discover or apply what they have learned. But the problem is that, individuals don’t know how and when to use it. Similarly, those abilities in problem solving are sometimes affected by different factors like age, sex, family, environment and etc.

Many schools, companies, and any social institutions conduct a test regarding the abilities of their members. Their purpose is to know the weaknesses and strength of the individuals to help them to be more progressive and to determine their capabilities in their field. The three main ability tests are verbal ability test, spatial-visualization ability test, and numerical ability test. These are the abilities that always exist in daily life, and there is a need to remember that individual differences must be considered.

### BACKGROUND OF THE STUDY

During the enrollment period, some of the students mentioned that they are afraid in mathematics subject. They also believed that they couldn’t pass the mathematics requirement because they are females or males. This is the conclusion of others that there is a gender difference in learning mathematics.

According to Abegail Norfleet James of Virginia Community College (2007), one of the reasons that students give for attending a community college is that the mathematics requirement is less rigorous. Many of her students have told her that they have chosen to seek an associate degree first because they do not feel confident that they can successfully complete the mathematics requirements at a 4-year institution.

Asian Institute of Technology and Education offers technical courses aim to train students develop their skills, personal discipline, creative thinking in line with modern technology and research, and produce committed individuals equipped with the necessary skills and knowledge that would contribute to the country’s goal towards progress and global competitiveness. To make those goals materialized, the curriculum is designed to meet the needs of the industries. On the other hand, industries prepared an assessment test to measure the abilities and performance of the applicants before they hire them. Some of the assessment tests are verbal ability test, spatial-visualization ability test, and numerical ability test.

The researcher noticed that most of the technical courses offered have lots of mathematics subjects and mathematics-related subjects like the Computer Hardware Servicing which consist of six (6) mathematics subjects and four (4) mathematics-related subjects. This is the reason why the researcher decided to conduct a study on the correlation of mathematics performance and problem solving abilities of freshmen students in Asian Institute of Technology and Education.

### CONCEPTUAL FRAMEWORK

This study purposely aimed to find out the relationship between mathematics performance of the college students of AITE and their perceptions regarding their problem solving abilities in terms of verbal, spatial, and numerical. The study further attempted to correlate the performance of the students in mathematics and assessment results in verbal ability test, spatial ability test and numerical ability test.

The conceptual paradigm of this study consists of independent and dependent variables. The independent variables are the person-related factors; perceived problem solving abilities and assessment test scores in verbal, spatial and numerical while the dependent variable is the students’ mathematics performance.

### RESEARCH PARADIGM

The Research paradigm was conceptualized and illustrated in the following hypothetical model.

Abbildung in dieser Leseprobe nicht enthalten

*Figure1. Relationship of Related Variables on Mathematics Performance*

Figure 1 shows the representation of the relationship of variables: Students-related factor, perceived problem solving abilities, assessment test scores correlated on their mathematics performance

### STATEMENT OF THE PROBLEM

This study aimed to determine the correlates between mathematics performance and problem solving abilities of freshmen students of Asian Institute of Technology and Education for the first semester, S.Y. 2009-2010. More specifically, the study attempted to answer the following questions:

1. What are the person-related factors of the respondents in terms of the following

a. Age;

b. Gender;

c. Course;

d. Socio-economic status:

d.1. Parents’ Educational Attainment;

d.2. Parents’ Monthly Income;

d.3. Source of Family Income; and

e. Type of school last attended?

2. What is the level of mathematics performance of the students in algebra?

3. How do the students perceive the following problem solving abilities in terms of

a. Verbal;

b. Spatial-visualization; and

c. Quantitative/ numerical?

4. What is the level of performance of the students in the assessment test with regards to

a. Verbal;

b. Spatial-visualization; and

c. Quantitative/numerical?

5. Is the students’ Mathematics performance significantly related to the perceived problem solving abilities in terms of

a. Verbal;

b. Spatial-visualization; and

c. Quantitative/numerical?

6. Does the mathematics performance significantly relate to the level of performance in the assessment test?

### HYPOTHESES

The following hypotheses served as guide in the conduct of this study.

1. The mathematical performance of the students is not significantly related to the perceived problem solving abilities in terms of

a. verbal;

b. spatial-visualization; and

c. numerical.

2. The mathematical performance of the students is not significantly related to the level of performance in the Assessment Test in terms of

a. verbal;

b. spatial-visualization; and

c. quantitative /numerical.

### SIGNIFICANCE OF THE STUDY

The findings of this study will be beneficial to the following:

**Mathematics Instructor.** It will be a guide to know the weaknesses of their would-be students in his subjects, so that he can adjust his strategies of teaching to have a good outcome. And he can also give an attention to the low level skills in terms of solving mathematical problem.

**The students.** They will benefit from this study because they will know the factor that affects their abilities in solving mathematical problems, and therefore they will find solutions or ways to improve their weaknesses.

**The parents**. It will help them to determine what they need to provide for the improvement of their children’s’ mathematics performances.

**The reader/future researcher**. This study will encourage them to pursue this kind of research to extend support or validate the possible findings of this research.

### SCOPE AND LIMITATION

This study looked into the correlates of mathematics performance and problem solving abilities of the freshmen students in Asian Institute of Technology and Education. It covered the evaluation of the mathematics performance in Algebra and the descriptive survey about the person-related factors in terms of age, gender, course, socio-economic status and type of school last attended and perceived problem solving abilities in terms of verbal, spatial and quantitative or numerical abilities of the freshmen students of Asian Institute of Technology and Education.

This study is limited to the freshmen students of Asian Institute of Technology and Education who were enrolled in technology courses like Computer Hardware Servicing, Computer Programming, Computer Education with E-Commerce and Bachelor of Science in Information Technology on the First Semester of this school year 2009-2010.

### DEFINITION OF TERMS

In order to provide a common frame of reference to the reader, the following terms used in this research are hereby defined operationally.

**Age.** It refers to the number of years the respondents have from the year they born up to the year 2009.

**Course**. It refers to the chosen program where the freshmen students of Asian Institute of Technology and Education are enrolled.

**Gender.** It refers to the respondents’ sexual category such as male or female. This pertains to sex.

**Mathematics performance.** This is the students’ achievements or general average in Mathematics (College Algebra) for the First Semester of the School Year 2009-2010.

**Problem solving abilities.** In this study, it refers to the abilities of the respondents in solving a problem in terms of spatial, verbal or quantitative.

**Quantitative/ Numerical Ability.** This is determined by a 40 items test from numerical estimation, numerical computation, numerical reasoning and data interpretation.

**Socio- economic status (SES).** This is categorized as the level of income, educational attainment and occupation of their parents.

**Spatial- visualization Ability**. This is determined by a 40 items test about the students’ ability to draw from memory visualize space relationships, shape matching, shape rotation, combining shapes, and the manipulation of other solid shapes in 2 and 3 dimensions.

**Type of school last attended –** This is the public or private school where the respondents had finished their high school level.

**Verbal Ability .** This is a 40 items test to measure the students’ ability to identify the incorrectly spelt words, understand the meaning of the words in the question and establish what exactly the relationship is between them and also to assess their ability to use word in a logical way.

## Chapter II

### REVIEW OF RELATED LITERATURE AND STUDIES

The researcher conducted a research for the related literature and studies in several libraries and web sites. Among the literature and studies that have relation or bearing to this study are presented below and in the succeeding pages of this chapter.

### RELATED LITERATURE

**Age**

Age is a period of human life, measured by years from birth, usually marked by a certain stage or degree of mental or physical development and involving legal responsibility and capacity.

The issue of age differences on mental test is another complex one. The makers of popular mental test believed that intelligence grows from infancy to Adolescence. Mental abilities were thought to stabilize after age 18 until the late twenties or early thirties. Then from 30 until age 60 there are usually plateaus or improvements in different sphere.

It cannot be denied that as we grow, we experience a general decline on the ways we process the information. In cognitive performances, older adults are expected to perform less than adolescents. In the study conducted by Campbell and Charnes in 1990 (Galloti, 2004) they found out that there are similar age-related declines in working memory. In their study, there were three groups (20-, 40-, and 60-year olds) as participants who were given algorithm task of squaring two digits numbers. Their findings indicated that adults who in turn made more errors than the youngest adults.

**Gender**

The difference between the male and female brain is not evidence of superiority or inferiority, but of specialization. Michael Levin, writing in Feminism and Freedom, notes that, in general, males have better spatial and math skills than females. While feminists often claim that these differences are due to social expectations and if girls were encouraged to be mathematicians, they would have the same ability as boys--there is evidence that these differences are inherited and appear in childhood, actually increasing during puberty. On the other hand, girls tend to be more vocal than boys, are better at hearing higher frequencies, and do better than boys in reading and vocabulary tests.

Males have a vastly superior ability to visualize a three-dimensional object than do women. This gives the male his often-observed superior abilities in math and geometrical reasoning. In addition, males are better skilled in gross motor movements than are girls. (Mayer – Bahlburg et al., 1995; Abelos, 2005).

Several research programs have shown that the spatial, verbal and mathematical performance of typical maturers-early maturing boys and late – maturing girls – are not in line with expectations. Early maturers of both sexes (the female pattern) tend to do relatively well on certain type of verbal tests (“female strength’) and less ably on task that require spatial and mathematical reasoning abilities (“female weaknesses”). Girls who mature late often match or outscore their masculine counterparts in mathematical reasoning and in spatial abilities. Late maturers also show evidence of a relatively high degree of laterality (specialization in two hemispheres). As of now, the data are from uniformly supportive of the maturation hypothesis, so it remains just that an intriguing hypothesis. (Mayer – Bahlburg et al.., 1995; Abelos, 2005).

**Socio- Economic Status**

Socio- economic status is an economic and sociological combined total measure of a person's work experience and of an individual's or family’s economic and social position relative to others, based on income, education, and occupation. When analyzing a family’s socio-economic status, the household income earners' education and occupation are examined, as well as combined income, versus with an individual, when their own attributes are assessed.

Socio- economic status typically broken into three categories, high socio- economic status, middle socio- economic status, and low socio- economic status to describe the three areas a family or an individual may fall into. When placing a family or individual into one of these categories any or all of the three variables (income, education, and occupation) can be assessed. (Wikipedia).

**Type of School**

The types of the school are public and private school. Private school is a school founded, conducted, and maintained by a private group rather than by the government, usually charging tuition and often following a particular philosophy, viewpoint, etc.

**Private schools** are not obligated by any laws regarding admission. Therefore, private school admission is competitive. Also, private schools are not required to provide educational programs for children with special needs. Private schools are also under no obligation to keep a student enrolled. If a child’s behavior disrupts the school’s milieu, they can be kicked out. Another scenario to keep in mind is that if a child’s academic progress is not acceptable, they may be kicked out as well. Graduation requirements for private schools are decided by each school and are not subject to any state requirements. Many private schools do choose to align themselves with private school associations which will mandate graduation requirements.

**Public schools** are obligated by law to educate all children, so to enroll in a public school you simply register your child by filling out the necessary forms. Public schools must accept any resident student who applies for admission, regardless of sex, race, religious affiliation, economic status or physical or mental handicap. Public schools must also meet state graduation requirements, which vary state by state. Public schools can kick children out if their behavior is too disruptive.

### PROBLEM SOLVING ABILITIES

Problem solving is a form of thinking. Considered the most complex of all intellectual functions, problem solving has been defined as higher-order cognitive process that requires the modulation and control of more routine or fundamental skills. It occurs if an organism does not know how to reach a desired goal state. It is part of the larger problem process that includes problem finding and problem shaping.

Krechevsky and Gardners (1990) as cited by Munguit, 2003) stated that both logical- mathematical and spatial intelligences are capacities including the ability to perceive forms and objects, the ability to manipulated or transform the objects on forms and the ability to produce a graphic likeness to one’s visual experience, even without reference to the original stimuli. Thurstone (1938) as cited by Munguit, 2003) was one of a number of psychometricians who argued for the existence of a separate spatial ability. This is the one intelligence, apart from the linguistic and logical- mathematical which most students of intelligence testing consider as a discrete form of intellect.

Verbal ability (Linguistic Intelligence) refers to our ability to use written or spoken language in the expression of feelings and information. It also deals with our ability to form thoughts clearly and utilize these competently through words to express these thoughts in speech, reading and writing (Lwin, Lyen. Khoo & Sim 2003).

Spatial ability refers to skill in perceiving the visual world, transforming and modifying initial perceptions, and mentally recreating spatial aspects of one's visual experience without the relevant stimuli. Several categories of spatial abilities may be distinguished. Spatial orientation is the ability to keep track of objects or locations in space even after a rotation or movement to a new location; spatial perception involves determining spatial relationships with respect to gravity or one's own body in spite of distracting information; and spatial manipulation involves the ability to mentally rotate two- or three-dimensional figures rapidly and accurately. (http://social.jrank.org/pages/604/Spatial-Abilities.html#ixzz6fq59niXK&B).

Likewise, Brownlow and Hicks (2000) as cited by Carey, (2004), recognized that among basic skills related to mathematics learning are the spatial skills which are concerned with understanding, manipulating, reorganizing or interpreting relationship in space and which classified into two types namely: Spatial –visualization and spatial orientation. Spatial-visualization requires the ability to rotate objects mentally while spatial orientation requires ability to remain unconfused by changing orientation and to determine spatial orientation with respect to one’s own body.

According to the Wikipedia, Older adults tend to perform worse on measures of spatial visualization ability than younger adults, and this effect seems to occur even among people who use spatial visualization frequently on the job, such as architects (though architects still perform better on the measures than non-architects of the same age). However, possible that the types of spatial visualization used by architects are not measured accurately by the tests.

### RELATED STUDIES

**Age**

Age is deemed to have influence on the academic performance of students as suggested by the study of Dilla and Dalusong (1995) as cited by Muguit (2003). He found out that old farm management technicians had a higher level of performance than the younger ones. Thus, there is significant relationship between age and job performance regardless of the job.

In like manner, Howard and Dalusong (1995) as cited by Muguit (2003) explained that ‘the older the person is, the better is his ability to sustain attention, follow direction and maintain a given value, if given a reaction type problem”.

In addition, according to the study of Cantero (2005) revealed that pupil’s age was significantly related to (a) NDEA-AT scores in English, Mathematics, Sibika at Kultura, Filipino and Science and Health and (b) to final grades in Mathematics, Religion, Filipino and Science and Health .

However, it was different to the studies of some researchers like what Balos (2002) found out to her students. The following statements are the findings of her investigations:

There is no significant between the performance level in Mathematics of the grade four pupils and their age in terms of Comprehension of Concepts. It doesn’t mean that the older or eleven year old pupils perform better than the nine-year old pupils or vice versa.

There is no significant difference between the performance level in mathematics of the grade four pupils and their age, which means that the age doesn’t matter on the performance level in Mathematics in terms of Basic operations.

There is no significant difference between the performance level in mathematics of the grade four pupils and their age in terms of Application of Concepts or Problem Solving. Meaning the Performance level does not depend on the pupil’s age or vice versa.

**Gender**

Sex can be a good predictor of Mathematics achievement. As shown in the study of *Morillo (2003),* the female students got better scores than the male respondents due to differences in study habits and attitudes between sexes. The girl got a higher mean (68.56) than the boys (59.84) in validated mathematics achievement test. Rusiana (2007) also found out that there is a significant difference in the Academic Performance of male and female student’s respondents. Female students posted a mean grade of 84.87, significantly higher than the 83.68 average grades of the males.

In addition, Ibesate (2004) revealed that gender influences academic achievement, on his study he found out that female pupil showed that they were positive in academic self-concepts and achievement than the male pupils do. Similarly, Rowe (2000) revealed that boys are significantly more disengaged with schooling and more likely to be at risk of academic underachievement- especially in literacy. Boys exhibit significantly greater externalizing behavior problems in the classroom and at home But according to Candiente (1996) as cited by Sibonga (2009) found out that there is no significant difference in the means of the female and male in the pre-admission variables such as high school grade point average, NCEE and college Scholastic Aptitude Test. This is also supported by the result of the study of Sibonga (2009) that there is no significant difference in the district achievement in mathematics of pupils as to their sex. This mean that male pupils did not necessarily perform better in mathematics compared to female pupils or vice-versa.

Eldon and Peterson (as cited by Pacer, 2002) concluded that employment while attending high school was noted for boys and girls. For boys, employment was not significantly associated with difference in academic achievement, extra-curricular involvement, socio-economic status or self-esteem although boys who worked have slightly higher grades and higher self-esteeem. For girls, employment was significantly associated with higher academic achievement and higher self-esteem.

Sherman (1979) as cited by Zheng Zhu (2007) that gender differences in spatial visualization have reported inconsistent results. Be-Chaim et. al (1988) as cited by Zheng Zhu (2007) found that there were statistically significant gender differences in spatial visualization among middle school students; while other researchers concluded that gender differences in spatial visualization were small or null among middle school students (Voyer et al, 1995 as cited by Zheng Zhu ,2007).

As supported to what Zheng Zhu (2007) cited on his study. Balos (2002) found out a different result regarding the mathematics performance and sex in different term. The following statements are the findings of his study.

There is no significant between the performance level in Mathematics of the grade four pupils and their sex in terms of Comprehension of Concepts. Meaning to say that performance level does not depend on sex or vice-versa.

There is significant difference between the performance level in mathematics and their age in terms of Application of Concepts or Problem Solving which means that females perform better than males.

**Socio- Economic Status**

The socio-economic status as a variable which covers the educational attainment, occupation and monthly income of the parents were related to the students’ ability and performance. As supported by Tauban as cited by Muguit (2003) that parental education, father’s occupation status and family income were positively related to offspring’s schooling, intelligence, occupation status and earnings.

In addition, Pacer, 2002 (as cited by Muguit, 2003) mentioned that a high income means more books and more time for a students studies. This is so because family can offered to hire helper. On the other hand, a low income means depriving the students of his having time for studies and researches and projects. This is so because he has to do household chores. A low income for the students means that he has to do part-time jobs in order to augment the family income and support his studies.

Likewise, Tapasok (1994) as cited by Macalangcan, (2007) emphasized that schooling is related to income in two ways: higher level and better quality education enable one to obtain a good job which earns higher income ; but higher income groups have greater access to higher level and better quality schooling. The findings of Turmos,(2000) also concluded that the higher the family income and the better the family relationship at home is the higher in the scholastic performance of the pupils.

In the study of Villaflor (1990) as cited by Galas (2001) conformed that college educated mothers, a socio-economic indicator, is the strongest determinant of the students’ academic performance. As the mother serves as the first teacher the child is in contact with, it is presumed that her educational attainment will greatly influence that of the child. Similarly, the findings of Taposok (1997) as cited by Macalangcan, (2003) showed that students with high ability had mothers who were well-educated and employed. This concept however, is negated with the finding of Bongalan (2002) that parent’s educational attainment has low relationship to mathematics achievement. The result revealed that whether parents had high or low educational attainment is not the basis that students will perform well. Also in the study it was found out that parent’s monthly income has very low relationship with the mathematics achievement.

**Type of School: Private and Public School**

Gapeza (2006) as cited by Peña (2009) noted that the public school has a significant difference between the scholastics performance of male and female students in College Algebra. Female had better performance than male students. While in private schools the scholastics performance of the students in College Algebra of male and female students did not vary.

According to Yeban F., et al (2004), the type of school is a significant factor in the respondent’s performance. Between public and private schools, the latter significantly performed better in the test than the former.

**Problem Solving Abilities**

Problem solving is defined as a process by which the learner discover a combination of previously learned rules that he/she can apply to achieve solution for novel problem situation. (Gagne 1970 as cited by Belen, 2008). Some of the problem solving abilities are verbal, spatial-visualization and quantitative or numerical abilities.

Verbal-logical abilities are regarded as being important to geometric problem solving for both genders (Battista, 1990). Evidence from variety of sources has shown that there were gender differences in verbal skills with females outperformed males on many verbal tasks (Halpen 2000,as cited by Zheng Zhu, 2007),. However, Hyde and Linn (1988) as cited by Zheng Zhu, (2007) concluded that gender difference in verbal abilities had declined and where negligible now. In addition, the gender difference in quantitative abilities was found among gifted boys and girls.

Fennema (1984) as cited by Garcia (1998) reported that spatial-visualization is logically related to mathematics. Scores on test of spatial-visualization ability and mathematics performance correlate in the range of 0.30 to 0.60. And the latter appears to her responsible for some of the variance in ability to solve mathematical problem. Likewise , Lezarda (1997) as cited by Balos (2002) stated on her investigation on the effects of training on spatial-visualization and cognitive development on the problem solving ability of college students in mathematics, found highly significant positive correlation between mathematical problem ability and a) spatial-visualization ability and b) cognitive ability.

However, in the study of Garcia (1998) revealed a direct and moderate relationship between spatial visualization ability and performance in mathematics as reflected by a correlation coefficient of 0.56. Thirty one percent of students’ performance in mathematics was attributed to their spatial-visualization ability as shown by the computed coefficient of determination equal to 31%. It was also found out that t-test was employed; this relationship was significant at .05 level of 106 degree of freedom.

Garcia (1998) also revealed that there was a direct and moderate relationship between numerical ability and performance in Mathematics as indicated by the performance in mathematics was due to their numerical ability as revealed by the coefficient of determination equal to 26%. The relationship was found to be significant when t-test was used at .05 level with 106 degrees of freedom.

This study is similar to the study of some researchers like Garcia (1998), who studied the effects of spatial-visualization ability and numerical ability to the mathematics performance; Fennema (1984) as cited by Garcia (1998) reported the relationship between spatial-visualization ability and mathematics; and other researcher investigated the relationship of gender to their abilities. But in this study the researcher combined the three problems solving abilities such as verbal, spatial-visualization and numerical abilities and which were correlated to the mathematics performance. The researcher also included in his study the perceptions of the respondents regarding the verbal abilities, spatial-visualization abilities, and numerical abilities.

## Chapter III

### RESEARCH METHODOLOGY

This chapter deals with the methods and procedures used to provide the readers a clear presentation on how this study was made. It describes in details the research design, respondent of the study, data gathering procedure and statistical instruments used for analysis.

### RESEARCH DESIGN

The researcher used the descriptive survey design of research to describe the condition of the problem in details. It includes summarizing, organizing and presenting of data into tables and figures.

All the needed data for the completion of this study were made using researcher’s prepared questionnaire about students-related factors, perceived in problem solving abilities, grading sheets in Mathematics (College Algebra) and 120 items problem solving ability test adopted from www.psychometric-success.com.

### RESPONDENTS OF THE STUDY

The respondents of this study were one hundred twenty-two (122) freshmen students of Asian Institute of Technology and education who were enrolled in the first semester of SY 2009-2010. The respondents came from all different technology courses of Asian Institute of Technology and Education like Computer Hardware Servicing, Computer Programming, Computer Education with E-Commerce and Bachelor of Science in Information Technology.

### RESEARCH INSTRUMENT

The following instruments used in gathering data for this study are as follows: Survey Questionnaire developed solely for the purpose of this study; Grades in Mathematics (College Algebra); and the Assessment test in problem solving abilities which was adopted from www.psychometric-success.com.

The distributed questionnaire consists of the student-related factors such as name, age, gender, course, socio-economic status (family income, source of income and educational attainment of their parents), and the type of school last attended. It also includes the questions about the perception of the students in verbal abilities, spatial-visualization abilities and the quantitative or numerical abilities and it was rated as excellent, very good, good, fair and poor.

To find out the level of mathematics performance of the respondents in this study, the final grades in Mathematics (College Algebra) in the First Semester, School Year (SY) 2009-2010 were taken from the office of the Registrar and were used.

Assessment test was employed to find out the level of performance on problem solving abilities of the respondent. The test questions in this assessment test were adopted from www.psychometric-success.com, an official website which aimed to measure attributes like intelligence, aptitude and personality of an individual. In this study, the researcher chose one hundred twenty (120) items about verbal, spatial-visualization, and numerical abilities. The first forty (40) items were questions about spelling, word meaning, word relationship and critical reasoning which measure the verbal ability of the respondents. The second forty (40) items were on spatial-visualization ability which covered the shape matching, shape rotation, combining shape and the manipulation of other solid shapes in 2 and 3 dimensions. And the last forty (40) items tested the quantitative or numerical abilities of the respondents in mathematics, specifically the numerical computation, numerical estimation, numerical reasoning and data interpretation.

To find out the level of performance in the assessment test on problem solving abilities such as verbal, spatial-visualization and quantitative/numerical abilities, the following descriptive equivalents of numerical ratings were used.

**Numerical Level of Performance Code**

Abbildung in dieser Leseprobe nicht enthalten

To interpret the level of mathematics performance, the following descriptive equivalent of numerical rating was used.

**Numerical Level of Performance Code**

Abbildung in dieser Leseprobe nicht enthalten

### RESEARCH PROCEDURE

All activities on this study were properly coordinated with the school officials especially to the head of academic affairs of Asian Institute of Technology and Education through letter of approval signed by the thesis adviser and other concerned authority.

The data for this study were gathered using the approved researcher made instrument, grading sheets in mathematics and assessment test on problem solving abilities (Verbal Ability Test, Spatial –Visualization Ability Test and Numerical Ability Test). The researcher was the one who personally administered in distributing the questionnaire and assessment test in problem solving abilities of freshmen students of Asian Institute of Technology and Education. The instruments were collected, checked, tallied and evaluated in order to find out the answer in the problems and to test the hypotheses of this study.

### STATISTICAL TREATMENT

The percentage, means, and standard deviation were computed for the tables presenting the distribution of subjects according to the variables as student-related factors, perceptions of students about verbal, spatial-visualization and numerical abilities, assessment test results in problem solving abilities and mathematics performance.

To compute the percentage, mean, and standard deviation of the result of the students’ perception, the following set codes was used for their descriptive response.

Abbildung in dieser Leseprobe nicht enthalten

The Pearson Product Moment Correlation was used at 0.5 level of significance to determine the relationship between the independent and dependent variables in this study.

`To easily understand and evaluate the obtained value in correlation of mathematics performance and problem solving abilities the following quantitative interpretation (according to Garrett as cited by Amid, 2005) was applied.

Abbildung in dieser Leseprobe nicht enthalten

## CHAPTER IV

### PRESENTATION, ANALYSIS AND INTERPRETATION OF DATA

This chapter presents the analysis and interpretation of the data according to the problems presented in this study.

**I. Person-Related Factor of the Respondents**

**a. Age**

Figure 2 presents the distribution of respondents according to age. The one hundred twenty-two students have ages that range from 16 to 32 years. The youngest student in this group was 16 years old and the oldest was 32 years old. It further shows that biggest percentage fell on the age range between 16 -19 years old with 86%. This implies that most of the students are normally in the age bracket of Freshmen College.

Abbildung in dieser Leseprobe nicht enthalten

**Figure 2: Distribution of Respondents according to Age**

**b. Gender**

Abbildung in dieser Leseprobe nicht enthalten

**Figure 3: Distribution of Respondents according to Gender**

Figure 3 shows the frequency and percentage distribution of the respondents’ gender. Fifty nine (59) respondents or 48.36 of the total respondents are male while sixty three (63) respondents or 51.64% of the total respondents are female. It implies that the distribution of gender enrolled in the first year college at Asian Institute of Technology and Education was almost equal.

**c. Course**

Figure 4 reveals the distribution of respondents according to course. The 48.36 % of the total respondents took up Computer Programming (CP) course which has the largest number of respondents and Computer Education with E-Commerce course had only 6.56% out of the total number of respondents. Computer Hardware Servicing (CHS) course has 27.05 % of the total respondents which is second to the largest number of respondents while the Bachelor of Science in Information Technology (BSIT) had 18.03%.

The findings reveal that Computer Programming and Computer Hardware Servicing are the marketable courses at Asian Institute of Technology and Education because the graduates of these courses were 99% employed and passed in their National Competency examination given by TESDA.

Abbildung in dieser Leseprobe nicht enthalten

**Figure 4: Distribution of Respondents according to Course**

**d. Socio- Economic Status**

The socio-economic status of the family of the respondents was categorized into three components such as: parent’s educational attainment, parents’ monthly income and source of family income. The results were presented and interpreted to the following tables and figures.

** d.1. Parent’s Educational Attainment**

Table 1 reveals the distribution of respondents according to the parents’ education attainment.

**Table 1**

**Distribution of Respondents according to Parents’ Educational Attainment**

Abbildung in dieser Leseprobe nicht enthalten

The data show that the highest number of respondents declared that their fathers and mothers graduated in high school with 36.89 % and 34.43% out of the 122 respondents respectively. It also shows that fifteen (15) of respondents’ fathers and twelve (12) of their mothers were elementary undergraduates. Fifteen (15) and twenty-two (22) of the respondents stated that their fathers and mothers graduated in college.

** d.2. Parents’ Monthly Income**

Abbildung in dieser Leseprobe nicht enthalten

** Figure 5: Distribution of Respondents according to Parents’ Monthly Income**

This figure shows that majority of the parents’ monthly income belongs between P3, 000.00 to P 5,999.00 bracket having 27.87% or 34 respondents out of 122 total number of respondents.

Only 2.46 % or 3 respondents belong to the family with an income of P21, 000.00 and above. Seventeen point twelve or 21 respondents are members of the family with a monthly income of less than P3,000.00; eighteen (18) respondents are from families with an income of P6,000.00 to P8,999.00 monthly; and P12,000.00- P14,999.00 and P15,000,00 – P17,999.000 have the same number of respondents with 9.02% or 11 respondents.

The findings supported by the succeeding figure (Figure 6) proved that monthly income of parents came from farming which depends on the crops they sold.

**d.3. Source of family Income**

Figure 6 shows the distribution of respondents according to the source of family income. The sources of their family income are salaries, farming, own business and practice of profession.

Abbildung in dieser Leseprobe nicht enthalten

** Figure 6: Distribution of Respondents according to the Source of Family Income**

The data reveal that forty-four percent (44%) of the respondents belong to families whose sources of income were salary based. Only three percent (3%) of them came from the family with an income source from practicing their profession. It also shows that 31% of the respondents belonged to the families with an income source from farming. It implies that the income of the families is based on their nature of work which is directly proportional to their educational attainment.

**e. Type of School last Attended**

Abbildung in dieser Leseprobe nicht enthalten

**Figure 7: Distribution of Respondents according to Type of School last Attended**

Figure 7 shows that majority of the respondents which is 84.43% graduated from public secondary school. Only 15.57% graduated from private secondary school. This figure implies that most of the respondents graduated from public secondary school for the reason that their families could not sustain the expenses in sending them for the private school.

**II. Level of Mathematics Performance of the Students.**

**Table 2**

**Distribution of Respondents as to their Mathematics Performance**

Abbildung in dieser Leseprobe nicht enthalten

Table 2 reveals the distribution of respondents as to their mathematics performance.

It shows that 55.74% or 68 respondents have an average score that ranges between 80 – 84; and only two (2) respondents has an average score that ranges between 90 to 94. Thirty-three (33) respondents got an average score between 75 - 79 and 55.57% or nineteen (19) respondents got a score of 85 to 89.

Generally, it is observed students with an average score of 81.14 which indicates that the respondents performed “good” in mathematics for the first semester of the School Year 2009-2010.

**III. Perceive Problem Solving Abilities**

The following tables show the result of students’ perceptions on problem solving abilities in terms of verbal, spatial, and numerical abilities.

**a. Verbal ability**

Table 3 presents the students’ perceptions on problem solving abilities in terms of verbal ability. It is composed of five indicators where the students give their rates as excellence (E), very good (VG), good (G), fair (F) or poor (P).

**Table 3**

** Students’ Perception on Problem Solving In terms of Verbal Ability**

Abbildung in dieser Leseprobe nicht enthalten

The data reveal that respondents perceived that they are “good” in verbal ability as indicated by the obtained means of 3.13, 3.15, 3.01, 2.98, and 2.96 respectively. It also reveals that the lowest mean which is 2.96 falls on the fifth indicator (Use words in a logical way).

The overall mean of students’ perceptions on verbal ability is 3.05 while the standard deviation is 0.088. The findings reveal that the respondents’ perceptions in verbal ability were “good” enough, especially in identifying incorrectly spelt word, understanding the word meaning, identifying the relationships between word groups in question and using word in logical way, since they were all college students.

**b. Spatial Ability**

Table 4 shows the mean, standard deviation and interpretation of the students’ perceptions on problem solving abilities in terms of spatial ability.

The respondents perceived their selves as “good” in combining 2 dimensional shape” with a mean value of 2.96 and standard deviation of 0.71. The second indicator which is the matching of two dimensional shapes had a mean of 3 and standard deviation of 0.71.This means that the respondents’ perception to their selves under this indicator is "average/good”. The third, fourth and fifth indicators have a mean range between 2.83 to 2.89.

This table implies that the overall mean of the students’ perceptions on spatial ability is 2.92 and standard deviation is 0.077. This finding means that the respondents’ perceptions regarding the spatial ability rated as “good” which reveals that the students have a confidence to think in images. Once they have formed an image in their mind they can imagine many different results. As computer students who are intended to be programmer, technician and computer analyst, they are interested in spatial activities like perceiving visual information, transform this information, and recreate visual images from memory. This is supported by Aquino (2009) that the typical professions of having spatial intelligence are architect, sculptors, designer, painter, artists, and mechanics who had a gift of sophisticated skills in the art and recognize how things are arranged in space.

**Table 4**

**Students’ Perceptions on Problem Solving In terms of Spatial Ability**

Abbildung in dieser Leseprobe nicht enthalten

**C . Numerical Ability**

Table 5 reveals the Students’ Perceptions on Problem Solving In terms of Numerical Ability with five indicators such as: recall the basic mathematics facts, procedures, rules and formulas; perform the mathematical operation accurately; remember/use the previously encountered patterns; apply the logical thinking in the completion of the number series and interpret data from a graph.

**Table 5**

**Students’ Perceptions on Problem Solving In terms of Numerical Ability**

Abbildung in dieser Leseprobe nicht enthalten

These five indicators have a mean range between 2.83 – 2.90 and standard deviation between 0.66 – 0.72.

The overall mean of students’ perceptions on numerical ability is 2.86 while the standard deviation is 0.042. This means that most of the respondents rated themselves as “good” which implies that they are equipped with the basic mathematics facts, procedures and rules as taught during elementary and high school.

**IV. Students’ Performance in Assessment Test**

**a. Verbal Ability Test**

Table 6 shows the students’ performance in the verbal ability test. It reveals that Ninety-eight (98) of the respondents got a score between 9 –16. It is interpreted that the level of performance in this group is “fair”. Seven (7) of the respondents got a score ranging 1-8, and seventeen (17) of the respondents got a score of 17-24, which is the highest score that they obtained in this assessment.

**Table 6**

**Students’ Performance in the Verbal Ability Test**

Abbildung in dieser Leseprobe nicht enthalten

The mean performance of the students in terms of verbal ability tests lies on the distribution of 12.98, which is on the score between 9-16. The result may imply that the level of performance of the respondents in this assessment was “fair”. It shows that majority of the freshmen students of Asian Institute of Technology and Education (AITE) have difficulties in spelling, vocabulary, grammar, and reading comprehension.

**b. Spatial Ability Test**

Table 7 presents the students’ performance in spatial ability test.

**Table 7**

**Students’ Performance in the Spatial Ability Test**

Abbildung in dieser Leseprobe nicht enthalten

It shows that 8.2% or 10 respondents have a score ranging between 33 – 40 with a descriptive equivalent of excellent; 46.72% or 57 respondents got a score of 25 to 32 with descriptive equivalent of “very good”; Forty-three (43) respondents got a score of 17 to 24 with descriptive equivalent of “good”; 9.02% or 11 respondents got a score of 9 to 16 with descriptive equivalent of “fair”; and only one (1) respondent has score of 1 to 8 with descriptive equivalent of “*poor”.*

This table also implies that the overall mean of 25.10 with standard deviation of 5.96, falls on the score between 25 to 32, means that the level performance of the students in spatial ability was “*very good”.*

Findings reveal that freshmen students are “very good” in manipulating figures or pictures rather than words as shown in table 6 (students’ performance in verbal ability test) and in table 7 ((students’ performance in spatial ability test). It is supported by the study of Hegarty M. and et.al (2004) that spatial ability and verbal ability are not well correlated. There are individuals who have low spatial ability but high in verbal and other individuals who have high spatial but low verbal.

**c. Numerical Ability Test**

Table 8 shows the students performance in the numerical ability test. The highest score obtained in this assessment test was 32.

**Table 8**

**Students’ Performance in the Numerical Ability Test**

Abbildung in dieser Leseprobe nicht enthalten

Thirteen (13) or 10.66% out of 122 respondents got a score of 25 to 32; Forty-nine (49) respondents got a score of 17 to 24; a score of 9 to 16 has a largest number of respondents which equals to 58 or 47.54% out of 122 total respondents and only two (2) respondents got a lowest score between 1 and 8.

This table also implies that the overall mean of 17.30 and standard deviation of 4.60, which fall on the scores between 17 to 24, means that the level of performance of the students in numerical ability was “good”.

Further, the findings reveal that students’ performance in assessment test in term of numerical ability was congruent to their mathematics performance. It could be also attributed to the fact that the performance in College Algebra was directly affected by the basic principles of arithmetic like addition, subtraction, multiplication and division.

**V. Correlation between Students’ Perceptions in Problem Solving Abilities and Mathematics Performance,**

Table 9 reveals the students’ perceptions in problem solving abilities in terms of verbal, spatial and numerical abilities.

**Table 9**

**Correlates Between Students’ Perceptions in Problem Solving Abilities and Mathematics Performance**

Abbildung in dieser Leseprobe nicht enthalten

The data in the table present the computed r values of 0.10 (verbal); and r= 0.02 for spatial-visualization when the respondents’ perceptions on their problem solving abilities were correlated to their mathematics performance. The results reveal no significant relationship between the indicated variables as shown by the above computed r- values which are less than the tabulated values of 0.195 at 0.05 level of significance.

On the other hand, students’ numerical ability when correlated with mathematics performance denotes low correlation (Garrett as cited by Amid, 2005) as revealed by computed r -value of 0.22 which is greater than the tabulated value of 0.0195 at .05 level of significance. This finding implies that there is a significant relationship between students’ perceptions in numerical ability and mathematics performance.

According to the survey conducted by the researcher most of the respondents perceived that they are good in terms of verbal, spatial and numerical abilities and 55.74% or 68 of the respondents have grades in mathematics ranging between 80 to 84 with a descriptive equivalent of “good”. The findings reveal that perceiving good in their problem solving abilities in terms of verbal and spatial-visualization abilities do not agree with having good mathematics performance in Algebra subject when correlated. Highly worded mathematical problems that involve critical analysis and abstraction couldn’t be easily understood by the students.

**VI. Correlation between Students’ Performances in the Assessment test **

** and Mathematics.**

The data in Table 10 reveal the test of correlation between the students’ performance in the assessment test and their performance in mathematics subjects.

This table (table 10) reveals data when the assessment test results involving the different problem solving abilities such as verbal ability, spatial-visualization and numerical were correlated to the students’ performance in Mathematics subject.

**Table 10**

**Correlates between Students’ Performances in the Assessment Test and Mathematics**

Abbildung in dieser Leseprobe nicht enthalten

Verbal ability with computed r-value of 0.30, and numerical ability with computed r- value of 0.27 which are greater than the tabulated r- value of 0.195 at 0.05 significance level reveal significant results when correlated to mathematics performance. Although the r-values mark low relationships, the findings may reveal that mathematics performance require skills from the students involving language proficiency, meanings, recall basic facts, concepts, formula and principles. All the mentioned information are interrelated and best understood using in combination.

Further the mathematical performance of the students is significantly related to the level of performance in the assessment test in terms of spatial skill. As revealed by the computed r-value of 0.43 which is greater than the tabulated r- value of 0.195 at 0.05 significance level, the spatial –visualization ability of the students is marked substantially related to mathematics performance. This finding could be attributed to the fact that solving a mathematical problem involves manipulating symbols and numbers, hence spatial intelligence is highly involved.

The above finding is supported by the reports of Garcia (1998) that there was a direct and moderate relationship between numerical ability and performance in Mathematics as indicated by the performance in mathematics was due to their numerical ability. It is also on the same agreement to the investigation of Lezarda (1997) as cited by Balos (2002) that there was a highly significant positive correlation between mathematical problem ability and a) spatial-visualization ability and b) cognitive ability.

## CHAPTER V

### SUMMARY OF FINDINGS, CONCLUSION AND RECOMMENDATION

This chapter presents the summary of the findings established from the data gathered in the study. It also gives the conclusions derived from the summary of findings and recommendations.

This study sought to find out the correlates of mathematics performance and problem solving abilities of freshmen students of Asian Institute of Technology and Education for the first semester, S.Y. 2009-2010. The specific problems which the research paper sought to answer the following: What are the person-related factors of the respondents in terms of the following: Age; Gender; Course; Socio-economic status (Parents’ Educational Attainment, Parents’ Monthly Income and Source of Family Income); and Type of school last attended?; What is the level of mathematics performance of the students in algebra?; How do the respondents perceive the following problem solving abilities in terms of: Verbal; Spatial-visualization; and Quantitative/ numerical?; What is the level of performance of the students in the assessment test with regards to : Verbal; Spatial; and numerical?: Is the students’ Mathematics performance significantly related to the perceived problem solving abilities in terms of : Verbal; Spatial; and numerical?; and Does the mathematics performance significantly relate to the level of performance in the assessment test?

**Summary of findings:**

The salient findings of this study are as follows:

1. Findings revealed that 86% of the respondents were 16 to 19 years of age, the distribution of gender was almost equal, majority of the respondents took up computer programming course, they came from the family with a monthly income of P3,000.00 to P5,999.00, and salaries and farming were the source of their family income. The highest number of respondents declared that their fathers and mothers graduated in high school with 36.89 % and 34.43% of the 122 respondents, respectively. It also found out that 84.43% or 103 respondents out of 122 total number of respondents graduated of public secondary schools.

2. Sixty-eight (68) or 55.74% of the respondents belonged to the mathematical average ranges 80 to 84. It implies that majority of the respondents’ level of mathematics performance was “good”.

3. This study shows that the respondents’ perceptions on problem solving abilities in terms of verbal, spatial, and numerical were” good” with overall mean values of 3.05, 2.92 and 2.86 respectively.

4. Findings in the level of performance in assessment test are as follows:

a. The mean verbal ability test of the respondents was found to be “fair” with a computed mean of 12.98 and standard deviation of 3.11.

b. The mean spatial ability test of the respondents was described to be “very good” with computed mean of 25.10 and standard deviation of 5.96.

c. The respondents earned the mean score of 17.30 indicating “good” level of performance in numerical ability test.

5. Results of this study showed that the students’ perceptions in problem solving abilities in terms of verbal and spatial- visualization have both “negligible correlation” with r- values of 0.02 and 0.14, respectively when correlated to their mathematics performance, while numerical ability denotes “low correlation” as revealed by r- value of 0.22. It reveals that perceiving good in their mathematical abilities in terms of verbal and special-visualization abilities do not agree with having good mathematics performance in Algebra subject when correlated. Highly worded mathematical problems that involve critical analysis and abstraction couldn’t be easily understood by the students.

6. This study revealed that the verbal ability test score with r-value of 0.30, and numerical ability test score with r-value of 0.27 were found to have low positive relationship when correlated to their mathematics performance while spatial ability test score with r-values of 0.43 indicates a “substantial relationship”. These findings implied that the mathematical performance of the students is significantly related to the level of performance in the assessment test in terms of verbal, spatial and numerical abilities.

### Conclusions

In the light of these findings, the following conclusions were drawn:

1. There is no significant relationship between mathematics performance of the students and their perceptions on problem solving abilities in terms of verbal; and spatial- visualization. However, there is a significant relationship between mathematics performance of the students and their perceptions on numerical ability.

Thus, the first hypothesis of this study is partially accepted and confirmed in terms of verbal and spatial-visualization abilities while it is not supported in terms of numerical ability.

2. The hypothesis stating that the level of mathematical performance of the students is not significantly related to the level of performance in the Assessment Test in terms of: verbal; spatial; and numerical is not supported in this study.

### Recommendations

Based on the findings and conclusions drawn, the following are recommended:

1. Since the result of the verbal ability test of the students was fair, they must be encouraged to enrich their vocabularies and grammar.

2. There is a need to improve the level of performance of the students in mathematics, from the level of good to very good, if not higher. It may be obtained through the evaluation of some related factors.

3. More problem solving strategies should be applied by the teachers or instructors to enhance the abilities of the learners in terms of verbal, spatial and numerical.

4. Further studies be conducted in other schools or educational institution for more comprehensive findings.

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www.psychometric.success.com

- Quote paper
- Elson Valencia (Author), 2019, Correlates of Mathematics Performance and Problem Solving Abilities of Freshmen Students in Asian Institute of Technology and Education of the First Semester, Munich, GRIN Verlag, https://www.grin.com/document/497308

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