# Mathimatical knowledge and a link to the real world

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Outside school, real-life problems and situations for which mathematical knowledge may be useful often do not present themselves in such familiar forms. The individual must translate the situation or problem into a form that exposes the relevance and usefulness of mathematics. If students are unpracticed at such a process, the potential power of mathematics to help deal with the situations and problems of their life may not be fully realized and may also result to problems.

Researches have shown that majority of students are experiencing problems in mathematics. The importance of mathematics is likely neglected because of students' performance over the subject (Kulak,1993).

Globally, almost all students are complaining about failure in mathematics because of negative attitude over the subject. (Betz, 1978; cited by Zakaria, 2010). Ashcraft (2002; cited by Hopper, 2010) supposes, because of math anxiety which has developed because of negative experience about mathematics, students tend to avoid mathematics which could lead to failure. According to a research conducted in Florida, the percentage of students who failed in math increases (http://www2.tbo.com/content/2009/oct/21/college-students-need-help-required-math-classes/news-breaking/).

According to Tobias (1993; cited by Philips, 2010), millions of adults are blocked from professional and personal opportunities because they fear or perform poorly in mathematics, these negative experiences remain throughout their adult lives. Moreover, negative attitudes towards mathematics can cause tears of frustrations (Sollesta, 2007). This could result to ignorance of numbers which could lead to struggles in simple subtraction and addition.

In the Philippines, Filipino students are having problems when it comes to math proficiency ( Malipot, 2009). In fact, only a few percent crossed the 75-percent level in math in the 2006 National Achievement Test (http://www.undp.org.ph/?link=news&news_id=231&fa=1). In addition, A number of students are dropping mathematics aside from science courses usually before and even after examination (E. Senajon et al; in www.philjol.info/index.php/EACRB/article/viewPDFIntersritial/...1286.). This is an indication of an existing perennial problem because of negative mathematics attitude that has been overlooked by concerned offices and department.

The problem of mathematics attitude leads to the formulation of different strategies to induce the interest of the students to study mathematics. In fact, the Department of Education (Ronda, 2009) created a strategy to encourage public school children to read as well as appreciate mathematics.

On the other hand, failure because negative attitude over mathematics can lead to lack of self-confidence to most Filipino students (Chua, 2006), which is perhaps a greatest obstacle to learning because beliefs govern a person. The belief that they cannot do something may push students unable to perform a task of which they are truly capable.

Locally, particularly in Cor Jesu College, a number of students failed in mathematics subjects specifically in the Division of Business and Accountancy based from the bluebook where failed students are listed.

This research is conducted for the purpose of knowing the relationship between mathematics attitude and mathematics performance to selected first year Bachelor Science in Accountancy students.

## Theoretical Framework

In previous researches (Di Martino & Zan, 2001, 2002, 2003; Zan & Di Martino, 2003) lack of theoretical clarity that characterizes research on attitude has been the issue of most researchers. The lack of theoretical framework that characterizes research on attitude toward mathematics is partially shown by the fact that a large portion of studies about attitude do not provide a clear definition of the construct itself: attitude tends rather to be defined implicitly and a posteriori through the instruments used to measure it (Leder, 1985; Daskalogianni & Simpson, 2000).

This study is anchored with Cognitive-Gestalt theory. According to Burns (1995; cited in http://www.brookes.ac.uk/services/ocsd/2_learn/theories.html) the emphasis of this theory is on the importance of experience, meaning, problem-solving and the development of insights. Which proves that the performance of the student depends on their experiences either at home or in school and how they give meaning to it.s

In the aspect of teacher's behavior and its strategy, Weiner's attribution analysis supposes that students' functioning is affected by the teachers' emotional and behavioral reactions (Stipek, 2002; p-73) which means, students' performance in the classroom can be brought about by teacher's behavior or approach towards the students and the subject itself. In addition, Weiner's attribution analysis brings in clear beliefs that the classroom is the place where judgment is conveyed, not only when it comes to students' behavior but also the teacher's response toward the students (Stipek, 2002; p-73). Silva, Tadeo, Delos Reyes, & Dadigan (http://math.usm.my/research/OnlineProc/ED12.pdf, 2009), assume that despite how knowledgeable the teachers are in teaching math, it is still not enough to teach the students and integrate that knowledge towards learning.

On the other hand, performance in mathematics can also be rooted from anxiety. According to Stodolsky (1975; cited by Stipek, 2002) mathematics instruction that is fostered in students saying that mathematics is something that is learned from an authority which cannot be figured out on one's own. Stodolsky supposes that the students perceive the subject as difficult to study on ones ability and rather needing an authority to learn the subject . This authority is the teacher as mentioned by Stodolsky.

The conceptual framework of the study elaborated the relationship between Mathematics Attitude (independent variable) which was measured into three dimensions: (a) Cognitive dimension, (b) Behavioral dimension, and (c) Affective dimension; and Mathematics Performance of Bachelor of Science in Accountancy Freshmen, school year 2010-2011 in the subject, College Algebra and Accounting 1. The See Fig.1

## Conceptual Framework

## Independent Variable Dependent Variable

## Mathematics Attitude

## Affective Dimension

## Behavioral Dimension

## Cognitive Dimension

## Mathematics Performance in

## College Algebra

## Accounting 1

## Fig. 1. Conceptual Paradigm of the Study

## Statement of the Problem

This research was examined the relationship between mathematics and mathematics attitude and mathematics performance of Bachelor of Science in Accountancy (BSA) freshmen, school year 2010-2011.

Specifically, it will also attempt to find the answers of the following sub-problems:

What is the profile of the students' mathematics attitude in terms of:

Cognitive,

Behavioral, and

Affective?

What is the students' mathematics performance in subject areas:

College Algebra and

Accounting 1?

Is there a significant relationship between mathematics attitude and mathematics performance?

## Hypothesis

Ho: There is no significant relationship between mathematics attitude and mathematics performance.

## Significance of the Study

The importance of this study is to guide the following people:

Students. The result of this study will help the students in knowing the possible reasons why they are anxious in math.

Parents. The outcome of this study will help the parents know the possible reason for their child's failure in math. It will be helpful for them to be cautious with their child's performance.

Teachers. The findings if this study will serve as a manual for the teachers particularly math teachers in determining what strategy to use knowing the information given in this study. The result of this research can be used as a basis to lessen, if not eliminate failures by undertaking changes and innovations in instructions and the curriculum in general. This will serve as an eye opener toward imbibing innovative ideas in teaching.

Psychologists and School counselor. The result of this study will be used as a basis for the school counselors as well as the psychologists to better understand why students behave or misbehave in math.

Administrators. The findings of this study can serve as one of the bases for curricular evaluation and planning. It will also guide the administrators in their conscious effort to undergo planned changes in drawing up systematic scheme of evaluating students' performance.

Researcher. The result of this study will provide a foundation for new research.

## Scope and Limitations of the Study

The study is limited to freshmen students who are enrolled in subjects College

Algebra and Accounting 1during the first semester, particularly the Bachelor of Science in Accountancy, Cor Jesu College confined to period of 2010-2011. The scope of the study is more likely for the benefit of the teachers regarding the percentage of students in terms of their mathematics attitude in relation to mathematics performance of the students.

Findings of the study would therefore, be true only for the subjects concerned and for the given period of time, although these could be used as basis for similar studies that would be conducted at the different colleges in the country.

## Definition of Terms

Cor Jesu College refers to the premier catholic institution in Southern Mindanao, particularly located in Digos City, Davao del Sur.

Mathematics attitude refers to the students' reaction towards mathematics as a subject and as an application. Specifically determined into three dimensions: (a) cognitive, (b) behavioral, and (c) affective.

Cognitive dimension refers to the mental aspect of attitude which concerns the thinking process about mathematics as a subject and as an application.

Behavioral dimension refers to the action aspect of attitude which concerns mathematics as a subject and as an application.

Affective dimension refers to the emotional aspect of attitude which involves in the students' perception about mathematics as a subject and as an application.

Mathematics performance refers to the students' competence in mathematics particularly in subjects College Algebra and Accounting 1.

Mathematics Attitude and Mathematics Performance refers to the relationship of the students' perception,

## Chapter 2

## REVIEW OF RELATED LITERATURE AND STUDIES

This chapter presents topics on mathematics attitude, mathematics performance, and the relationship of Mathematics Attitude and Mathematics Performance as related literatures and studies.

## Related Literature

Articles and some write-ups concerning mathematics attitude, mathematics performance, and the relationship between mathematics attitude and mathematics performance are abundant. Majority of these articles draw a fact that mathematics attitude and mathematics performance show a significant connection in mathematics performance.

## Mathematics Attitude

Mathematics is the language of technology. It is used to formulate, interpret, and solve problems in fields as diverse as engineering, economics, communication, seismology, and ecology. It is the bedrock for the computer revolution. Mathematics provides us with powerful theoretical and computational techniques to advance our understanding of the modern world and societal problems and to develop and manage the technology industries that are the backbone of our economy.

Attitude. According to Liska (cited in;http://www.nd.edu/~rwilliam/xsoc530/attitudes.html), attitude is either be favorable or unfavorable evaluative reaction toward something or someone, exhibited in ones beliefs, feelings, or intended behavior. It is a social orientation - an underlying inclination to respond to something either favorably or unfavorably.

The everyday notion of attitude refers to someone's basic liking or disliking of a familiar target. These studies have shown that, for example, girls tend to have more negative attitudes towards mathematics than boys (Frost et al., 1994; Leder, 1995), and that attitudes tend to become more negative as pupils move from elementary to secondary school (McLeod, 1994). The general attitude of the class towards mathematics is related to the quality of the teaching and to the social-psychological climate of the class (Haladyna et al., 1983).

The effort to promote positive attitudes has been somewhat successful on the individual level. For example, mathematics anxiety can be reduced through systematic desensitisation (Hembree, 1990). On the whole class level the efforts to reform teaching to promote desired attitudes have generally been unsuccessful (McLeod, 1994). However, recent evidence suggests that collaborative approaches can promote positive attitudes among students (e.g. Boaler, 1997a, b, 1998; Ridlon, 1999). An important aim of mathematics education is to develop in students positive attitudes towards mathematics. The notion of having a positive attitude towards mathematics encompasses both liking mathematics and feeling good about one's own capacity to deal with situations in which mathematics is involved. In this setting, attitudes are perceived as being closely linked to beliefs, emotions, and motivation to engage in the subject.

(Australian Education Council, 1991; cited in, )

According to Lopez (cited in http://www.articledashboard.com, February 15, 2011), attitude is a lasting evaluation of people, objects, or ideas which may be positive or not. The concept of attitude is composed of three components which include cognitively-based attitudes, affectively-based attitude, and behaviorally-based attitude.

Attitude toward mathematics is defined as a general emotional

disposition toward the school subject of mathematics" (Haladnya et al.,

1983, p. 20). Maple and Stage (as cited in Schiefele & Csikszentmihalyi,

1995) found that "attitude toward mathematics significantly influenced

choice of mathematics major. "One of the most important reasons for

nurturing a positive attitude in mathematics is that it may increase one's

tendency to elect mathematics courses in high school and college and

possibly to elect careers in a math related field" (Schiefele &

Csikszentmihalyi, 1995)

Mathematics Attitudes

Efforts in the classroom to redress the common societal perception that

"mathematics is difficult" are often exacerbated no less due to the already entrenched

attitudes and feelings that students have by the time they reach secondary level.

Kloosterman & Gorman (1990) suggest that the formation of the belief that some

students learn more readily than others and not everyone will be high achievers in schoolcan lead to a notion that affects achievement in mathematics: the notion that it makes little sense to put forth effort when it does not produce results that are considered desirable. Also affecting learning and attitude are other factors such as motivation, the quality of instruction, time-on-task, and classroom conversations (Hammond & Vincent, 1998; Reynolds & Walberg, 1992) and as a result of social interactions with their peers (Reynolds & Walberg, 1992; Taylor, 1992).

Many studies have been conducted on mathematics attitudes and teaching (Leder, 1987; McLeod, 1992; Zan, Brown, Evans, & Hannula, 2006) but for the purposes of this project, McLeod's (1992) definition of attitudes is adopted: "affective responses that involve positive or negative feelings of moderate intensity and reasonable stability" (p. 581). McLeod contends that attitudes develop with time and experience and are reasonably stable, so that hardened changes in students' attitudes may have a long-lasting effect. Lefton (1997) also argues that attitude is a learned pre-disposition to respond in a consistently favourable or unfavourable manner towards a given object. Positive and negative experiences of school activities produce learned responses which may in turn

impact on students' attitudes as they get older, when positive attitudes towards mathematics appear to weaken (Dossey, Mullis, Lindquist, & Chambers, 1988).

According to Hart (1989), mathematics attitude should be viewed as a predisposition to respond in an unfavorable or favorable way to mathematics. By accepting this view, mathematics attitude includes relevant beliefs (e.g. "Mathematics helps me understand science lessons"), behavior (e.g. "I will apply for a job involving mathematics") and attitudinal or emotional reactions (e.g. "I like solving mathematical problems", "I feel upset when solving mathematical problems"). In other words, by extrapolating from Key (1993), it can be said that an instrument measuring mathematics attitude should sample cognitive, affective and behavioral domains, possibly represented, as the previous analysis suggests, by self-confidence in learning mathematics, liking mathematics and usefulness of mathematics, for example.

Cognitive. Mathematics is believed as an exceptionally difficult subject that everybody needs some knowledge acquired during the primary and middle stage will suffice. Its study requires special ability and intelligence (Sidhu, 1995).

The importance of math is likely neglected because of students' performance in the subject. The majority of students referred for school psychology services are experiencing some academic problems. Although reading skills deficits are the common of these academic problems, researches have shown that the majority of students experiencing problems in mathematics (Kulak, 1993).

Malipot (2009) believes that teachers and the government (Sabater, 2006) can help students in improving their ability in the field of mathematics. Dr. Balmaceda (Garcia, 2007) dispels the popular misconception that math is only about quantities (how many). Most fail to see the creative aspect of mathematics.

Affective. It is a phenomenon that is often considered when examining students' problems in mathematics (Hopper,2010). On the other hand, Chua (2006) supposes that math anxiety is a product of a teaching strategy. At first, anxiety may not take place. Skills which are developed based on drills, practice, and memorization seem rewarding to teacher and student alike. When lessons become more advanced and more complicated, the number of points to be memorized gives an impossible burden to students' memory. The student would then feel that he has reached a stage at which his apparent success desserts him. Here an anxiety-provoking situation starts to confront the learner. The harder the student tries, the worse he/she performs because the students will inevitably use the only approach he/she knows, which is mathematics.

Emotions are seen in connection to personal goals. Emotions are also seen to involve a physiological reaction, as a distinction from non-emotional cognition. Thirdly, emotions are also seen to be functional, i.e. they have an important role in human coping and adaptation. (E.g. Buck, 1999; Lazarus, 1991; Power & Dalgleish, 1997; Mandler, 1989 as cited by Hannula,2010)

## Mathematics Performance

Student engagement in mathematics refers to students' motivation to learn mathematics, their confidence in their ability to succeed in mathematics and their emotional feelings about mathematics. Student engagement in mathematics plays a key role in the acquisition of math skills and knowledge - students who are engaged in the learning process will tend to learn more and be more receptive to further learning. Student engagement also has an impact upon course selection, educational pathways and later career choices

## The Relationship Between Mathematics Attitude and Mathematics Performance

Ma and Kishor (1997) synthesised 113 survey studies of the relationship between attitude towards mathematics and achievement in mathematics. The causal direction of the relationship was from attitude to the achievement. Although the correlations were weak in the overall sample, they were stronger throughout grades 7 to 12, and in studies that had done separate analysis of male and female subjects (Hannula, 2010).

According to Ma and Kishor (1997a), there is a positive interaction between

mathematics attitude and mathematics achievement (Kadijevich, February 17, 2011)

## Chapter 3

## METHODOLOGY

This chapter presents the design, setting, participants, measure, procedures, and data analysis.

## Design

This study made used of descriptive-correlation design (Ariola, 2006) since the aim of the study was to determine whether or not there is a relationship between mathematics attitude and mathematics performance.

This study determined the significant relationship between mathematics attitude and mathematics performance of the Bachelor of Science in Accountancy freshmen students who were enrolled in College Algebra and Accounting 1 during the first semester. The independent variable was the mathematics attitude, which has sub-variables namely: cognitive, behavioral, and affective. Furthermore, the dependent variable of the study was mathematics performance which was determined from the final grades of the respondents in College Algebra and Accounting 1.

## Setting

The study was conducted in the premise of Cor Jesu College campus located in the City of Digos, Province of Davao del Sur.

## Participants

The participants of the study were the randomly selected Bachelor of Science in Accountancy freshmen students who took up College Algebra and Accounting 1 in the first semester A.Y. 2010-2011.

The sampling procedure was done based on random selection from its total population of 155. Slovin's formula (Ariola, 2006) was used to determine the sample size of 113 students. Using the formula below:

n = __N__

1 + NeĀ²

Where;

n = sample size

N = total size

e = desired margin of error (0.05)

Thereafter, the respondents were selected using the lottery method (Ariola, 2006). The total population was arranged sequentially and assigned numeral identifications. Corresponding numbers were marked on separate tabs and were put into a container. This was to ensure that every individual has the same chance of being chosen as every other individual (Ariola, 2006).

## Measures

The research instrument used in the study was the Mathematics Attitude Scale (MAS), retrieved from the study of Acejalado, Limjap. The author of the study was asked by the researcher a permission to use the questionnaire. However, the e-mail account of the author was deactivated.

The survey questionnaire was composed of fifty items with statements based from the dimensions of attitude, namely: affective dimension, behavioral dimension, and cognitive dimension of students' perception about mathematics as a subject and as an application.

The respondents were asked to evaluate the statements through checking using the following measurement (Likert's scale): Strongly agree- 1, Disagree- 4, Agree- 2, Strongly disagree- 5, and Neutral- 3.

The scale of the interpretation of the mean scores of the dimensions of mathematics attitude set by the psychometrician are as follows: 4.4-5.0 very high, 3.6-4.3 high, 2.8-3.5 moderate, 1.9-2.7 low, 1.0-1.8 very low.

## Procedure

A letter of permission to the Dean of College requesting the approval for the permission to conduct a research study in the college department. After which, another letter of permission submitted to the Dean of the Division of Business and Accountancy, (DBA). After having the approval, a requisition letter was sent to the head registrar for the determination of the total population of DBA freshmen students.

The data was gathered from the concerned institutions and offices such as the College Dean and the Dean of DBA through a formal letter. After having the approval, the names of the students who took up College Algebra and Accounting 1 during the first semester were asked from the school registrar through a formal consent. After which, random sampling was made to identify the respondents.

The instrument administration was given in January 2011 based from the availability of the respondents. The questionnaire was follow-upped every now and then.

After gathering the entire answered questionnaire, each item was tallied in accordance to each respondent.

## Data Analysis

## CHAPTER 4

## RESULTS AND DISCUSSION

This chapter deals with the presentation, analysis and interpretation of the data gathered using research instrument. Results and discussions are presented according to the problem and hypothesis of the study.