ATTITUDES TOWARDS MATHEMATICS, SELF …

1 Thematic Group 2 EUROPEAN RESEARCH IN mathematics EDUCATION IIIM. Nicolidau, G. Philippou1 ATTITUDES TOWARDS mathematics , self -EFFICACYAND achievement IN PROBLEM-SOLVING*Maria Nicolaidou and **George Philippou*Post-graduate student, **Professor, University of CyprusThe aim of this study was to explore relationships between students ATTITUDES TOWARDS MATHEMATICS, self - efficacy beliefs in problem-solving and achievement . The possibility of ATTITUDES and self - efficacy to predict problem-solving performance was also examined. Attitude and efficacy scaleswere completed by 238 fifth-grade pupils. Problem-solving performance was measured by aspecially prepared test, including simple and multi-step problems. The analysis of the dataindicated significant relationship between ATTITUDES and achievement and a stronger relationshipbetween efficacy and achievement .

2 ATTITUDES and efficacy were also correlated and both predictedachievement in problem-solving. However, efficacy was a more powerful predictor than gender difference was found in any of the examined on ATTITUDES , as a factor related to students difficulties in mathematics , andparticularly in solving problems, dates from the 1960s. Recently, many connectedconcepts have been studied, such as conceptions and beliefs of mathematics and itslearning, motivation and self -regulation, self -concept, self -esteem and general tenet is that human beings are not only cognitive individuals, but alsosocial persons with beliefs, emotions and views that influence their development aslearners. Actually, a person s behavior and choices, when confronted with a task, aredetermined more by her/his beliefs and personal theories, rather than by her/hisknowledge of the specifics of the refers to attitude as a learned predisposition or tendency of an individual torespond positively or negatively to some object, situation, concept or another positive or negative feeling is of moderate intensity and reasonable stability;sometimes it is especially resistant to change.

3 In the variety of definitions of attitudestowards mathematics (ATM) proposed in research studies, two main categories canbe identified. Using a simple definition, ATM is just a positive or negative emotionaldisposition TOWARDS mathematics (Mc Leod, 1994). Using a multidimensionaldefinition, ATM comprises three components: an emotional respond to MATHEMATICS, positive or negative, a conception about mathematics , and a behavioral tendency withregard to mathematics (Hart, 1989). Ma & Kishor (1997) propose a wider definition;they conceive ATM as an aggregated measure of a liking or disliking of mathematics , atendency to engage in or avoid mathematical activities, a belief that one is good or bad atMathematics, and a belief that mathematics is useful or useless (p. 27). The present studyadopts a rather simple definition of ATTITUDES , that includes, however, different kindsof feelings TOWARDS mathematics and problem-solving, such as love, hate, anxiety,interest, and a perception of the usefulness of mathematics in life, in order tofacilitate young children to express their views.

4 Thus, statements such as I likeMathematics or mathematics is boring are defined as Group 2 EUROPEAN RESEARCH IN mathematics EDUCATION IIIM. Nicolidau, G. Philippou2 With regard to the emergence of negative ATTITUDES , Mandler s discrepancy theory(1989) provides a ground for interpretation. He argues that a negative attitude is aresult of frequent failures or interruptions of planned actions, which were intended toface mathematical tasks. Repeated emotional reactions result in the formation of anoverall schema about mathematics , which becomes relatively number of studies have so far indicated that many children begin schooling withpositive ATM; these ATTITUDES , however, tend to become less positive as childrengrow up, and frequently become negative at the high school (Ma & Kishor, 1997). Itseems that the pressure exercised on students to cope with highly demanding tasks,often at a pace beyond their ambition, together with unimaginative instruction andnon-positive teacher ATTITUDES , have destructive impact on their ATM (Philippou &Christou, 1998).

5 However, the junior school years have been identified as a crucialperiod in the course of development of students ATM, meaning that teachers haveboth, opportunity and responsibility, to promote their students positive ATTITUDES andhigh achievement , the two elements widely acclaimed to be the favorable outcomes ofschooling (Ma & Kishor, 1997, p. 41).Current efforts in mathematics education reform are driven by the belief that allstudents can learn. Motivation needs have led researchers to study the relationshipbetween ATM and achievement . Theory assumes that even moderate fluctuations inpositive feelings could systematically affect cognitive processing and soperformance. Research, however, failed to provide consistent findings regarding thisrelationship, since a number of researchers found a positive relationship between thetwo variables, but others did not. To assess the magnitude of this relationship, Ma &Kishor (1997) conducted a meta-analysis on 113 primary studies.

6 They found that theoverall mean effect size was statistically significant, rather weak at the primaryschool and stronger at the secondary school level. Researchers attribute the lowcorrelation at the primary school to the fact that ATTITUDES tend to be unstable in earlyyears and young pupils may not be able to express their ATTITUDES precisely. They alsoclaim that the weak effect sizes indicate that the attitude measures are perhaps lessreliable and valid at the elementary school level. Ruffell et al. (1998) agree on this,and argue that the attitude measures need to be more age-specific. They also wonderwhether pupils answers reflect their real ATTITUDES or just their temporary feelingstowards the is hard to refer to cause effect relationship between ATM and achievement . Resultsfrom the IEA s Third Study of mathematics revealed that although Japanese studentsoutperform students from other countries, they have negative mathematics ATTITUDES (Mullis et al.)

7 , 2000). This could be attributed to culture differences. However, theparticular relationship is a multi-dimensional construct and it is not easy to beanalyzed (Ruffell et al., 1998).Regardless of the relationship between ATTITUDES and achievement , teachers andMathematics educators tend to believe that children learn more effectively when theyare interested in what they learn and they achieve better if they like what they learnThematic Group 2 EUROPEAN RESEARCH IN mathematics EDUCATION IIIM. Nicolidau, G. Philippou3(Ma & Kishor, 1997). Thus, students who come to enjoy mathematics , increase theirintrinsic motivation to learn, and vice-versa. It is obvious, therefore, that continualattention should be directed TOWARDS creating, developing and reinforcing positiveattitudes TOWARDS any subject of the curriculum (Pintrich, 1999; Middleton & Spanias,1999). Nevertheless, ATTITUDES are relatively stable and one should not expectnoteworthy changes to occur over a short period of (SE) beliefs constitute a key component in Bandura s social cognitivetheory.

8 The construct signifies a person s beliefs, concerning her or his ability tosuccessfully perform a given task or behavior. It was found that SE is a majordeterminant of the choices that individuals make, the effort they expend, theperseverance they exert in the face of difficulties, and the thought patterns andemotional reactions they experience (Bandura, 1986). Furthermore, SE beliefs playan essential role in achievement motivation, interact with self -regulated learningprocesses, and mediate academic achievement (Pintrich, 1999).Bandura (1997) postulates four sources of SE information; mastery experiences,vicarious experiences, verbal-social persuasion and physiological and emotionalarousal which has to do with the level of emotional and physiological readiness of theindividual to undertake a specific task. Although all four sources of SE informationplay roles in the creation of efficacy beliefs, it is the interpretation of this informationthat is critical.

9 Cognitive processing determines how the sources of information willbe weighed and how they will influence the analysis of the task and the assessment ofpersonal differs from related motivational constructs, such as outcome expectancy, self -concept, self -esteem or locus of control, which are more general self -descriptiveconstructs that incorporate many forms of self -knowledge and self -evaluatingfeelings (Pajares, 1996). Bandura (1986) argues that SE refers to personal judgmentsof one s capabilities to organize and execute courses of action to attain specific goals,and measuring SE should focus on the level, generality and strength across specificactivities and contexts. Therefore, whereas a subject-specific self -concept test itemmight require the respondent to react to the statement I am a good student inMathematics , the SE item would require reaction to the statement I can solve percentproblems.

10 Ignoring of this tenet, leads to insufficient research findings, and that iswhy Pajares (1996) argues that if the purpose of a study is to find relationshipsbetween SE and performance, SE judgments should be consistent with and tailored tothe domain of the task under (1986) claims that young students are generally overconfident about theirabilities. He argues that some overestimation of capability is useful, since it increaseseffort and persistence. However, attention is needed for the protection of childrenfrom the danger of disappointment, in the case of continual failures. Children s SEbeliefs become more accurate and stable over time, and it is very difficult to change(Bandura, 1997).Thematic Group 2 EUROPEAN RESEARCH IN mathematics EDUCATION IIIM. Nicolidau, G. Philippou4 The relationship among efficacy , academic motivation and achievement inMathematics has been widely studied.