Students' Attitude in Mathematics Education

Comp. by: KJayaraja Stage: Proof Chapter No.: 146 Date:11/10/13 Time:14:46:47 Page Number: 1

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Students’ Attitude in Mathematics Education Rosetta Zan and Pietro Di Martino Dipartimento di Matematica, University of Pisa, Pisa, Italy

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Keywords

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Affect; Beliefs; Emotions; Interpretative approach; Students’ failure in mathematics

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Definition

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The construct of attitude has its roots in the context of social psychology in the early part of the twentieth century. In this context, attitude is considered as a state of readiness that exerts a dynamic influence upon an individual’s response (Allport 1935). In the field of mathematics education, early studies about attitude towards mathematics already appeared in 1950, but in many of these studies the construct is used without a proper definition. In 1992, McLeod includes attitude among the three factors that identify affect (the others are emotions and beliefs), describing it as characterized by moderate intensity and reasonable stability. But the definition of the construct remains one of the major issues in the recent research on attitude: as a matter of fact, there is

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no general agreement among scholars about the very nature of attitude. Therefore, in this entry, the issue of the definition of attitude towards mathematics (and also of the consequent characterization of positive and negative attitude) is developed in all its complexity.

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The Origin of the Construct

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Since the early studies, research into attitude has been focused much more on the development of measuring instruments than towards the theoretical definition of the construct, producing methodological contributions of great importance, such as those of Thurstone and Likert. As far as mathematics education is concerned, early studies about attitude towards mathematics already appeared in 1950: Dutton uses Thurstone scales to measure pupils’ and teachers’ attitudes towards arithmetic (Dutton 1951). The interest in the construct is justified by the vague belief that “something called ‘attitude’ plays a crucial role in learning mathematics” (Neale 1969, p. 631). In these studies, both the definition of the construct and the methodological tools of investigation are inherited from those used in social psychology: in particular, attitude is seen as “a learned predisposition or tendency on the part of an individual to respond positively or negatively to some object, situation, concept, or another person” (Aiken 1970, p. 551). Recourse to the adverbs “positively or negatively” is very

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S. Lerman (ed.), Encyclopedia of Mathematics Education, DOI 10.1007/978-94-007-4978-8, # Springer Science+Business Media Dordrecht 2014

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evident: indeed a lot of attention by researchers is focused on the correlation between positive/ negative attitude and high/low achievement. Aiken and Dreger (1961), regarding this alleged correlation between attitude and achievement, even speak of a hypothesis of the etiology of attitudes towards maths. Aiken (1970, p. 558) claims: “obviously, the assessment of attitudes toward mathematics would be of less concern if attitudes were not thought to affect performance in some way.”

The Problematic Relationship Between Attitude and Achievement Until the early nineties, research into attitude within the field of mathematics education focuses much more on developing instruments to measure attitude (in order to prove a causal correlation between positive attitude towards maths and achievement in mathematics) rather than on clarifying the object of the research. But the correlation between attitude and achievement that emerges from the results of these studies is far from clear. Underlining the need for research into attitude, Aiken (1970) refers to the need of clarifying the nature of the influence of attitude on achievement: he reports the results of many studies in which the correlation between attitude and achievement is not evident. Several years later, Ma and Kishor (1997), analyzing 113 studies about attitude towards mathematics, confirmed that the correlation between positive attitude and achievement is not statistically significant. In order to explain this “failure” in proving a causal correlation between positive attitude and achievement, several causes have been identified: some related to the inappropriateness of the instruments that had been used to assess attitude (Leder, 1985) and also achievement (Middleton and Spanias 1999), others that underline the lack of theoretical clarity regarding the nature itself of the construct attitude (Di Martino and Zan 2001). In particular, until the early nineties, most studies did not explicitly provide a theoretical definition of attitude and settled for operational

Students’ Attitude in Mathematics Education

definitions implied by the instruments used to measure attitude (in other words, they implicitly define positive and negative attitude rather than giving a characterization of attitude). Up until that time, in mathematics education, the assessment of attitude in mathematics is carried out almost exclusively through the use of self-report scales, generally Likert scales. Leder (1985) claims that these early attempts to measure attitudes are exceptionally primitive. These scales generally are designed to assess factors such as perspective towards liking, usefulness, and confidence. In mathematics education a number of similar scales have been developed and used in research studies, provoking the critical comment by Kulm (1980, p. 365): “researchers should not believe that scales with proper names attached to them are the only acceptable way to measure attitudes.” Other studies have provided a definition of the construct that usually can be classified according to one of the following two typologies: 1. A “simple” definition of attitude which describes it as the positive or negative degree of affect associated to a certain subject. 2. A “multidimensional” definition which recognizes three components of the attitude: affective, cognitive, and behavioral. Both the definitions appear to be problematic: first of all a gap emerges between the assumed definitions and the instruments used for measuring attitude (Leder 1985). Moreover, the characterizations of positive attitude that follow the definitions are problematic (Di Martino and Zan 2001). In the case of the simple definition, it is quite clear that “positive attitude” means “positive” emotional disposition. But even if a positive emotional disposition can be related to individual choices (e.g., which and how many mathematics courses to take), there are many doubts about the correlation between emotional disposition and achievement (McLeod 1992, refers to data from the Second International Mathematics Study that indicates that Japanese students had a greater dislike for mathematics than students in other countries, even though Japanese achievement was very high). Moreover, a positive emotional

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disposition towards mathematics is important, but not a value per se: it should be linked with an epistemologically correct view of the discipline. In terms of multidimensional definition, it is more problematic to characterize the positive/ negative dichotomy: it is different if the adjective “positive” refers to emotions, beliefs, or behaviors (Zan and Di Martino 2007). The assessment tools used in many studies try to overcome this difficulty returning a single score (the sum of the scores assigned to each item) to describe attitude, but this is inconsistent with the assumed multidimensional characterization of the construct. Moreover, the inclusion of the behavioral dimension in the definition of attitude exposes research to the risk of circularity (using observed behavior to infer attitude and thereafter interpreting students’ behavior referring to the inferred attitudes). In order to avoid such a risk, Daskalogianni and Simpson (2000) introduce a bidimensional definition of attitude that does not include the behavioral component. An interesting perspective is that identified by Kulm who moves to a more general level. He considers the attitude construct functional to the researcher’s self-posed problems and for these reason he suggests (Kulm 1980, p. 358) that “it is probably not possible to offer a definition of attitude toward mathematics that would be suitable for all situations, and even if one were agreed on, it would probably be too general to be useful.” This claim is linked to an important evolution in research about attitude, bringing us to see attitude as “a construct of an observer’s desire to formulate a story to account for observations,” rather than “a quality of an individual” (Ruffell et al., 1998, p. 1).

Changes of Perspective in Research into Attitude in Mathematics Education In the late 80s, two important and intertwined trends strongly influenced research about attitude in mathematics education.

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In the light of the high complexity of human behavior, there is the gradual affirmation of the interpretative paradigm in the social sciences: it leads researchers to abandon the attempt of explaining behavior through measurements or general rules based on a cause-effect scheme and to search for interpretative tools. Research on attitudes towards mathematics developed, in the last 20 years, through this paradigm shift from a normative-positivistic one to an interpretative one (Zan et al. 2006). In line with this, the theoretical construct of “attitude towards mathematics” is no longer a predictive variable for specific behaviors, but a flexible and multidimensional interpretative tool, aimed at describing the interactions between affective and cognitive aspects in mathematical activity. It is useful in supporting researchers as well as teachers in interpreting teaching/learning processes and in designing didactical interventions. Furthermore, the academic community of mathematics educators recognized the need for going beyond purely cognitive interpretations of failure in mathematics achievement. Schoenfeld (1987) underlines that lack at a metacognitive level may lead students to a bad management of their cognitive resources and eventually to failure, even if there is no lack of knowledge. The book “Affect and mathematical problem solving” (Adams and McLeod 1989) features contributions by different scholars regarding the influence of affective factors in mathematical problem solving. This gives a new impulse to research on affect, and therefore on attitude, in mathematics, with a particular interest on the characterization of the constructs. There is the need for a theoretical systematization and a first important attempt in this direction is done by McLeod (1992). He describes the results obtained by research about attitude, in particular underlining the significant results concerning the interpretation of gender differences in mathematics (Sherman and Fennema 1977); but he also points out the problems that emerged in the research about attitude (and more general affective construct), underlining the need for theoretical studies to

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better clarify the mutual relationship between affective constructs (emotions, beliefs, and attitudes): “research in mathematics education needs to develop a more coherent framework for research on beliefs, their relationship to attitudes and emotions, and their interaction with cognitive factors in mathematics learning and instruction” (McLeod 1992, p. 581). Moreover, McLeod highlights the need to develop new observational tools and he also emphasizes the need for more qualitative research. Following this, narrative tools began to assume a great relevance in characterizing the construct (Zan and Di Martino 2007), in observing changes in individual’s attitude (Hannula 2002), in assessing influence of cultural and environmental factors on attitude (Pepin 2011), and in establishing the relationship between attitudes and beliefs (Di Martino and Zan 2011).

The TMA Model: A Definition of Attitude Grounded on Students’ Narratives In the framework described, following an interpretative approach based on the collection of autobiographical narratives of students (more than 1800 essays with the title “Maths and me” written by students of all grade levels), Di Martino and Zan (2010) try to identify how students describe their relationship with mathematics. This investigation leads to a theoretical characterization of the construct of attitude that takes into account students’ viewpoints about their own experiences with mathematics, i.e., a definition of attitude closely related to practice. From this study it emerges that when students describe their own relationship to mathematics, nearly all of them refer to one or more of these three dimensions: • Emotions • Vision of mathematics • Perceived competence These dimensions and their mutual relationships therefore characterize students’ relationship with mathematics, suggesting a three-dimensional model for attitude (TMA) (Fig. 1):


The multidimensionality highlighted in the model suggests the inadequacy of the positive/ negative dichotomy for attitude which referred only to the emotional dimension. In particular the model suggests considering an attitude as negative when at least one of the three dimensions is negative. In this way, it is possible to outline different profiles of negative attitude towards mathematics. Moreover, in the study a number of profiles characterized by failure and unease emerge. A recurrent element is a low perceived competence even reinforced by repeated school experience perceived as failures, often joint with an instrumental vision of mathematics. As Polo and Zan (2006) claim, often in teachers’ practice the diagnosis of students’ negative attitude is a sort of black box, a claim of surrender by the teacher rather than an accurate interpretation of the student’s behavior capable of steering future didactical action. The identification of different profiles of attitude towards mathematics can help teachers to overcome the “black box approach” through the construction of an accurate diagnosis of negative attitude, structured in the observation of the three identified dimensions, and aimed at identifying carefully the student’s attitude profile.

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Cross-References

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▶ Affect in Mathematics Education ▶ Gender in Mathematics Education ▶ Metacognition in Mathematics Education ▶ Teacher Beliefs, Attitudes and Self-Efficacy in Mathematics Education

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References

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Adams V, McLeod D (1989) Affect and mathematical problem solving: a new perspective. Springer, New-York Aiken L (1970) Attitudes toward mathematics. Rev Educ Res 40:551–596 Aiken L, Dreger R (1961) The effect of attitudes on performance in mathematics. J Educ Psychol 52:19–24

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Allport G (1935) Attitudes. In: Murchinson C (ed) Handbook of social psychology. Clark University Press, Worcester, pp 798–844 Daskalogianni K, Simpson A (2000) Towards a definition of attitude: the relationship between the affective and the cognitive in pre-university students. In: Nakahara T, Koyama M (eds) Proceedings of the 24th conference of the international group for the psychology of mathematics education 3. PME, Hiroshima, pp 217–224 Di Martino P, Zan R (2001) Attitude toward mathematics: some theoretical issues. In: van den Heuvel-Panhuizen M (ed) Proceedings of the 25th conference of the international group for the psychology of mathematics education 3. PME, Utrecht, pp 351–358 Di Martino P, Zan R (2010) ‘Me and maths’: towards a definition of attitude grounded on students’ narratives. J Math Teach Educ 13:27–48 Di Martino P, Zan R (2011) Attitude towards mathematics: a bridge between beliefs and emotions. ZDM Int J Math Educ 43:471–482 Dutton W (1951) Attitudes of prospective teachers toward arithmetic. Elem Sch J 42:84–90 Hannula M (2002) Attitude toward mathematics: emotions, expectations and values. Educ Stud Math 49:25–46 Kulm G (1980) Research on mathematics attitude. In: Shumway R (ed) Research in mathematics education. National Council of Teachers of Mathematics, Reston, pp 356–387 Leder G (1985) Measurement of attitude to mathematics. Learn Math 34:18–21 Ma X, Kishor N (1997) Assessing the relationship between attitude toward mathematics and achievement

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in mathematics, a meta-analysis. J Res Math Educ 28:26–47 McLeod D (1992) Research on affect in mathematics education: a reconceptualization. In: Grouws D (ed) Handbook of research on mathematics teaching and learning: a project of the NCTM. Macmillan, New York, pp 575–596 Middleton J, Spanias P (1999) Motivation for achievement in mathematics: findings, generalizations, and criticism of the research. J Res Math Educ 30:65–88 Neale D (1969) The role of attitudes in learning mathematics. Arith Teach 16:631–641 Pepin B (2011) Pupils’ attitudes towards mathematics: a comparative study of Norwegian and English secondary students. ZDM Int J Math Educ 43:535–546 Polo M, Zan R (2006) Teachers’ use of the construct ‘attitude’. Preliminary research findings. In: Bosch M (ed) Proceedings of the fourth congress of the European Research in Mathematics Education. FundEmi, Barcelona. [CD ROM]. http://ermeweb.free.fr/CERME4/ CERME4_WG2.pdf. Accessed 1 Aug 2012 Ruffell M, Mason J, Allen B (1998) Studying attitude to mathematics. Educ Stud Math 35:1–18 Schoenfeld A (1987) What’s all the fuss about metacognition? In: Schoenfeld A (ed) Cognitive science and mathematics education. Lawrence Erlbaum Associates, Hillsdale, pp 189–216 Sherman J, Fennema E (1977) The study of mathematics by high school girls and boys: related variables. Am Educ Res J 14:159–168 Zan R, Brown L, Evans J, Hannula M (2006) Affect in mathematics education: an introduction. Educ Stud Math 63:113–121 Zan R, Di Martino P (2007) Attitudes towards mathematics: overcoming positive/negative dichotomy. Mont Math Enthus Monogr 3:157–168

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EMOTIONAL DISPOSITION

VISION OF MATHEMATICS

PERCEIVED COMPETENCE

Students’ Attitude in Mathematics Education, Fig. 1 The TMA model for attitude (Di Martino and Zan 2010)