Beliefs: A Hidden Variable in Mathematics Education? by G.C. Leder (Editor), Erkki Pehkonen (Editor), Günter Törner

By G.C. Leder (Editor), Erkki Pehkonen (Editor), Günter Törner (Editor)

This e-book specializes in elements of mathematical ideals, from quite a few diversified views. present wisdom of the sphere is synthesized and present limitations are prolonged. the amount is meant for researchers within the box, in addition to for arithmetic educators educating the subsequent new release of scholars.

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We are well aware that the state of the art of the research field does not allow the development of a comprehensive theory at the moment. Nevertheless an attempt will be made in this chapter to clarify the conceptual discussion and to introduce a framework for students' mathematicsrelated beliefs that might be a further step in that direction. 16 PETER OP 'T EYNDE, ERIK DE CORTE, AND LIEVEN VERSCHAFFEL To direct our research activities we have chosen to start from the following very broad and to some extent intuitive, working definition of students’ mathematicsrelated beliefs: Students’ mathematics-related beliefs are the implicitly or explicitly held subjective conceptions students hold to be true, that influence their mathematical learning and problem solving.

In addition, we further clarify the relation between beliefs and knowledge. Thirdly, starting from this analysis of the nature and the structure of beliefs, we introduce a theoretical framework and a more elaborated definition of students' mathematics-related beliefs that thoughtfully tries to integrate the major components of the models reviewed in the first part. Some final comments focusing on directions for future research conclude the chapter. 2. STUDENTS' BELIEFS AND MATHEMATICAL LEARNING AND PROBLEM SOLVING: A REVIEW To develop a more comprehensive understanding of the different kinds of students’ beliefs considered to determine mathematical learning and problem solving, and the way they relate to each other, we conducted a search of the literature for the period 1984 to 2000 in the ERIC and PSYCINFO databases, entering the key words “mathematics” and “beliefs”, and their derivatives.

They seem to stay much closer to the complex way our mind actually works. Third, although closely related in their functioning, there are fundamental differences between the structure of belief and knowledge systems, one of the distinctive characteristics being that a belief system has a quasi-logical structure, where a knowledge system has a logical structure. Indeed, the equilibrium a belief system is trying to achieve is psychological in nature. The underlying rationale are the needs, desires and goals of the self.

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