Rethinking Characterizations of Beliefs

In this chapter we consider beliefs and the related concepts of conceptions and knowledge. From a review of the literature in different fields we observe that there is a diversity of views and approaches in research on these subjects. We report on a small research project of our own attempting to clarify the understanding of beliefs among specialists in mathematics education. A panel of 18 mathematics educators participated in a panel that we termed “virtual”, since the participants communicated with us only by e-mail. We sent nine characterizations related to beliefs, selected from the literature, to the panelists, asked them to express their agreement or disagreement with the statements, and also asked each to give their own characterization of the term. The answers were analyzed, searching for the elements around which the concept of beliefs has developed along the years. We discuss issues on which there was agreement and disagreement and conjecture what lies behind the differences. As a final step we make some suggestions relating to characterization of the term belief and ways of dealing with it in future research.

[1]  P. Cobb,et al.  Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. , 1996 .

[2]  J. Nespor.  The Role of Beliefs in the Practice of Teaching. , 1987 .

[3]  M. Pajares,et al.  Teachers’ Beliefs and Educational Research: Cleaning Up a Messy Construct , 1992 .

[4]  Joe Garofalo,et al.  Self-Confidence, Interest, Beliefs, and Metacognition: Key Influences on Problem-Solving Behavior , 1989 .

[5]  Rosa Maria Bottino,et al.  The emerging of teachers' conceptions of new subjects inserted in mathematics programs: the case of informatics , 1996 .

[6]  A. Thompson.  Teachers' beliefs and conceptions: A synthesis of the research. , 1992 .

[7]  M. Zanna,et al.  Attitudes and Attitude Change , 1993 .

[8]  Robert P. Abelson,et al.  Differences Between Belief and Knowledge Systems , 1979, Cogn. Sci..

[9]  Thomas F. Green.  The activities of teaching , 1971 .

[10]  Freema Elbaz,et al.  Teacher Thinking , 2018 .

[11]  Douglas B. McLeod,et al.  Beliefs, Attitudes, and Emotions: New Views of Affect in Mathematics Education , 1989 .

[12]  J. Mason,et al.  Studying attitude to mathematics , 1998 .

[13]  Douglas B. McLeod,et al.  Affect and mathematical problem solving : a new perspective , 1989 .

[14]  Douglas B. McLeod,et al.  Research on affect in mathematics education: A reconceptualization. , 1992 .

[15]  M. Franke,et al.  Teachers' knowledge and its impact. , 1992 .

[16]  Paul Ernest,et al.  The Philosophy of Mathematics Education , 2003 .

[17]  Ulrich Raatz,et al.  Einstellungen gegenüber Mathematik bei Mathematiklehrern , 1998 .

[18]  E. Pehkonen.  On Teachers’ Beliefs and Changing Mathematics Teaching , 1994 .

[19]  Douglas B. McLeod,et al.  Affect and Mathematical Problem Solving , 1989 .

[20]  Alan H. Schoenfeld,et al.  Mathematical Problem Solving , 1985 .

[21]  Elements for a Typology of Teachers' Conceptions of Physics Teaching. , 1992 .

[22]  R. Gorsuch,et al.  Beliefs, attitudes, and values , 1968 .

[23]  J. Hintikka.  Knowledge and belief , 1962 .

[24]  R. Audi.  Belief, justification, and knowledge , 1987 .

[25]  Edward A. Silver,et al.  Teaching and Learning Mathematical Problem Solving : Multiple Research Perspectives , 1985 .

[26]  A. Sfard.  On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin , 1991 .

[27]  A. Schoenfeld.  Learning to Think Mathematically: Problem Solving, Metacognition, and Sense Making in Mathematics (Reprint) , 2009 .

[28]  Thomas J. Cooney,et al.  Conceptualizing Belief Structures of Preservice Secondary Mathematics Teachers. , 1998 .

[29]  Robert B. Davis,et al.  Constructivist Views on the Teaching and Learning of Mathematics , 1990 .

[30]  A. Schoenfeld.  Cognitive Science and Mathematics Education , 1987 .

[31]  L. Hart.  Describing the Affective Domain: Saying What We Mean , 1989 .

[32]  Gwendolyn M. Lloyd,et al.  Supporting Innovation: The Impact of a Teacher's Conceptions of Functions on His Implementation of a Reform Curriculum. , 1998 .

[33]  T. Gardiner.  The art of knowing , 1998, The Mathematical Gazette.

[34]  Stefan Grigutsch,et al.  „Mathematische Weltbilder” bei Studienanfängern — eine Erhebung , 1994 .