The Knowledge, Beliefs and Attitudes of the Mathematics Teacher: a model

Abstract Official pressure for reforms in the teaching of mathematics overlooks a key factor: the psychological foundations of the practice of teaching mathematics, including the teacher's knowledge, beliefs and attitudes. Research on teaching and teacher education also under‐emphasises this area, which Shulman terms the ‘missing program’ in research on teacher cognitions. The present paper addresses this lack by proposing an analytic model of the different types of knowledge, beliefs and attitudes of the mathematics teacher, and their relationship with practice. Of particular note is the importance accorded to the teacher's practical knowledge of the teaching of mathematics (both pedagogical and curricular knowledge), knowledge of classroom organisation, and knowledge of the school context. Also notable is the importance ascribed to the teacher's beliefs concerning the nature of mathematics, and concerning the processes of teaching and learning mathematics. The model has implications for teacher educatio...

[1]  D. Yorke.  Construing Classrooms and Curricula: a framework for research , 1987 .

[2]  G. Ryle,et al.  心的概念 = The concept of mind , 1962 .

[3]  M. Battista.  The Relationship of Mathematics Anxiety and Mathematical Knowledge to the Learning of Mathematical Pedogogy by Preservice Elementary Teachers , 1986 .

[4]  E. Stones.  2 Perspectives in pedagogy , 1983 .

[5]  I. Lakatos,et al.  Proofs and Refutations: Frontmatter , 1976 .

[6]  Hilary Putnam,et al.  Philosophy of mathematics : selected readings , 1984 .

[7]  L. S. Schulman.  Paradigms and research programs in the study of teaching , 1986 .

[8]  Thomas J. Cooney.  A Beginning Teacher's View of Problem Solving. , 1985 .

[9]  L. Aiken.  Attitudes Toward Mathematics , 1970 .

[10]  A. Thompson.  The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice , 1984 .

[11]  Paul Ernest,et al.  The philosophy of mathematics and mathematics education , 1985 .

[12]  L. Shulman.  Knowledge and Teaching: Foundations of the New Reform , 1987 .

[13]  Paul Ernest.  Philosophy, mathematics and education , 1989 .

[14]  Stephen Lerman.  Alternative views on the nature of mathematics and their possible influence on the teaching of mathematics , 1986 .

[15]  Richard J. Shavelson,et al.  Research on Teachers’ Pedagogical Thoughts, Judgments, Decisions, and Behavior , 1981 .

[16]  Colin Lacey,et al.  The socialization of teachers , 1977 .

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

[18]  I. Lakatos.  PROOFS AND REFUTATIONS (I)*† , 1963, The British Journal for the Philosophy of Science.

[19]  K. M. Evans,et al.  Attitudes and Interests in Education , 1965 .

[20]  Pinchas Tamir,et al.  Subject matter and related pedagogical knowledge in teacher education , 1988 .

[21]  Freema Elbaz.  The Teacher's "Practical Knowledge" Report of a Case Study , 1981 .

[22]  L. Shulman.  Those Who Understand: Knowledge Growth in Teaching , 1986 .

[23]  Philip J. Davis,et al.  The Mathematical Experience , 1982 .

[24]  H. Schofield.  Teacher Effects on Cognitive and Affective Pupil Outcomes in Elementary School Mathematics. , 1981 .

[25]  Darrell L. Parks,et al.  Agenda for action , 2005, Including the Excluded.

[26]  Warren Bower.  New directions , 1937 .

[27]  Stephen Lerman.  Problem‐solving or knowledge‐centred: the influence of philosophy on mathematics teaching , 1983 .

[28]  M. Lampert.  What Can Research on Teacher Education Tell Us about Improving Quality in Mathematics Education , 1988 .

[29]  Thomas Tymoczko.  New Directions in the Philosophy of Mathematics , 1985 .

[30]  G. Leinhardt,et al.  Expertise in mathematics instruction: Subject matter knowledge. , 1985 .

[31]  K. Start,et al.  Mathematics Attitudes and Achievement among Student Teachers , 1978 .

[32]  Neville Bennett.  The Effective Primary School Teacher: The Search for a Theory of Pedagogy. , 1988 .

[33]  Geoffrey Howson,et al.  Critical Variables In Mathematics Education , 1980, The Mathematical Gazette.

[34]  René Thom,et al.  Developments in Mathematical Education: Modern mathematics: does it exist? , 1973 .