Thompson (1992) (handbook)
Thompson's Teachers' Beliefs and Conceptions: A Synthesis of the Research (1992)
Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 127–146). Reston, VA: National Council of Teachers of Mathematics.
The Study of Beliefs: A Brief History
Beliefs and Knowledge
Distinctions Between Beliefs and Knowledge
Belief Systems
Green's 3 dimensions of belief systems:
- Beliefs are never in total independence of all other beliefs; they have a quasi-logical structure with some primary beliefs and some derivative beliefs
- Beliefs can vary in strength, being central or peripheral
- Beliefs are held in clusters, more or less in isolation from other clusters, making it possible to have conflicting sets of beliefs
Beliefs and Mathematics Teaching and Learning
Ernest (1988) noted key elements that influence the practice of math teaching:
- The teacher's mental contents or schemas, particularly the system of beliefs concerning math and its teaching and learning
- The social context of the teaching situation, particularly the constraints and opportunities it provides
- The teacher's level of thought processes and reflection.
Mathematics Teachers' Beliefs and Conceptions
Overview
Teachers' Conceptions of Mathematics
"A teacher's conception of the nature of mathematics may be viewed as that teacher's conscious or subconscious beliefs, concepts, meanings, rules, mental images, and preferences concerning the discipline of mathematics" (p. 132).
Together, this roughly makes up a teacher's philosophy, but it might not be coherent
Skemp's work seems fascinating!
The Relationship Between Conceptions of Mathematics and Instructional Practice
Teachers' Conceptions of Mathematics Teaching and Learning
This seems similar to the previous subsection, but I think the previous one is more about enactment of practice, while this is more about beliefs of mathematics teaching and learning.
Models of Mathematics Teaching
Good stuff here from Kuhs & Ball (1986)