Investigating Mathematics Teaching: A Constructivist Enquiry

By Barbara Jaworski | Go to book overview

Notes
1
Although Ernest (1991a) argues that constructivism should be regarded as a philosophy rather than a theory, since ‘Neither its key terms, nor the relationships between them are sufficiently well or uniformly defined for the term “theory” to be strictly applicable.’
2
The case study in Chapter 7 includes an example of the situation described theoretically here. A pupil Phil, had the dilemma of two different solutions for the area of a triangle. The account addresses the teacher’s coming to know more about Phil’s conceptions, and consequent effort to create dissonance—i.e., a constraint to confront Phil with a contradiction in his reasoning.
3
This also became very obvious in Ben’s ‘Kathy-Shapes’ lesson, when a group of girls was tackling areas of triangles in which their image of ‘vertical height’ differed from mine and from that of the teacher. See Jaworski, 1991, Appendix 5
4
See Edwards and Mercer (1987) for a research study which set out to identify aspects of ‘common knowledge’ in classrooms. The authors point to important consequences of classroom interactions for the development of common and individual understandings.
5
See Chapter 4 for elaboration, in my usage, of the difference between ‘manifestations’ and ‘examples’ of theoretical ideas.
6
The discrepancy of dates (Kilpatrick, 1987, quoting Davis and Mason, 1989) arises from the existence of Davis and Mason (1989) as an occasional paper distributed by the authors in 1986.

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