Interpretations of a constructivist philosophy in mathematics teaching

Jaworski, Barbara (1991). Interpretations of a constructivist philosophy in mathematics teaching. PhD thesis The Open University.

DOI: https://doi.org/10.21954/ou.ro.0000dff0

Abstract

This thesis is a research biography which reports a study of mathematics teaching. It involves research into the classroom teaching of mathematics of six teachers, and into their associated beliefs and motivations. The teachers were selected because they gave evidence of employing an investigative approach to mathematics teaching, according to the researcher's perspective. A research aim was to characterise such an approach through the practice of these teachers.

An investigative approach was seen to be embedded in a radical constructivist philosophy of knowledge and learning. Observations and analysis were undertaken from a constructivist perspective and interpretations made were related to this perspective.

Research methodology was ethnographic in form, using techniques of participant-observation and informal interviewing for data collection, and triangulation and respondent validation for verification of analysis. Analysis was qualitative, leading to emergent theory requiring reconciliation with a constructivist theoretical base. Rigour was sought by research being undertaken from a researcher-as-instrwnent position, with the production of a reflexive account in which interpretations were accounted for in terms of their context and the perceptions of the various participants including those of the researcher.

Research showed that those teachers who could be seen to operate from a constructivist philosophy regularly made high level cognitive demands which resulted in the incidence of high level mathematical processes and thinldng skills in their pupils.

Levels of interpretation within the study led to the identification of investigative teaching both as a style of mathematics teaching and as a form of reflective practice in the teaching of mathematics. These forms were synthesised as a constructivist pedagogy and as an epistemology for practice which may be seen to forge links between the theory of mathematics teaching and its practice.

The research is seen to have implications for the teaching of mathematics, and for the development of mathematics teaching itself through professional development of mathematics teachers.