Secondary Pre-service Teachers’ Use of Vee Diagrams to Analyse Problems and Illustrate Multiple Solutions

Karoline Afamasaga-Fuata'i


This article presents data from a group of secondary pre-service teachers who used
vee diagrams to illustrate their conceptual and methodological analyses of a
problem, as part of a required mathematics methods course assignment. The
individually constructed vee diagrams were analysed in terms of the extent to which
they displayed principles and main concepts, adequately justified the mathematics
applied in their multiple methods, and the appropriateness of the methods for early
secondary level. Constructing vee diagrams prompted the pre-service teachers to repackage
their own understanding of the mathematics embedded in the problem
context, by organising the material in ways that were pedagogically meaningful,
developmentally sound, and flexibly arranged to meet a range of ability levels. The
vee diagrams’ overall ratings indicate the degree to which pre-service teachers
differentially achieved their intentions, conceptually and methodologically. Three
exemplars provide further insights into the nature of responses that collectively
differentiate between vee diagram types. Findings suggest vee diagrams provide a
useful tool to illustrate the pre-service teachers’ pedagogical intentions,
understanding and interpretations of the mathematics contextualised in a problem.


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