Teachers pose and design context-based mathematics tasks: what can be learned from product evolution?

Abstract

This study proposes a model of several dimensions through which products of teachers’ context-based mathematics problem posing (PP) can be modified. The dimensions are Correctness, Authenticity, Task Assortment (consisting of Mathematical Diversity, Multiple Data Representations, Question–Answer Format, Precision-Approximation, and Generalization), Task Flow, and Student Involvement. A study was conducted in the context of a professional development (PD) program in which eight secondary school teachers iteratively designed 22 context-based mathematics tasks. Using the variation theory of learning as a theoretical framework and qualitative content analysis methodology, we compared different versions of the same tasks, focusing on items participants added or revised. To demonstrate the usability of the resulting semi-hierarchical model, we apply it to characterize the teachers’ final products of context-based PP. We found that most items teachers composed did not deviate from what we call the “common item form”—items that require numeric, exact, particular-case-related, and close-form answers without involving students in decision-making. Our findings may inform teacher educators and researchers on planning and implementing context-based mathematics task development by teachers in PD.