Describing and Interpreting the Space of Classroom Learning in Problem-Solving-Based Mathematics Instruction: Variation as an Analytical Lens

Abstract

The field of mathematics education research has been promoting problem-solving-based mathematics instruction (PS-based MI) to afford opportunities to develop students’ conceptual understanding and problem-solving abilities in mathematics. Given its usefulness, there is still little knowledge in the field about how it can afford such opportunities in real classrooms. In this study, an attempt was made to make in-depth observations of such classrooms from the perspective of variation. We examined the differences in the space of learning provided by two lessons of the same teacher in two Ethiopian primary school classrooms. Based on the literature, we identified three key aspects for analysis: mathematical tasks, lesson structure and classroom interaction patterns. Our analysis showed that, even though both lessons focused on the same topic of solving linear inequalities, they were enacted differently. The lesson that employed a PS-based MI approach constituted a wider space of learning than the lesson employing a conventional approach. This study demonstrates the usefulness of our analytical approach for describing and documenting PS-based MI practice, and for qualitatively interpreting the differences in what is mathematically made available to learn. We suggest that it can provide guidelines for mathematics teachers to reflect upon and to enhance learning spaces in their own classrooms.

Keywords

• problem-solving-based mathematics instruction
• sequences of mathematical tasks
• lesson structure
• pattern of classroom interactions
• dimension of variation
• space of learning