Jacques, Laurie; (2023) Primary Teachers' Design Principles and Pedagogical Practices for Promoting Mathematical Learning from Procedural Variation Tasks. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

Since 2014 mathematics teaching in primary schools in England has undergone pedagogical reform, influenced by practices developed in Shanghai. A particular practice involves designing a set of equations using deliberate variation and invariance – a one-problem-multiple-changes procedural variation task. This set of equations becomes an exercise that can be considered as a single mathematical object. Set in the context of this reform, eight in-service primary teachers in England participated in three novel professional learning sessions, Task-Design Lesson Study (TDLS), during which they designed one-problem-multiple-changes procedural variation tasks and used them to promote pupils’ mathematical learning. Video-recordings of the pre- and post- lesson discussions and the lesson episodes were analysed using qualitative content analysis, guided by the conceptual framework, ‘teaching-with-variation’ and in particularly the principles for procedural variation. The findings provide a cultural interpretation of teaching-with-variation from England, revealing fresh insight into the factors contributing to teachers’ design of one-problem-multiple-changes procedural variation tasks and accompanying pedagogical practices. This study contributes to knowledge of mathematics task design in three notable ways. Firstly, teachers deliberately choose to vary arbitrary features of the equations in order to draw pupils’ attention to an invariant property of the set of equations, described as a dependency relationship. Secondly, by arranging the set of equations in an orderly way, teachers can support pupils to discern invariance by working horizontally, treating the equations individually, and vertically, treating the set of equations as a single mathematical object. Finally, the study expands the conceptual framework of ‘teaching-with-variation’ by adding ‘bringing convergence’ as the intended outcome from using such tasks. Additionally, the study makes a methodological contribution to task design research with Task-Design Lesson Study, a novel setting with which to conduct research where teachers and researchers are partners in task design.

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