Differences in how teachers make mathematical content available to learners over time

The study was an investigation into the teaching decisions that mathematics teachers make over time. I view a mathematics classroom as a didactical system of teacher, learners and content within an educational institution, where content is the material that brings teachers and learners together. Within such a system I view the teacher’s role as making content available to learners. Prior research has often investigated the teacher’s role by comparing teaching practices nationally or internationally, but these comparisons have tended to use the lesson as the unit of analysis. I propose that how teachers make content available can change over the course of a series of lessons and so my study used the lesson series as the unit of analysis. I purposefully designed the study so that it involved four cases, which allowed me to explore the role of the teacher and the topic in how content was made available. To investigate how teachers made content available to learners in each case, I developed an analytical approach from which I could study the modes of teacher interaction that featured across the lesson series, the forms of mathematical content made available and the sequencing of these forms. Attending to forms of content – rather than content itself – allowed for comparison of teaching of different topics. This original analytical approach represents a contribution to both mathematics education and mixed methods research. Within this small sample of cases, quantifiable differences were identified in how content was made available between classwork and seatwork, from lesson to lesson and between cases. Between-case differences in the nature of teaching ‘between-the-desks’ during seatwork were also identified. These differences illuminated teaching decisions to which teachers and classroom researchers may not routinely attend. The findings therefore contribute – and identify additional lines of enquiry that might contribute further – to a more extensive understanding of teaching practices.