There is an increasing trend within mathematics education in England toward the use of centrally produced lesson presentations. These presentations vary in their scope of use but may span teachers within a single school, teachers across many schools linked through Multi Academy Trusts, and teachers across the country connected through nationally resourced schemes of work. One notable feature of many of these standardised lesson presentations has been the explanation of mathematics based around small steps. It is claimed this implicit pedagogical approach provides pupils with a coherent journey and is a prerequisite for a progression in understanding of all pupils.

With the increase in centrally produced lesson presentations, the Documentational Approach to Didactics (DAD) provides a structure to examine the relationship between lesson resources and teachers’ pedagogical approaches. Within the notion of instrumental genesis, the intertwined relationship of how an individual acts upon resources (instrumentalization), and how those resources act upon the individual (instrumentation) can be considered. Whilst traditionally seen as a dialectic relationship resulting in a new position, in this study I place a focus on interpreting the significance of the changes to the lesson presentations and the teachers’ thinking.

In this comparative case study, the instrumental genesis around lessons on rearranging mathematical formulae are contrasted between two groups. In total, four mathematics teachers participated in the study and were grouped as two experienced mathematics teachers and two trainee mathematics teachers. Data from the teachers has been collected in the form of adapted lesson presentations and semi-structured interviews around the process. This data has been subsequently interpreted through Reflexive Thematic Analysis to identify similarities and differences between the two groups.

Emerging interpretations of the data highlight difference in both the instrumentalization and instrumentation aspects of the two groups. Whilst experienced teachers were seen to adapt lesson presentations to align more closely to their existing pedagogical approach, trainee teachers made very few changes. Accordingly, these trainee teachers were more receptive than the experienced teachers to the implicit small step pedagogy within the centralised lesson presentations. In addition, both groups were influenced by the clarity of definitions provided in the centrally produced lesson presentations.

Stemming from my emphasis on seeing significance in change, I suggest the increase in centrally prepared lesson presentations requires careful management in England. Within the process of instrumental genesis, mathematical definitions, examples, and implicit pedagogical approaches are understood differently by experienced and trainee teachers. Therefore, I firstly argue there is a need for teacher training programmes to engage with the examination of implicit pedagogies and the adaptation of resources. Secondly, within the wider mathematics teaching profession in England I argue there is a greater need, and opportunity for success, around the development of professional learning communities examining centrally produced lesson presentations.

Keywords: Mathematics education, Documentational Approach to Didactics, professional learning, resources.