A professional development programme for teaching mathematics through problem solving
Authors:   , Sawyer Robert 
Published: January 2024

This thesis documents the design, implementation and evaluation of a professional learning programme to support teachers in developing their ability to teach mathematics through problem solving. Teaching mathematics through problem solving is recognised as an effective way to teach mathematics. However, there are a number of different approaches with different descriptors such as problem posing and problem-based learning. In this study, teaching mathematics through problem solving is an approach where learners explore a problem or a task and their responses to the task are ‘orchestrated’ by the teacher to introduce and develop the mathematics to be learned. The development of this teaching approach involves the principles of task design and planning the sequencing of anticipated responses to be orchestrated. The professional development programme was informed by research on task design and the features of effective professional learning for teachers. The programme was built around the professional learning programme Lesson Study and was modified with a ‘pause’ in the research lesson and the use of remote visualisers to observe and analyse the work of the pupils. This latter feature was an adaption of the original programme design to respond to conditions arising in schools during the Covid-19 pandemic. Also a number of additional modifications were made to accommodate the ambitions of the programme. A qualitative approach was adopted using the methodology of design research and comprising two research cycles. The cohort in the first cycle were secondary school teachers and in the second cycle they were primary school teachers, all working in England. The aim of the study was to understand the effect of the programme on the participants’ knowledge, skills and confidence in teaching mathematics through problem solving. Existing frameworks in the literature on the known characteristics of effective professional learning were synthesised to evaluate the effectiveness of the programme. The main outcomes from this research confirm that the designed features of the PD programme were effective in supporting teachers in developing their ability to teach mathematics through problem solving. The use of task design principles in conjunction with the development of the teaching technique of orchestration resulted in gains in teacher confidence and subject and pedagogical knowledge. The pause in the research lesson and the use of visualisers to observe and analyse the pupils’ work provided the participants with a focused learning opportunity to develop the teaching approach. The evaluation of the programme using the designed analytical framework for CPD identified [a range of] known characteristics of effective CPD in the programme as designed and implemented. Three main implications emerged from the study, the first of which concerns the future development of teaching mathematics through problem solving. It was apparent that there were contextual barriers to the approach becoming an established part of teachers’ practice. To address these, the design of mathematics teaching resources would need to reflect the ambition to teach mathematics through problem solving. This is an issue for curriculum designers. There would also need to be recognition of the problem-solving skills that pupils require to access the problems, which would need to be taught either as part of teaching through problem solving or as a separate approach known as teaching for problem solving. The second implication identifies the challenges associated with introducing this type of programme into the current landscape of professional learning for teachers of mathematics in England, including the need for greater coherence between the professional learning of teachers of mathematics and their own workplace contexts. Finally, the third implication relates to the use of Lesson Study. This study described how the use of design research can develop Lesson Study variants that can make a positive contribution to professional learning environments for teachers without compromising the key principles of Lesson Study.