Learning to teach contextualised problem solving in a non-calculus mathematics pathway

Abstract We report on the professional learning of a small purposive sample of teachers beginning to teach an English post-16 mathematics course centred around contextualised problem solving. We describe their accounts of change, their intentions and justification for those, and how development was supported. The demands of the course require ‘boundary crossing’ between contexts and mathematics that was novel for these teachers and their students, and learning to teach for such approaches is known to be demanding. By drawing on peer support and their own robust subject knowledge, though, these teachers were able to accommodate change to classroom authority and expertise, attention to students’ relationship with mathematics, longer- term planning sequences, and growth in their own management of uncertainty within the classroom. Keywords: Contextualised problem-solving, mathematics in context, teacher beliefs, teacher affect, boundary crossing. Introduction This paper focuses on teacher change and professional learning in an important context that is known to present difficulties. In recent years, England has seen concerted policy moves (e.g. ACME, 2012 a, b) to extend participation in post-16 mathematics beyond the relatively small cohort (Hodgen et al, 2013) taking ‘A-level’ Mathematics, the standard English calculus-rich pre-university course. ‘Core Maths’ was introduced in September 2014. Although there are six versions of the qualification offered, our focus is on features that are shared and potentially new to teachers. All versions are intended to be studied over two years, earning half the credit of A-level Mathematics and accessible to students with a standard level of mathematics qualification (GCSE) at 16. They are designed for enactment around contextualised problem-solving tasks (DfE, 2015), featuring what Ainley, Pratt and Hansen (2006) call utility (appreciation of when, how and why mathematics is useful) and purpose (meaningful outcomes for the student), and with learning objectives to • Deepen competence in the selection and use of mathematical methods and techniques. • Develop confidence in representing and analysing authentic situations mathematically and in applying mathematics to address related questions and issues. • Build skills in mathematical thinking, reasoning and communication (DfE 2015). Because Core Maths aims primarily at building up application of mathematical skills rather than enhancing students’ repertoire of mathematical facts and procedures, we hypothesised that successful teaching of Core Maths might require teachers to develop new pedagogies and even new mathematical skills. We report a small study which asked, ‘How and why do teachers develop their teaching to accommodate the distinctive demands of Core Maths – and with what support?’ It contributes to knowledge of the ways that teachers develop their practice to promote mathematical utility and purpose, including its assessment, the support needed, and teachers’ capacity for change. Unlike studies of comparable initiatives that report reform- related teacher deficits, we show these teachers were confident to make initial changes to practice within a collaborative support programme that focused on pedagogic resources and only indirectly addressed mathematical knowledge. Moreover, in the absence of formal assessment guidelines or the pressures of high-stakes accountability, teachers developed teaching repertoires that underpinned valued student outcomes and informed their wider practice. And centrally, we show they promoted change to classroom authority and expertise, and paid deep attention to developing students’ meaningful relationship with mathematics.