Grima, G; Golding, J; (2018) Assessment to support the development of problem-solving goals in mathematics curricula 5-16. Presented at: 19th AEA Annual Conference, Arnhem–Nijmegen, Netherlands.

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Abstract

Current mathematics education policy perspectives in England, as well as in many other developed nations, privilege problem solving as a key 21st century skill (e.g. DfE, 2014; Kaur, 2014). Importantly, there is among the mathematics, mathematics education and end-user communities widespread embrace of problem solving as a centrally valued mathematical activity (e.g. ACME, 2011). However, English teachers and assessors often have limited experience of teaching for/assessing genuine problem solving, and performance in mathematics in England is high-stakes (Ofsted, 2012). Problem solving is therefore unlikely to be widely developed in classrooms unless summatively assessed at key points including GCSE, the standard English external assessment at age 16. A coherent curriculum system (Schmidt and Prawat, 2006) whereby intended curriculum, assessments, resources and teacher development are aligned and consistent, is key to supporting principled enactment (Golding, 2017). We report on a set of longitudinal efficacy studies which, among other intentions, evaluate the impact on teachers and students of a leading curriculum and assessment provider’s support for, and assessment of, problem solving for the 2014 Mathematics National Curriculum for 5-16 year olds (DfE, 2014). These are highly influential in England because they are widely adopted: the provider’s GCSE assessments at 16, for example, accounted for about two-thirds of all cohort entries in 2017. Key theoretical constructs used are those of performativity (Ball, 1994) and curriculum coherence (Schmidt and Prawat, 2006). Teacher interviews (n=452), student focus groups (n=172), classroom observations (n=101) and student survey responses (n~3300) over two early years of curriculum enactment show teachers and students perceive the approaches adopted in related curriculum materials and in the first set of provider GCSE examination papers not only employ highly valid assessment of, and approaches to, mathematical problem solving, but support that with provision of free surround materials specifically designed to build up students' ability to demonstrate related skills in summative timed assessments. However, we also evidence early and emerging constraints on both assessment and classroom enactment of problem solving in the curriculum: teacher skills and knowledge for related teaching across the range of students, teacher time and opportunity to harness the (additional or included) professional development opportunities provided with the resources, perceptions of superficial interpretations of ‘problem solving’ in national assessments at age 11, and pressures on schools and GCSE assessors to adopt enactments of ‘problem solving’ that are of limited validity, or for a subset of students only. Teachers attribute this to a) the challenges associated with defining an agreed meaning for mathematical problem solving and b) perceived in-school tensions between validly enacting that and meeting high-stakes performance measures. We discuss some implications.

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