The use of real-world contextual framing in UK university entrance level mathematics examinations

Abstract

Although there has been considerable research into real-world contexts in elementary mathematics, little work has been done at a more advanced, post-16 level. This thesis explores the origin, function and effect of real-world contextual framing (RWCF)in GCEA/AS mathematics examinations. The study develops an evaluation framework (ARTA)based on the notions of accessibility, realism and task authenticity, derived from assessment theory, and considers ‘context’ in relation to theoretical ideas such as Realistic Mathematics Education, construct validity and construct-irrelevant variance.

The function and effect of RWCF are investigated using the ARTA framework on samples of A/AS questions. Its effect is explored using sequence questions with the same solutions with and without real-world context, set to a sample of nearly 600 students, together with a questionnaire that surveys students’ attitudes to RWCF. Quantitative differences in the use of RWCF are established and traced to early project syllabuses such as SMP and MEI. The study finds that RWCF in general adds to the difficulty of questions, unless they can be solved by ‘thinking within the context’. The accessibility of questions with RWCF is a function of comprehensibility of language, and the explicitness of the match between context and mathematical model. The study distinguishes between natural and synthetic contexts, according to the extent to which the context matches reality, or reality is configured to match the mathematics. Natural contexts are more realistic; but synthetic contexts can serve the purpose of reifying abstract mathematical ideas. At best, RWCF in examination questions require solvers to engage in pseudo-modelling: they cannot test aspects of the modelling cycle such as discussing assumptions, refining, and critical reading of longer arguments. There is, moreover, a gender difference in students’ attitudes to RWCF, with boys in general expressing more favourable views about its use in pure mathematics questions.

These findings have the following implications for A/AS assessment. Current examination questions are not able to satisfy current QCDA (Qualifications and Curriculum Authority, 2002) assessment objectives on mathematical modelling. Questions with RWCF need to be authentic, and require careful construction to ensure that language is precise and unambiguous. Longer questions, which present and invite comparison of more than one model, are desirable, in order that students appreciate the relationship between reality and mathematical models.

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ORCID for Keith Jones: orcid.org/0000-0003-3677-8802

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