Resisting reductionism in mathematics pedagogy

Abstract

Although breaking down a mathematical problem into smaller parts can often be an effective solution strategy, when the same reductionist approach is applied to mathematics pedagogy the effects are far from beneficial for students. Mathematics pedagogy in UK schools is gaining an increasingly reductionist flavour, as seen in an excessive focus on bite‐sized learning objectives and a tendency for mathematics teachers to path‐smooth their students’ learning. I argue that a reductionist mathematics pedagogy severely restricts students’ opportunities to engage in authentic mathematical thinking and deprives them of the enjoyment of solving richer, more worthwhile problems, which would forge connections across diverse areas of the subject. I attribute the rise of a reductionist mathematics pedagogy partly to an assessment‐dominated curriculum and partly to a systemic de‐professionalisation of teachers through a performative accountability culture in which they are constantly required to prove to non‐specialist managers that they are effective. I argue that pedagogical reductionism in mathematics must be resisted in favour of a more holistic approach, in which students are able to bring a variety of mathematical knowledge and skills to bear on rich, challenging and non‐routine mathematical tasks. Some principles for achieving this are outlined and some examples are given.

Developing mathematical fluency: comparing exercises and rich tasks

“…Traditional exercises are widely used by teachers not because they are perceived to be imaginative and creative sets of tasks but because they are believed to work in the narrow sense of developing fluency at necessary procedures. If there were some other way to achieve this, that did not entail the tedium of repetitive drill, it would presumably be Foster, 2013d) preferred-provided that it were equally effective at the main job. For this reason, in these studies the focus was entirely on the effect of etudes on procedural fluency.…”

“…It may also be that an excessive focus on basic procedures fails to kindle students' interest in mathematics and could be linked to students, especially girls, not choosing to pursue mathematics beyond a compulsory phase (Boaler, 2002). Nevertheless, in a high-stakes assessment culture, where procedural skills are perceived to be the most straightforward ones to assess, the backwash effect of examinations is likely to lead to schools and teachers feeling constrained to prioritise the development of procedural fluency over these other aspects of learning mathematics (Foster, 2013c;Ofsted, 2012;Taleporos, 2005).…”

Exploiting Unexpected Situations in the Mathematics Classroom

“…This study shows ways in which unexpected situations can be exploited mathematically and highlights factors that may predispose the teacher to do this more effectively. However, it does not address the powerful cultural and institutional factors that push teachers away from using their professional judgment to adapt classroom learning to the contingent needs and interests of the students as they present themselves there and then (Foster, 2013a). However, responding to interruptions to lessons by deviating from the intended lesson to exploit an unexpected situation can lead students into intense and enjoyable mathematical engagement, such as that characterised by Csikszentmihalyi (1988Csikszentmihalyi ( , 2002 as flow.…”

“…Although this perspective on the complexity of the mathematics classroom highlights the value of teachers adopting an improvisational stance, it is reported that mathematics teachers frequently lack a sense of autonomy and feel uneasy about deviating too far from the lesson plan (Pelletier & Sharp, 2008;Foster, 2013a). The institutional culture within a school may discourage teachers from responding mathematically to unexpected situations.…”

Primary school students’ perspectives on questions that bridge science and religion: Findings from a survey study in England

“…Within this framework, one category of objectives is focused on: the science classroom. Foster, 2013;K€ otter & Hammann, 2017). Our research is contextualised by a wider call for schools to strengthen students' epistemic insight by exploring the nature of science in real-world contexts and multidisciplinary arenas (see e.g.…”