Connecting the everyday with the formal: the role of bar models in developing low attainers’ mathematical understanding

Hough, Sue, Gough, Stephen and Solomon, Yvette (2019) Connecting the everyday with the formal: the role of bar models in developing low attainers’ mathematical understanding. In: Congress of the European Society for Research in Mathematics Education (CERME11), 06 February 2019 - 10 February 2019, Utrecht, The Netherlands.

Preview

Accepted Version Download (802kB) | Preview

Abstract

Use of the bar model has gained momentum in England in recent years through the introduction of Singapore maths. Yet bar models originating from the Dutch approach known as Realistic Mathematics Education (RME), such as the fraction bar, the percentage bar and the double number line, have been available since the late 1990s. In this paper, we discuss the use of the bar in an intervention with low-attaining students in which we employed the RME approach. RME bases understanding in the everyday, where the role of the bar is to sustain modelling across multiple contexts, building on students’ informal models. We argue that this context-driven ‘bottom-up’ use of the bar is crucial in supporting progress towards formal mathematics, highlighting important issues to consider in the use of bar modelling, particularly with low attaining students. We suggest a consequent need for caution in use of the Singapore bar as a potential ‘top-down’ model.