Low-attaining students' representational strategies: tasks, time, efficiency, and economy

There are many potential ways to represent arithmetical tasks, but students' choices may be limited by beliefs that only certain standardised representations are 'legitimate' in school mathematics. Furthermore, concern for the quantity and speed of 'work done' can override opportunities for meaningful engagement with the content. This paper draws on a sample of the informal representational strategies observed during a microanalytic study of 11-15-year-old students with low prior attainment in mathematics. In the absence of pressure to provide quick answers, or to obtain them in a prescribed manner, students worked flexibly, participating in arithmetical reasoning, attempting and succeeding in tasks they were previously unable to engage with. The relationships between representational strategies, economy, and efficiency are discussed in relation to multiplicative thinking. These have pedagogical implications for the representational expectations placed on students with difficulties in mathematics, particularly in learning support and intervention contexts.