What Effect has Context on the Mental Computation Performance

Abstract in English:

This paper reports on part of a larger study that investigated this question with students in the Perth Metropolitan area who were given the same mental computation test twice – once with the items in context and once without. Money was used as the context and students’ experience with money was also measured. Despite many curriculum documents espousing the importance of teaching and learning mathematics in context, this study found that neither experience with nor use of the context of money had any effect at all, except in Year 3.
Keywords: context, mental computation, number sense, primary school, secondary school
Teaching and learning mathematics in context is often considered to be a significant goal in school mathematics, as confirmed in various curriculum documents (Australian Education Council, 1991; Curriculum Council, 1998; NCTM, 2000). However, it is generally accepted that this goal is given much less prominence in Asian countries. The landmark study by Carraher, Carraher and Schliemann (1985) clearly demonstrated students’ higher performance on market-place mathematics – a context within their experience – compared to the same items presented in a ‘school mathematics’ format. Maier (1980) used the term ‘folk mathematics’ to define mental computation and estimation that is developed by individuals through self-discovery – as distinct from school mathematics which is often unrelated to real life. The nature of folk mathematics implies that it is embedded in context. A number of researchers have used money as a context – for example, Guberman (1992); Nunes, Schliemann, and Carraher (1993); and Irwin (2001) – but these studies have been somewhat limited in scope.
Current mathematics curricula are devoting greater attention to mental computation. This is stressed by leading researchers in the area of number sense who see mental computation as the way forward in the development of number sense, alongside the need to reduce traditional written computation due to the widespread use of calculators (McIntosh & Sparrow, 2004). In a study in Taiwan, Yang (1995) found that while students performed well in written computation items, they struggled when the same items were presented as requiring an estimate – thus the need to use mental computation and number sense.