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Computing solutions to algebraic problems using a symbolic versus a schematic strategy
Lee, K., Yeong, S. H. M., Ng, S. F., Venkatraman, V., Graham, S., & Chee, M. W. L. (2010). Computing solutions to algebraic problems using a symbolic versus a schematic strategy. ZDM: International Journal of Mathematics Education, 42(6), 591-605.
To improve access to algebraic word problems, primary aged students in Singapore are taught to utilise schematic models. Symbolic algebra is not taught until the secondary school years. To examine whether the two methods drew on different cognitive processes and imposed different cognitive demands, we used functional magnetic resonance imaging to examine patterns of brain activation while problem solvers were using the two methods. To improve our ability to detect differences attributable to the two methods -- rather than participant’s abilities to use the two methods --- we used adult problem solvers who had high levels of competency on both methods. In a previous study, we focused on the initial stages of problem solving: translating word problems into either schematic or symbolic representations (Lee et al. 2007, Brain Research, 1155:163-171). In this study, we focused on the later stages of problem solving: in computing numeric solutions from presented schematic or symbolic representations. Participants were asked to solve simple algebraic questions presented in either format. Greater activation in the symbolic method was found in the middle and medial frontal gyri, anterior cingulate, caudate, precuneus, and intraparietal sulcus. Greater activation in the model condition was found largely in the occipital areas. These findings suggest that generating and computing solutions from symbolic representations require greater general cognitive and numeric processing resources than do processes involving model representations. Differences between the two methods appear to be of both a quantitative and qualitative nature.
This is the original draft, prior to peer-review, of a manuscript published in ZDM: International Journal of Mathematics Education. The published version is available online at http://link.springer.com/article/10.1007%2Fs11858-010-0265-6
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