Title: Reasoning, modelling and knowledge codification in solving well-structured mathematics problems

Authors: Kumar Laxman

Addresses: Centre for Excellence in Learning and Teaching, Nanyang Technological University, 76 Nanyang Walk, Block N2.1, Singapore, 637331, Singapore

Abstract: In problem-based learning, the instructional process begins with the introduction of the problem statement, one that is usually real-world-oriented. Students in groups are encouraged to tackle and solve the problem, in the process of which they build up their own individual conceptual knowledge schemas in relation to the given problems. In developing PBL-centred curriculum, problems selected as the cognitive stimulus in initiating knowledge construction could be either well or ill-structured problem representations. The study described in this paper adopted a case study approach to investigate the cognitive reasoning and analytical strategies students employed in conceptualising and deconstructing story and arithmetic well-structured problems. It is hoped that the findings of this study will shed more light on the heuristic ways in which students approach well-structured problem solving and inform the educational design of effective problem solving environments.

Keywords: problem solving; knowledge codification; modelling; problem-based learning; PBL; instructional processes; problem statements; real world; conceptual knowledge schemas; group work; curriculum; cognitive stimulus; knowledge construction; problem representations; cognitive reasoning; analytical strategies; conceptualisation; deconstruction; mathematics; well-structured problems; mathematical problems; arithmetic; heuristics; educational design; first-year students; polytechnics; tertiary institutions; higher education; Singapore; innovation.

DOI: 10.1504/IJLIC.2011.041078

International Journal of Learning and Intellectual Capital, 2011 Vol.8 No.3, pp.348 - 358

Published online: 30 Jun 2011 *

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