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Project

Unravelling the conceptual obstacles in mathematical reasoning.

This project connects to Part III of GOA project 2006/01 on Adaptive expertise in mathematics education. This part of the GOA project deals with the adaptive application of mathematical models in problem solving. Research is conducted on students inclination to routinely rely on well-practiced procedures and superficial problem characteristics in their problem solving behaviour, and how this inclination (negatively) affects adaptive expertise. An important goal is to determine the essential properties and the origins of a routine and an adaptive problem solving process, and which subject, task, and context characteristics lead to these processes. One of the research lines is to rely on cognitive-psychological dual process theories (e.g.. Stanovich & West, 2000) to show and unravel the routine/intuitive/heuristic or the adaptive/analytic nature of a thinking process. Our studies so far have shown that two central assumptions of dual process theory (namely that intuitive processes occur faster and require less working memory capacity) also hold for improper linear reasoning and for various More A-More B intuitive reasoning tasks. This proposal intends to extend this research to new domains, and explore its link with another theoretical framework, namely conceptual change theory. In a recent endeavour ,several European research groups have used this theoretical account to explain how pupils prior knowledge and formal instructional experiences can hinder later mathematical problem solving. The theoretical account for the obstacles in students mathematical reasoning given by conceptual change theory mostly deals with the development of these obstacles, in terms of the interaction and incompatibility between prior knowledge and newly acquired knowledge, while the dual process theoretical framework primarily focuses on momentary states in which subjects either stick to a first, intuitive response, or switch to analytic kinds of reasoning. Nevertheless, it seems that both frameworks are compatible, and may complement each other in important ways. Conceptual change theory assumes that pupils prior knowledge is organized on the basis of certain presuppositions, which children are unaware of, and that these robust presuppositions continue to influence their reasoning, even after being exposed to formal instruction. It has indeed been shown that adults often make errors similar to those of pupils, indicating that they have not always entirely overcome such presuppositions. It is at this point when the presuppositions are not entirely overcome while the correct knowledge is acquired ­ that a dual process theoretical account may explain the occurrence of errors: When reasoning analytically, a subject is not affected by the presuppositions, while in a heuristic mode, the presuppositions may still affect reasoning. A first aims at replication in a Flemish context. The other studies focus on the hypothesis that there are similar cognitive mechanisms underlying mathematical reasoning errors in the domains that are studied in the groups in Athens and in Leuven. We assume that when students are confronted with a mathematical task, the answer coming to mind first is in line with the students presuppositions in the particular domain, and this sometimes needs to be inhibited for a correct, counterintuitive answer to be given. This hypothesis is in line with dual process accounts of reasoning (e.g., Stanovich & West, 2000), which assume that humans have an intuitive/heuristic system (S1) that is fast, automatic, associative and undemanding of working memory capacity, and an analytic system (S2) that is controlled, deliberate and effortful, and where similar inhibition mechanisms are postulated. We will do reaction time research where adult subjects, as well as with secondary school students and with expert mathematicians, in order to detect different paterns in their responses and their reaction times.
Date:15 Sep 2009 →  14 Jun 2010
Keywords:Intuitive reasoning, Mathematical reasoning, Conceptual change, Problem solving
Disciplines:Education curriculum, Education systems, General pedagogical and educational sciences, Specialist studies in education, Other pedagogical and educational sciences