Reference : A web-based system for mathematical problem understanding and solving
Scientific journals : Article
Social & behavioral sciences, psychology : Multidisciplinary, general & others
http://hdl.handle.net/10993/12368
A web-based system for mathematical problem understanding and solving
English
Busana, Gilbert mailto [University of Luxembourg > Faculty of Language and Literature, Humanities, Arts and Education (FLSHASE) > Educational Measurement and Applied Cognitive Science (EMACS) >]
Martin, Romain mailto [University of Luxembourg > Faculty of Language and Literature, Humanities, Arts and Education (FLSHASE) > Educational Measurement and Applied Cognitive Science (EMACS) >]
Langers, Christian mailto [University of Luxembourg > Faculty of Language and Literature, Humanities, Arts and Education (FLSHASE) > Educational Measurement and Applied Cognitive Science (EMACS) >]
2008
International Journal of Psychology
Routledge
43
729
Yes (verified by ORBilu)
International
0020-7594
Hove
United Kingdom
[en] Educational Technology ; Computer in Education ; Mathematical Problem Solving
[en] In the domain of educational multimedia for primary school a lot of research has been done in the field of computer assisted calculation frameworks. However, much less work has been done in the area of problem solving and especially in the area of problem understanding. The present project aims at the development and the scientific assessment of a computer assisted framework for mathematical problem understanding and solving (CAMPUS) based on analogical representations in form of number lines (Klein, Beishuizen, & Treffers, 1998; Petitto, 1990) and graphs. This tool will be deployed by our formerly developed computer assisted testing platform (http://www.tao.lu) [see our proposal on TAO] and will be the first learning tool on that system. The CAMPUS framework will help teachers to more efficiently analyze the different steps of the problem solving strategies of their students and thereby allow them to give more adapted feedback in order to guide the learner’s process.

The main characteristic of this platform is the use of the computer as a framework for the development of problem solving strategies in mathematics. The tool imposes no restrictions in the resolution processes of the learner, but avoids him to get lost in those steps of solving that are obviously wrong (for example: addition of objects of different classes). In this way, the CAMPUS architecture is a sort of a cognitive tool that helps the student in structuring his thinking by telling him which calculations are mathematically or logically not permitted, but it does not suggest him a precise way towards the solution. In contrary, each logically correct action will be accepted by the system. Consequently, the CAMPUS tool is not a drill-and-practice tool, but it proposes a framework for the student in which he can develop problem solving strategies in complex situations. CAMPUS is based on a (socio-)cognitive approach, which means that the tool permits to solve the problems in an individual or a group situation, even if the teamwork is explicitly desirable in such a pedagogical approach (Webb, 1994; Yadrick, Regian, Connolly Gomez, & Robertson Schule, 1997). The tool is intended to be integrated into daily classroom teaching as a tool for triggering the learning process and therefore has not to be considered as a separate or additional exercising tool. The students learning process should be supported by the tool on one hand and by additional teacher support on the other hand. The learner and his learning process are at the centre of the learning activity (Tardif, 1998) and the teacher plays a supervision and support role in this sort of learning environment (Hudson, 1997; Tardif, 1998).

Moreover, the use of analogical representations (of the operations to be taken) and graphs (representing the resolution steps adopted by the learner) should favour, on the learner’s side, the establishment of mental models including analogical representations and supporting the resolution process of this type of problems, even beyond the use of this computerized platform. We could expect that the learner will develop, through his experiences with the platform (which prevents experimentation with arbitrary meaningless calculations), thorough knowledge concerning the solving of mathematical problems based, at least partially, on non-explicit learning processes as described, for example, in the connectionist models of learning theories (Spitzer, 2000). These connectionist models show in fact that significant learning can be achieved in a non-explicit manner if the learner is placed in an environment which structures his behavior along certain regularities (even if these regularities are not taught in an explicit manner).



The CAMPUS framework is based on a conceptual idea that emerged from previous research (Busana, 1999) where a prototype using a similar architecture has been developed in an alpha-version using Quest. This alpha-version was developed in only one language (German) and ran only under Windows. The new CAMPUS-tool will be published under the open-source licence, will be platform independent (plays in Macromedia’s Flash Player) and will be delivered over the Internet.
http://hdl.handle.net/10993/12368

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