How Concrete is Concrete?

Koeno Gravemeijer

Abstract


If we want to make something concrete in mathematics education, we are inclined introduce, what we call, ‘manipulatives’, in the form of tactile objects or visual representations. If we want to make something concrete in a everyday-life conversation, we look for an example. In the former, we try to make a concrete model of our own, abstract, knowledge; in the latter, we try to find an example that the others will be familiar with. This article first looks at the tension between these two different ways of making things concrete. Next another role of manipulatives, will be discussed, namely that of means for scaffolding and communication. In this role, manipulatives may function as means of support in a process that aims at helping students to build on their own thinking while constructing more sophisticated mathematics.

Keywords


Conceret Learning Materials; School Math; Common Sense; Scaffolding; Communication

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References


Freudenthal, H. (1987). Mathematics starting and staying in reality. In I. Wirszup & R. Street (Eds.), Proceedings of the USCMP conference on mathematics education on development in school mathematics education around the world. Reston, VA: National Council of Teachers of Mathematics.

Gravemeijer, K.P.E. & Nelissen, J.M.C. (2007). Hoezo concreet? Op zoek naar concretiseringen die het kinderlijke denken ondersteunen. Volgens Bartjens, 26(3), pp. 14-16.

Treffers, A. (1990). Rekenen tot twintig met het rekenrek (addition and subtraction up to twenty with the arithmetic rack). Willem Bartjens, 10 (1), 35-45.

van Hiele, P.M. (1973). Begrip en inzicht: werkboek van de wiskundedidaktiek. Purmerend: Muusses.




DOI: https://doi.org/10.22342/jme.2.1.780.1-14

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Journal on Mathematics Education
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