Representation is primarily something that stands in place of something else. For each representation we
need to define: (1) representational world, (2) world that representational world represents (hereinafter
world that represents), (3) which aspects of the world that it represents, are represented, (4) which aspects
of the representational world represent, and (5) the link between the world that represents and
representational world.
The most important activity in math class is the activity of abstract mathematical concepts’
representation. A distinction is made between internal (mental images) and external representations
(environment). External representations consist of structured symbolic elements, whose role is an
'external' presentation of certain mathematical 'reality'. At math class we mainly use exact
representations, graphic representations, representations of mathematical symbols, and other
representations, recently especially ICT representations. In this paper, we focus on the importance of using different external representations in the process of
teaching and learning mathematics. We highlight the integration of representations as a key factor in
learning mathematics, which we illustrate with a model of representational mapping. Under this model,
we define two concepts: understanding and signification. Students' understanding of the mathematical
concept we understand as his ability to transfer between the various external representations, and the
signification as his ability of handling a particular external representation. At the same time we also
indicate limitations because some mathematical concepts by their nature do not allow transitions
between all the different representations, but only between some.
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