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(2005) Activity and sign, Dordrecht, Springer.
By means of an epistemological analysis of a teaching episode from a mathematics classroom the paper tries to exemplify and to concretize some fundamental ideas developed in a theoretical perspective by Michael Otte towards the basic role of visualizations and metaphors for mathematics teaching. The metaphor "The equation is a balance" is taken as a paradigmatic case. "The equation is a balance is a sentence not to be taken verbally, and the seemingly abstract (the algebraic equation) cannot be limited to the seemingly concrete and empirical (the balance) in a process of reduction and of visualization, but on the contrary, the balance represents the highly general meaning of the interaction or the reciprocity or it stands for the dynamic and compensation. … The real balance has meaning for the equation. The algebraic concept of equation could not have been constituted without the experience of the balance" (Otte 1984).
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Full citation:
Steinbring, H. (2005)., Do mathematical symbols serve to describe or construct "reality"?, in M. H. G. . Hoffmann, J. Lenhard & F. Seeger (eds.), Activity and sign, Dordrecht, Springer, pp. 91-104.
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