Abstract
Typical solution processes of (pre-)algebraic problems live dialectically between two opposite polarities: procedural and relational. The former is a-symmetric; is ruled by “the logic of when”; is close to the meaning of symbols; its main epistemological style is arithmetic. The latter is symmetric; is ruled by “the logic of iff”; is syntactic, insofar concrete meaning have evaporated; its epistemological style is anti-arithmetic. But procedural thinking allows pupils to do concrete experiments and get feedbacks from the problematic-situation; and this, in the long run, is useful in order to jump to relational polarity, where more formal algebraic manipulations can be done.
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© 1992 Springer-Verlag Berlin Heidelberg
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Arzarello, F. (1992). Pre-Algebraic Problem Solving. In: Ponte, J.P., Matos, J.F., Matos, J.M., Fernandes, D. (eds) Mathematical Problem Solving and New Information Technologies. NATO ASI Series, vol 89. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58142-7_11
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DOI: https://doi.org/10.1007/978-3-642-58142-7_11
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