Keywords
Multiplicative problems of Cartesian product
Elementary School mathematics
How to Cite
Abstract
The paper concerns the construction of the combinatory reasoning
when problems of Cartesian product are solved by 3rd to 6th grade Elementary
School students’. Stemming from the revision of hierarchies described in earlier
studies, it is based on Piaget’s and Vergnaud’s proposals. The participants, 110
students attending State Elementary Schools (mean age 10;5), answered a paper
and pencil instrument containing four multiplicative problems of Cartesian
product. A qualitative and a quantitative analysis result in a revised hierarchy of
the combinatory reasoning, and show its absence on solutions in all grades and
problems, but a significant tendency to advanced solutions in 4th grade to some
problems. Concerning the hierarchy, the discussion underlines the progressive
combination of variables; the passage from arithmetical to algebraic reasoning
and from additive to multiplicative schemata; the progressive overture to the
possibilities in its interplay with the necessities. Methodological restrictions and
implications for mathematical education are presented.
References
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