Combining historical, foundational, and developmental insights to build children's first steps in mathematics
Résumé
How can we design mathematical instructional activities that reveal children's early mathematical competence in an analogous way as school activities that exploit children's mother language competence? We put forward a list of mathematical conceptions young children may have been taught previously and some subsequent actions developed to observe them and guide their first steps in mathematics in an instructional context. The list has been developed on the basis of insights from modern axiomatic presentation of arithmetic and geometry contrasted with historical results and epistemology of mathematics. We discuss the application of the list in a singular context, a group of eight 3 to 8 year-old Spanish children with Trisomy 21, to show the suitability of this tool for revealing early mathematical competence.
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