Fostering process-object transitions and a deeper understanding in the domain of number
DOI:
https://doi.org/10.48489/quadrante.23030Keywords:
process-object transition, addition, subtraction, conceptual understanding, skillsAbstract
The gist of this article is that a shift is needed towards a mathematics curriculum in which teaching for understanding is the main objective. Before elaborating on what such a shift might entail, two compelling arguments for making such a change are presented. One is based on research, which showed that a one-sided emphasis on skills induced the teaching of isolated, topic-specific, skills – leading to a low level of proficiency. The other argument is grounded in the observation that the role of mathematics in society is changing and that, as a consequence thereof, the importance of mastering routine skills diminishes, while the need for mathematical understanding grows. On the basis of these two arguments, a shift is advocated, from an emphasis on skills, to an emphasis on understanding. This is connected to the thesis that deep mathematical understanding can only be achieved when students construct mathematical objects by reifying mathematical processes. For the domain of number, the idea of mathematical objects is linked to the notion of junctions in networks of number relations. The core of the article is an exploration of what mathematics education in the number domain might look like if it would be organized along the line of process-object transitions, and how number relations can be used for solving the kind of number tasks that are commonly solved with standard procedures. This exploration is closed with a sketch of a potential instructional sequence for addition and subtraction up to 100.
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