Mathematics Education based on Modelism

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It was pointed to at least two distinct meanings for model in respect of their epistemological assumptions and implications for teaching. The two distinct meanings we identify are: (1) models as hypothetical spaces in which we conceptualize a particular world situation in order to think about and work on it in order to solve a problem, and (2) models as physical/mental entities for comparing and contrasting which we can use to refer to a different familiar situation, and which can be compared or contrasted among themselves in terms of their capacity to represent and deepen our understanding of some particular phenomenon in the world. Two roles of models are discussed concretely both in elementary and secondary mathematics.