pure mathematics activities (in which the symbols are concrete objects rather than abstract notation), whereas two of the three stages of our modeling approach focus on applied mathematics activities (which are explicitly based on children's' real-life experiences), even though all three stages are aimed at demonstrating the power of pure mathematical activities.
Our modeling approach to instruction is deliberately consistent with the way modern mathematicians think about their own activities in mathematics and mathematical modeling. Also, it was explicitly created to be consistent with three of the most basic principles of modern cognitive science, namely, (i) humans interpret their experiences by mapping them to internal models, (ii) these internal models must be constructed, and (iii) constructed models result in situated knowledge that is gradually extended and decontextualized to interpret other structurally similar situations. Moreover, our modeling approach to instruction is also consistent with a constructivist philosophy about how human knowledge develops.
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