This special issue of Mathematical Thinking and Learning describes
models and modeling perspectives toward mathematics problem
solving, learning, and teaching. The concern is not only the mature
forms of models and modeling in communities of scientists and
mathematicians, but also the need to initiate students in these
forms of thought. The contributions of this issue suggest a variety
of ways that students (children through adults) can be introduced
to highly productive forms of modeling practices. Collectively,
they illustrate how modeling activities often lead to remarkable
mathematical achievements by students formerly judged to be too
young or too lacking in ability for such sophisticated and powerful
forms of mathematical thinking. The papers also illustrate how
modeling activities often create productive interdisciplinary
niches for mathematical thinking, learning, and problem solving
that involve simulations of similar situations that occur when
mathematics is useful beyond school.
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