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Foundational Reasoning Abilities That Promote Coherence in Students' Function Understanding

Abstract

This article provides an overview of essential processes involved in knowing and learning the function concept. We have included discussions of the reasoning abilities
involved in understanding and using functions, including the dynamic conceptualizations
needed for understanding major concepts of calculus, parametric functions, functions of several variables, and differential equations. Our discussion also provides information
about common conceptual obstacles to knowing and learning the function concept that students have been observed encountering. We make frequent use of examples to illustrate the 'ways of thinking' and major understandings that research suggests are essential for students' effective use of functions during problem solving, and that are needed for students' continued mathematics learning. We also provide some suggestions
for promising approaches for developing a deep and coherent view of the concept of function.

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