Abstract
This chapter offers a perspective on what conceptual understanding means when we focus on a particular mathematical topic or concept and what differentiates conceptual understanding from fragile understanding. The chapter answers these questions through illustrating what in-depth understanding of mathematical topics Newton focuses on in her research might look like. Newton describes two major criteria and a framework that outlines central characteristics exemplified in mathematical conceptual understanding and illustrates how these characteristics manifest themselves in specific topics she has conducted research on. This chapter is foundational in terms of setting a benchmark against the kinds of understanding that teachers are exposed to which can be characterized as fragmented, incoherent, and superficial.
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