Connecting Research to Teaching: Visual and Analytic Thinking in Calculus

A frequent message in mathematics education focuses on the benefits of multiple representations of mathematical concepts (Aspinwall and Shaw 2002). The National Council of Teachers of Mathematics, for instance, claims that “different representations support different ways of thinking about and manipulating mathematical objects” (NCTM 2000, p. 360). A recommendation conveyed in the ongoing calculus reform movement is that students should use multiple representations and make connections among them so that they can develop deeper and more robust understanding of the concepts.