This paper presents a conceptual analysis for students' images of graphs and their extension to graphs of two-variable functions. We use the conceptual analysis, based on quantitative and ...

Functions of two variables can be visualized in many ways: heat maps in 2D, contour curves in 2D, wireframes in 3D, surfaces in 3D. We begin by defining a function of two variables, building an array ...

Educational Studies in Mathematics, Vol. 73, No. 1 (Jan., 2010), pp. 3-19 (17 pages) This study is part of a project concerned with the analysis of how students work with two-variable functions. This ...

THIS is emphatically a text-book, deductive in method and Euclidean in arrangement; as such, it has the defects of its qualities, but its merits are undeniable. In this volume the author deals with ...