On the Complexity of “Simple” Linear-Algebraic Concepts
Guershon Harel
Why do students encounter major difficulties grasping seemingly simple concepts, such as “span”, “linear independence”, “basis”, “matrix representation of a linear transformation”, etc.? and what instructional approaches found to be effective in helping students reason linear algebraically? The talk will be organized around two themes: (1) Sources of students’ difficulties, such as inadequate attention to conceptual understanding; hodgepodge of concepts, ideas, and symbolism disconnected from students’ prior knowledge; and lack of concrete algebraic models from which students can abstract concepts and ideas. (2) An instructional approach that puts the students’ intellectual need at the center of the instructional effort.
