Megan Wawro, Virginia Tech |

A realistic approach to instruction in linear algebra |

ABSTRACT: The purpose of this study is to investigate how students conceptualize span and linear (in)dependence, and to utilize the construct of mathematical activity to provide insight into these conceptualizations. The data under consideration are portions of individual interviews with students in an inquiry-oriented linear algebra course. Through grounded analysis via the framework of concept image (Tall & Vinner, 1991), the range of student conceptions of span and linear (in)dependence are organized into four concept image categories: travel, geometric, vector algebraic, and matrix algebraic. To further illuminate participantsâ€™ conceptions, a framework was developed to classify engagement in types of mathematical activity: defining, proving, relating, example generating, and problem solving. The coordinated analysis of concept image with engagement in mathematical activity facilitates a nuanced and rich characterization of studentsâ€™ connections within and between the concepts of span and linear (in)dependence. The talk will include a brief description of the curricular materials, based on the instructional design theory of Realistic Mathematics Education (Freudenthal, 1991), that were implemented within this linear algebra course. |

# Friday, April 5 at 2:00pm in Fretwell 120

Categories: Spring 2013