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Title: “The shape will have no volume”: Relationships students observed about determinants in a dynamic geometric applet.
We discuss two Dynamic Geometry Software applets designed as part of an Inquiry-Oriented instructional unit on determinants and share students' generalizations based on using the applet. Using the instructional design theory of Realistic Mathematics Education, our team developed a task sequence supporting students' guided reinvention of determinants. This unit leverages students' understanding of matrix transformations as distortion of space to meaningfully connect determinants to the transformation as the signed multiplicative change in area that objects in the domain undergo from the linear transformation. The applets are intended to provide students with feedback to help connect changes in the matrix to changes in the visualization of the linear transformation and, so, to changes in the determinant. Critically, the materials ask students to make generalizations while reflecting on their experiences using the applets. We discuss patterns among these generalizations and implications they have on the applets' design.  more » « less
Award ID(s):
1914841
PAR ID:
10465470
Author(s) / Creator(s):
; ;
Editor(s):
Cook, S.; Katz, B.; Moore-Russo, D.
Date Published:
Journal Name:
Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education
ISSN:
2474-9346
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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