TY - JOUR
T1 - Inverse, composition, and identity
T2 - The case of function and linear transformation
AU - Bagley, Spencer
AU - Rasmussen, Chris
AU - Zandieh, Michelle
N1 - Publisher Copyright:
© 2014 Elsevier Inc.
PY - 2015/3/1
Y1 - 2015/3/1
N2 - In this report we examine linear algebra students' reasoning about composing a function or linear transformation with its inverse. In the course of analyzing data from semi-structured clinical interviews with 10 undergraduate students in a linear algebra class, we were surprised to find that all the students said the result of composition of a function and its inverse should be 1. We examined how students attempted to reconcile their initial incorrect predictions, and found that students who succeeded in this reconciliation used what we refer to as "do-nothing function" and "net do-nothing function" reasoning. We provide examples of these patterns of reasoning, and propose explanations for why this reasoning was helpful. We also discuss possible sources for this incorrect prediction, and provide implications for classroom practice.
AB - In this report we examine linear algebra students' reasoning about composing a function or linear transformation with its inverse. In the course of analyzing data from semi-structured clinical interviews with 10 undergraduate students in a linear algebra class, we were surprised to find that all the students said the result of composition of a function and its inverse should be 1. We examined how students attempted to reconcile their initial incorrect predictions, and found that students who succeeded in this reconciliation used what we refer to as "do-nothing function" and "net do-nothing function" reasoning. We provide examples of these patterns of reasoning, and propose explanations for why this reasoning was helpful. We also discuss possible sources for this incorrect prediction, and provide implications for classroom practice.
KW - Function
KW - Linear algebra
KW - Linear transformation
KW - Mathematics education
KW - Process/object pairs
KW - Undergraduate mathematics education
UR - http://www.scopus.com/inward/record.url?scp=84920266394&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84920266394&partnerID=8YFLogxK
U2 - 10.1016/j.jmathb.2014.11.003
DO - 10.1016/j.jmathb.2014.11.003
M3 - Article
AN - SCOPUS:84920266394
SN - 0732-3123
VL - 37
SP - 36
EP - 47
JO - Journal of Mathematical Behavior
JF - Journal of Mathematical Behavior
ER -