TY - JOUR
T1 - Symbolizing while solving linear systems
AU - Zandieh, Michelle
AU - Andrews-Larson, Christine
N1 - Funding Information:
Funding was provided by National Science Foundation (Grant no. DUE 1712524).
Publisher Copyright:
© 2019, FIZ Karlsruhe.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - Solving systems of linear equations is of central importance in linear algebra and many related applications, yet there is limited literature examining the symbolizing processes students use as they work to solve systems of linear equations. In this paper, we examine this issue by analyzing final exam data from 68 students in an introductory undergraduate linear algebra course at a large public research university in the United States. Based on our analysis, we expanded our framework (Larson & Zandieh, 2013) for interpretations of matrix equations to include augmented matrices and symbolic forms commonly used in solving linear systems. We document considerable variation in students’ symbolization processes, which broadly occurred along two primary trajectories: systems trajectories and row reduction trajectories. Row reduction trajectories included at least five symbolic shifts, two of which students executed with a great deal of success and uniformity. Students’ symbolizing processes varied more in relation to the other three shifts, and these variations were often linked to trends of variable renaming, variable creation, or imagined parameter reasoning. Students were more flexible in their solution strategies when solving systems involving lines than for systems involving planes.
AB - Solving systems of linear equations is of central importance in linear algebra and many related applications, yet there is limited literature examining the symbolizing processes students use as they work to solve systems of linear equations. In this paper, we examine this issue by analyzing final exam data from 68 students in an introductory undergraduate linear algebra course at a large public research university in the United States. Based on our analysis, we expanded our framework (Larson & Zandieh, 2013) for interpretations of matrix equations to include augmented matrices and symbolic forms commonly used in solving linear systems. We document considerable variation in students’ symbolization processes, which broadly occurred along two primary trajectories: systems trajectories and row reduction trajectories. Row reduction trajectories included at least five symbolic shifts, two of which students executed with a great deal of success and uniformity. Students’ symbolizing processes varied more in relation to the other three shifts, and these variations were often linked to trends of variable renaming, variable creation, or imagined parameter reasoning. Students were more flexible in their solution strategies when solving systems involving lines than for systems involving planes.
KW - Augmented matrices
KW - Linear algebra
KW - Student reasoning
KW - Systems of equations
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U2 - 10.1007/s11858-019-01083-3
DO - 10.1007/s11858-019-01083-3
M3 - Article
AN - SCOPUS:85073972302
SN - 1863-9690
VL - 51
SP - 1183
EP - 1197
JO - ZDM - Mathematics Education
JF - ZDM - Mathematics Education
IS - 7
ER -