Symbolizing while solving linear systems

Michelle Zandieh, Christine Andrews-Larson

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish (US)
JournalZDM - Mathematics Education
DOIs
StateAccepted/In press - Jan 1 2019
Externally publishedYes

Fingerprint

Linear Systems
Trajectory
System of Linear Equations
Linear algebra
student
Augmented matrix
Matrix Equation
Uniformity
Reasoning
Line
interpretation
university
trend

Keywords

  • Augmented matrices
  • Linear algebra
  • Student reasoning
  • Systems of equations

ASJC Scopus subject areas

  • Education
  • Mathematics(all)

Cite this

Symbolizing while solving linear systems. / Zandieh, Michelle; Andrews-Larson, Christine.

In: ZDM - Mathematics Education, 01.01.2019.

Research output: Contribution to journalArticle

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