An Inquiry-Oriented Approach to Span and Linear Independence: The Case of the Magic Carpet Ride Sequence

Megan Wawro; Chris Rasmussen; Michelle Zandieh; George Franklin Sweeney; Christine Larson

doi:10.1080/10511970.2012.667516

An Inquiry-Oriented Approach to Span and Linear Independence: The Case of the Magic Carpet Ride Sequence

Megan Wawro, Chris Rasmussen, Michelle Zandieh, George Franklin Sweeney, Christine Larson

Research output: Contribution to journal › Article › peer-review

41 Scopus citations

Abstract

In this paper we present an innovative instructional sequence for an introductory linear algebra course that supports students' reinvention of the concepts of span, linear dependence, and linear independence. Referred to as the Magic Carpet Ride sequence, the problems begin with an imaginary scenario that allows students to build rich imagery and formal definitions. The approach begins by focusing on vectors, their algebraic and geometric representations in ℝ² and ℝ³, and their properties as sets. Samples of student work are provided to illustrate the variety of student solutions and how these solutions lead to the creation of formal definitions.

Original language	English (US)
Pages (from-to)	577-599
Number of pages	23
Journal	PRIMUS
Volume	22
Issue number	8
DOIs	https://doi.org/10.1080/10511970.2012.667516
State	Published - Dec 2012

Keywords

Linear algebra
linear independence
research in undergraduate mathematics education
span
student thinking

ASJC Scopus subject areas

Mathematics(all)
Education

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10.1080/10511970.2012.667516

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abstract = "In this paper we present an innovative instructional sequence for an introductory linear algebra course that supports students' reinvention of the concepts of span, linear dependence, and linear independence. Referred to as the Magic Carpet Ride sequence, the problems begin with an imaginary scenario that allows students to build rich imagery and formal definitions. The approach begins by focusing on vectors, their algebraic and geometric representations in ℝ2 and ℝ3, and their properties as sets. Samples of student work are provided to illustrate the variety of student solutions and how these solutions lead to the creation of formal definitions.",

keywords = "Linear algebra, linear independence, research in undergraduate mathematics education, span, student thinking",

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An Inquiry-Oriented Approach to Span and Linear Independence: The Case of the Magic Carpet Ride Sequence

Abstract

Keywords

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