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This book originated from a Discussion Group ( Teaching Linear Algebra ) that was held at the 13th International Conference on Mathematics Education (ICME-13). The aim was to consider and highlight current efforts regarding research and instruction on teaching and learning linear algebra from around the world, and to spark new collaborations. As the outcome of the two-day discussion at ICME-13, this book focuses on the pedagogy of linear algebra with a particular emphasis on tasks that are productive for learning.

The main themes addressed include: theoretical perspectives on the teaching and learning of linear algebra; empirical analyses related to learning particular content in linear algebra; the use of technology and dynamic geometry software; and pedagogical discussions of challenging linear algebra tasks.

Drawing on the expertise of mathematics education researchers and research mathematicians with experience in teaching linear algebra, this book gathers work from nine countries: Austria, Germany, Israel, Ireland, Mexico, Slovenia, Turkey, the USA and Zimbabwe.

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Part I. Theoretical Perspectives Elaborated through Tasks

The Learning and Teaching of Linear Algebra through the Lenses of Intellectual

Need and Epistemological Justification and Their Constituents

Guershon Harel

Learning Linear Algebra Using Models and Conceptual Activities

María Trigueros

Moving between the embodied, symbolic and formal worlds of mathematical thinking with specific linear algebra tasks

Sepideh Stewart

Part II. Analyses of Learners´ Approaches and Resources

Systems of linear equations - a key element in the learning of Linear Algebra

Asuman Oktac

Rationale for Matrix Multiplication in Linear Algebra Textbooks

John Paul Cook and Dov Zazkis

An Action Process Object Schema (APOS) analysis of the understanding of determinants of matrices by Zimbabwean undergraduate mathematics students

Catherine Kazunga & Sarah Bansilal

Difficulties associated with understanding the concept of vector subspace: A case

study of Zimbabwean teachers

Lillias H.N. Mutambara and Sarah Bansilal

Stretch Directions and Stretch Factors: A Sequence Intended to Support Guided Reinvention of Eigenvector and Eigenvalue Stretch Directions and Stretch Factors: A Sequence Intended to Support Guided Reinvention of Eigenvector and Eigenvalue

David Plaxco, Michelle Zandieh, and Megan Wawro

Examining Students´ Procedural and Conceptual Understanding of Eigenvectors

and Eigenvalues in the Context of Inquiry-Oriented Instruction

Khalid Bouhjar, Christine Andrews-Larson, Muhammad Haider, & Michelle Zandieh

Part III. Dynamic Geometry Approaches

Mental Schemes of Linear Algebra Visual Constructs

Hamide Dogan

How DGS mediates students´ reasoning on 3D linear transformations: a combined

analysis from thinking modes and semiotic perspectives

Melih Turgut

Fostering Students´ Competences in Linear Algebra with digital Resources

Ana Donevska-Todorova

Part IV. Challenging tasks with pedagogy in mind

Linear Algebra-a Companion of Advancement in Mathematical Comprehension

Damjan Kobal

An algebraic/computational approach to systems of linear equations in a Linear

Algebra Course for students of computer science, physics, and mathematics

Franz Pauer

Nonnegative Factorisation of a Data Matrix as a Motivational Example for Basic Linear Algebra

Barak A. Pearlmutter & Helena Smigoc

Motivating Examples, Meaning and Context in Teaching Linear Algebra

David Strong

Holistic Teaching and Learning Holistically, exemplified through one example

from Linear Algebra

Frank Uhlig

Using Challenging problems in Teaching Linear Algebra

Abraham Berman

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