Challenges and Strategies in Teaching Linear Algebra / edited by Sepideh Stewart, Christine Andrews-Larson, Avi Berman, Michelle Zandieh.

Format:

Book

Contributor:

Stewart, Sepideh., Editor.

Andrews-Larson, Christine., Editor.

Berman, Avi., Editor.

Zandieh, Michelle., Editor.

Series:

ICME-13 Monographs, 2520-8330

Language:

English

Subjects (All):

Mathematics--Study and teaching.

Mathematics.

Teachers--Training of.

Teachers.

Mathematics Education.

Teaching and Teacher Education.

Local Subjects:

Mathematics Education.

Teaching and Teacher Education.

Physical Description:

1 online resource (382 pages) : illustrations.

Edition:

1st ed. 2018.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2018.

Summary:

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. .

Contents:

Contents

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

Learning Linear Algebra Using Models and Conceptual Activities

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

Part II. Analyses of Learners' Approaches and Resources

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

Rationale for Matrix Multiplication in Linear Algebra Textbooks

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

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

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

Examining Students' Procedural and Conceptual Understanding of Eigenvectors and Eigenvalues in the Context of Inquiry-Oriented Instruction

Part III. Dynamic Geometry Approaches

Mental Schemes of Linear Algebra Visual Constructs

How DGS mediates students’ reasoning on 3D linear transformations: a combined analysis from thinking modes and semiotic perspectives

Fostering Students’ Competences in Linear Algebra with digital Resources

Part IV. Challenging tasks with pedagogy in mind

Linear Algebra-a Companion of Advancement in Mathematical Comprehension

An algebraic/computational approach to systems of linear equations in a Linear Algebra Course for students of computer science, physics, and mathematics

Nonnegative Factorisationof a Data Matrix as a Motivational Example for Basic Linear Algebra

Motivating Examples, Meaning and Context in Teaching Linear Algebra

Holistic Teaching and Learning Holistically, exemplified through one example from Linear Algebra

Using Challenging problems in Teaching Linear Algebra.

Notes:

Includes bibliographical references at the end of each chapters and indexes.

ISBN:

9783319668116

3319668110