Challenges and Strategies in Teaching Linear Algebra

Description

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. Front Matter ....Pages i-xiii Front Matter ....Pages 1-1 The Learning and Teaching of Linear Algebra Through the Lenses of Intellectual Need and Epistemological Justification and Their Constituents (Guershon Harel)....Pages 3-27 Learning Linear Algebra Using Models and Conceptual Activities (María Trigueros)....Pages 29-50 Moving Between the Embodied, Symbolic and Formal Worlds of Mathematical Thinking with Specific Linear Algebra Tasks (Sepideh Stewart)....Pages 51-67 Front Matter ....Pages 69-69 Conceptions About System of Linear Equations and Solution (Asuman Oktaç)....Pages 71-101 Rationale for Matrix Multiplication in Linear Algebra Textbooks (John Paul Cook, Dov Zazkis, Adam Estrup)....Pages 103-125 Misconceptions About Determinants (Cathrine Kazunga, Sarah Bansilal)....Pages 127-145 Dealing with the Abstraction of Vector Space Concepts (Lillias H.N. Mutambara, Sarah Bansilal)....Pages 147-173 Stretch Directions and Stretch Factors: A Sequence Intended to Support Guided Reinvention of Eigenvector and Eigenvalue (David Plaxco, Michelle Zandieh, Megan Wawro)....Pages 175-192 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)....Pages 193-216 Front Matter ....Pages 217-217 Mental Schemes of: Linear Algebra Visual Constructs (Hamide Dogan)....Pages 219-239 How Does a Dynamic Geometry System Mediate Students’ Reasoning on 3D Linear Transformations? (Melih Turgut)....Pages 241-259 Fostering Students’ Competencies in Linear Algebra with Digital Resources (Ana Donevska-Todorova)....Pages 261-276 Front Matter ....Pages 277-277 Linear Algebra—A Companion of Advancement in Mathematical Comprehension (Damjan Kobal)....Pages 279-298 A Computational Approach to Systems of Linear Equations (Franz Pauer)....Pages 299-316 Nonnegative Factorization of a Data Matrix as a Motivational Example for Basic Linear Algebra (Barak A. Pearlmutter, Helena Šmigoc)....Pages 317-336 Motivating Examples, Meaning and Context in Teaching Linear Algebra (David Strong)....Pages 337-351 Holistic Teaching and Holistic Learning, Exemplified Through One Example from Linear Algebra (Frank Uhlig)....Pages 353-367 Using Challenging Problems in Teaching Linear Algebra (Abraham Berman)....Pages 369-378 Back Matter ....Pages 379-382