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E-raamat: Challenges and Strategies in Teaching Linear Algebra

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  • Formaat: EPUB+DRM
  • Sari: ICME-13 Monographs
  • Ilmumisaeg: 01-Feb-2018
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319668116
  • Formaat - EPUB+DRM
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  • Formaat: EPUB+DRM
  • Sari: ICME-13 Monographs
  • Ilmumisaeg: 01-Feb-2018
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319668116

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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.

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
3(26)
Guershon Harel
Learning Linear Algebra Using Models and Conceptual Activities
29(22)
Maria Trigueros
Moving Between the Embodied, Symbolic and Formal Worlds of Mathematical Thinking with Specific Linear Algebra Tasks
51(20)
Sepideh Stewart
Part II Analyses of Learners' Approaches and Resources
Conceptions About System of Linear Equations and Solution
71(32)
Asuman Oktac
Rationale for Matrix Multiplication in Linear Algebra Textbooks
103(24)
John Paul Cook
Dov Zazkis
Adam Estrup
Misconceptions About Determinants
127(20)
Cathrine Kazunga
Sarah Bansilal
Dealing with the Abstraction of Vector Space Concepts
147(28)
Lillias H. N. Mutambara
Sarah Bansilal
Stretch Directions and Stretch Factors: A Sequence Intended to Support Guided Reinvention of Eigenvector and Eigenvalue
175(18)
David Plaxco
Michelle Zandieh
Megan Wawro
Examining Students' Procedural and Conceptual Understanding of Eigenvectors and Eigenvalues in the Context of Inquiry-Oriented Instruction
193(26)
Khalid Bouhjar
Christine Andrews-Larson
Muhammad Haider
Michelle Zandieh
Part III Dynamic Geometry Approaches
Mental Schemes of: Linear Algebra Visual Constructs
219(22)
Hamide Dogan
How Does a Dynamic Geometry System Mediate Students' Reasoning on 3D Linear Transformations?
241(20)
Melih Turgut
Fostering Students' Competencies in Linear Algebra with Digital Resources
261(18)
Ana Donevska-Todorova
Part IV Challenging Tasks with Pedagogy in Mind
Linear Algebra---A Companion of Advancement in Mathematical Comprehension
279(20)
Damjan Kobal
A Computational Approach to Systems of Linear Equations
299(18)
Franz Pauer
Nonnegative Factorization of a Data Matrix as a Motivational Example for Basic Linear Algebra
317(20)
Barak A. Pearlmutter
Helena Smigoc
Motivating Examples, Meaning and Context in Teaching Linear Algebra
337(16)
David Strong
Holistic Teaching and Holistic Learning, Exemplified Through One Example from Linear Algebra
353(16)
Frank Uhlig
Using Challenging Problems in Teaching Linear Algebra
369(10)
Abraham Berman
Author Index 379(2)
Subject Index 381