Challenges and Strategies in Teaching Linear Algebra

ISBN-13: 9783319668109 / Angielski / Twarda / 2018 / 382 str.

Sepideh Stewart; Christine Andrews-Larson; Avi Berman

Opis

This volume presents research on students' conceptual difficulties with linear algebra. It discusses the following research questions: a. How can applications of Linear Algebra be used as motivation for studying the topic? b. What are the advantages of proving results in Linear Algebra in different ways? c. In what ways can a linear algebra course be adapted to meet the needs of students from other disciplines, such as engineering, physics, and computer science? d. How can challenging problems be used in teaching Linear Algebra? e. In what way should technology be used in teaching Linear Algebra? f. What is the role of visualization in learning Linear Algebra? g. In what order (picture, symbols, definitions and theorems) should we teach Linear Algebra concepts? h. How can we educate the students to appreciate the importance of deep understanding of the Linear Algebra concepts? The above research questions are used as a starting point, however the volume also covers a wider spectrum of issues in teaching and learning of Linear Algebra. It therefore includes a section with research based papers followed by a section with practical ideas on teaching Linear Algebra tasks.

Spis treści

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 ˇSmigoc 

               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

Blurb

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.