What Is Or What Might Be the Benefit of Using Computer Algebra Systems in the Learning and Teaching of Calculus?

Abstract

This book addresses key issues of Technology and Innovation(s) in Mathematics Education, drawing on heterogeneous ways of positioning about innovation in mathematical practice with technology. The book offers ideas and meanings of innovation as they emerge from the entanglement of the various researchers with the mathematical practice, the teacher training program, the student learning and engagement, or the research method that they are telling stories about. The multiple theoretical or empirical perspectives capture a rich landscape, in which the presence of digital technology entails the emergence of new practices, techniques, environments and devices, or new ways of making sense of technology in research, teaching and learning. Foreword by Ferdinando Arzarello -- Contents -- 1 Introduction: Innovative Spaces for Mathematics Education with Technology -- References -- Opening Scenery -- 2 From Acorns to Oak Trees: Charting Innovation Within Technology in Mathematics Education -- Abstract -- 1 Introduction -- 2 Defining Innovation from the ICTMT Conference Series Perspective -- 2.1 Innovation in the Design and Evaluation of Technological Tools -- 2.2 Innovation in the Design and Evaluation of Classroom Tasks -- 3 Some Key Innovations in Mathematics Education 3.1 The Concept of a Mathematical â#x80;#x98;Figureâ#x80;#x99; and the New Action of â#x80;#x98;Draggingâ#x80;#x99;3.1.1 Figures and Dragging from the Perspective of the Innovative Design/Evaluation of Tools -- 3.1.2 Figures and Dragging from the Perspective of the Innovative Design and Evaluation of Classroom Tasks -- 3.2 The Concept of Multiple Representations -- 3.2.1 Multiple Representation from the Perspective of the Innovative Design/Evaluation of Tools -- 3.2.2 Multiple Representations from the Perspective of the Innovative Design/Evaluation of Classroom Tasks and Lesson 4 Ways of Interacting with Mathematics Through Technology5 Conclusions -- References -- Appendix 1. The ICTMT Conference Series and Proceedings -- New Spaces for Research -- 3 Returning to Ordinality in Early Number Sense: Neurological, Technological and Pedagogical Considerations -- Abstract -- 1 Introduction -- 2 How Does Neuroscience Change Our Way of Thinking About and Doing Research? -- 2.1 A New Space for Research on Early Number? -- 2.2 A New Space for Research Methodologies? -- 3 Returning to Ordinality: An Interlude of Pedagogical Considerations 4 How Can the Use of Technology Support and Foster Innovative Ways of Learning?5 Discussion -- References -- 4 The Coordinated Movements of a Learning Assemblage: Secondary School Students Exploring Wii Graphing Technology -- Abstract -- 1 Introduction -- 2 The Context and Wii Technology -- 3 WiiGraph Software: Line and Versus Graphs -- 4 The Teaching Experiment -- 5 Discussion: Assemblage Theory -- References -- 5 Using Digital Environments to Address Studentsâ#x80;#x99; Mathematical Learning Difficulties -- Abstract -- 1 Introduction 1.1 The Murky Notion of â#x80;#x9C;Students with MLDâ#x80;#x9D;1.2 How Can Software â#x80;#x9C;Addressâ#x80;#x9D; Specific MLD? -- 2 Theoretical Background -- 2.1 Means of Information Access and Production, with Particular Attention to Mathematical Information -- 2.2 Universal Design for Learning -- 3 Examples of Digital Environments to Promote the Development of Number Sense and Spatial Orientation -- 3.1 Software to Promote â#x80;#x9C;Number Senseâ#x80;#x9D; -- 3.1.1 Software Promoting Number Sense Through Fingers -- 3.1.2 Software Promoting Number Sense Through the Number Line Las ventajas y desventajas del uso de tecnologías digitales (DT) y especialmente de sistemas de álgebra computarizada (CAS) en las lecciones de matemáticas se discuten de manera controvertida en todo el mundo. Numerosos estudios empíricos muestran el beneficio del uso de DT en las aulas y también hay muchos ejemplos útiles sobre su uso. Sin embargo, a pesar de estos resultados inspiradores y las innumerables ideas, sugerencias en el aula, planes de lecciones e informes de investigación, el uso de DT, y especialmente CAS, no ha tenido éxito, como muchos esperaban durante las últimas décadas ver Hoyles & Lagrange, (2010 ). La tesis de este artículo es que no hemos podido convencer a profesores, profesores de la universidad y padres de familia del beneficio de CAS en las aulas de forma suficiente. ¿Cuáles son los argumentos que justifican el uso de CAS en el aula? El artículo da ejemplos de un uso fructífero de CAS con respecto a las metas o estándares generalmente aceptados de la educación matemática, como el fomento de las habilidades de los estudiantes en la resolución de problemas, el modelado, la demostración o la comunicación, y las materias que se enseñan en la escuela secundaria. La base de la argumentación es un modelo de competencia que clasifica la relación entre contenidos o temas: secuencias y límites, funciones y ecuaciones; representaciones de DT o CAS: estáticas aisladas, estáticas múltiples, dinámicas aisladas y dinámicas múltiples representaciones; y actividades de aula: calcular, consultar, controlar, comunicar y descubrir