Learning Mathematics and Logo

Celia Hoyles e Richard Noss

The MIT Press | 1992 | 492 páginas | pdf | 22,4 Mb

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These original essays summarize a decade of fruitful research and curriculum development using the LISP-derived language Logo. They discuss a range of issues in the areas of curriculum, learning, and mathematics, illustrating the ways in which Logo continues to provide a rich learning environment, one that allows pupil autonomy within challenging mathematical settings.
Essays in the first section discuss the link between Logo and the school mathematics curriculum, focusing on the ways in which pupils' Logo activities relate to and are influenced by the ideas they encounter in the context of school algebra and geometry.
In the second section the contributions take up pedagogical styles and strategies. They tackle such cognitive and metacognitive questions as, What range of learning styles can the Logo setting accommodate? How can teachers make sense of pupils' preferred strategies? And how can teachers help students to reflect on the strategies they are using?
Returning to the mathematical structures, essays in the third section consider a variety of mathematical ideas, drawing connections between mathematics and computing and showing the ways in which constructing Logo programs helps or does not help to illuminate the underlying mathematics.

Contents
Contributors vii
Series Foreword ix
Foreword by Seymour Papert xi
Preface xvii
Acknowledgments xxiii
LOGO IN THE CURRICULUM
Introduction to Part I 3
The Notion of Variable in the Context of Turtle Graphics 11
Joel Hillel
2 What Is Algebraic about Programming in Logo? 37
Rosamund Sutherland
3 Conceptually Defined Turtles 55
Herbert Loethe
4 The Turtle Metaphor as a ToOl for Children's Geometry 97
Chronis Kynigos
5 A Logo Microworld for Transformation Geometry 127
Laurie D. Edwards
II STYLES AND STRATEGIES
Introduction to Part II 159
6 LEGO-Logo: A Vehicle for Learning 165
Sylvia Weir
7 On Intra- and Interlndividual Differences in Children's Learning Styles 191
Tamara Lemerise
8 Mathematics in a Logo Environment: A Recursive Look at a Complex Phenomenon 223
Thomas E. Kieren
9 Between Logo and Mathematics: A Road of Tunnels and Bridges 247
Jean-Luc Gurtner
III EXPRESSING MATHEMATICAL STRUCTURES
Introduction to Part ", 27 1
10 Processes: A Dynamical Integration of Computer Science into Mathematical Education 279
Bruno Vitale
Of Geometry, Turtles, and Groups
Uri Leron and Rina Zazkis
Patterns, Permutations, and Groups
Trevor Fletcher
Avoiding Recursion 393
Brian Harvey
IV AFTERWORD
Introduction to Part IV 429
Looking Back and Looking Forward
Richard Noss and Celia Hoyles
Index 47 1