Authors:
- This book offers a unique perspective of mathematical phenomena through the concept of invariance and change
- The activities in this book – as they are presented with their theoretical background, mathematical explanations, and didactic discussion – explore the concept of change and invariance to encourage and develop algebraic thinking on numbers and shapes
- This is a textbook for pre- and in-service mathematics teachers and their educators, but is also fascinating reading for any lover of elementary mathematics
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About this book
The world is an interplay of variation and constancy – a medley of differences and similarities – and this change and invariance is, largely, a language of science and mathematics. This book proposes a unique approach for developing mathematical insight through the perspective of change and invariance as it applies to the properties of numbers and shapes.
After a short introductory chapter, each of the following chapters presents a series of evolving activities for students that focus on a specific aspect of interplay between change and invariance. Each activity is accompanied by detailed mathematical explanations and a didactic discussion. The assignments start with tasks familiar from the school curriculum, but progress beyond the menial to lead to sophisticated generalizations. Further activities are suggested to augment the chapter’s theme. Some examples: “How to represent all the integers from zero to 1000 using ten fingers?”, “How to win at the game of Nim?”, “Why do different square lattice polygons with the same area often have the same perimeter?”
This book can be used as a textbook for pre-service mathematics teachers and is primarily intended for their academic instructors. Essentially, students, teachers and anyone interested in elementary mathematics will enjoy the elegant solutions provided for the plethora of problems in elementary mathematics through the systematic approach of invariance and change."
Authors and Affiliations
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Gordon Academic College of Education, Shaanan Religious College of Education, Israel
Ilya Sinitsky
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Hemdat Hadarom Academic College of Education, Israel
Bat-Sheva Ilany
Bibliographic Information
Book Title: Change and Invariance
Book Subtitle: A Textbook on Algebraic Insight into Numbers and Shapes
Authors: Ilya Sinitsky, Bat-Sheva Ilany
DOI: https://doi.org/10.1007/978-94-6300-699-6
Publisher: SensePublishers Rotterdam
eBook Packages: Education, Education (R0)
Copyright Information: SensePublishers-Rotterdam, The Netherlands 2016
eBook ISBN: 978-94-6300-699-6Published: 25 November 2016
Edition Number: 1
Number of Pages: XIV, 378
Topics: Education, general