Role of Language in Teaching Children Math

Bernice Kastner

Description

It can be difficult to recognize that in spite of the precision and power of mathematics, both the verbal and symbolic language it uses have the same qualities of ambiguity as every other human language. In The Role of Language in Teaching Children Math, Dr. Kastner reveals strategies to overcome the fact that traditional and current mathematics curricula, beginning in the early grades, fail to provide students with the conceptual understanding required to advance to levels where the delight of geometry and calculus become accessible. Kastner's clear prose and organic organization assists teachers, parents, and students to untangle abstract meanings required for mastery in the field of mathematics. "As teachers of mathematics, it is critical that we continually foster meaningful mathematical conversations with children in order for them to develop a deep understanding of the math. Bernice's extraordinary, thought-provoking book is a primer on how the language we use to teach and talk about mathematics can either obscure or illuminate the profound beauty of mathematics. The Role of Language in Teaching Children Math should be read by any serious teacher of mathematics." --Debby Halperin, Recipient of the Presidential Award for Excellence in Mathematics Teaching 2014

Informations

• Publié par: Austin Macauley Publishers
• Date de parution: 28 février 2019
• Nombre de lectures: 0
• EAN13: 9781645369486
• Langue: English

Extrait

The Role of Language in Teaching Children Math
Bernice Kastner
Austin Macauley Publishers
2019-02-28
The Role of Language in Teaching Children Math About the Author Dr. Kastner’s publications include: Articles: Public Information: Dedication Copyright Information Acknowledgments Preface Chapter 1: Different Meanings for Mathematical Terms and Symbols English Number Words The meaning of the word “number” The meaning of the word “angle” Mathematical symbols with multiple interpretations Chapter 2: Different Names or Symbols for the Same Concept Fractions Algebraic Fractions The fraction bar and the slash (/) Chapter 3: The Dangers of Oversimplification Geometric terminology in the primary grades The operations of arithmetic Chapter 4: The Importance of Context The number line We don’t always say what we mean Chapter 5: Psychological Impact of Language and Notation Chapter 6: When We Let Convenience Overrule Fundamental Issues Arbitrary conventions in the context of numbers Sequential constructions The “order of operations” conventions Order of operations for calculators Cancellation Chapter 7: The Joy of Math Notes and References
About the Author
Dr. Bernice Kastner received her BS Honors in Mathematics and Physics from McGill University in Montreal. She is a professor emeritus of Towson University, having received her Ph.D. in Math Education from the University of Maryland. Dr. Kastner has developed curriculum for Simon Fraser University in British Columbia, Montgomery College, the University of Maryland, and other universities.

Dr. Kastner’s publications include:
Study Guide: Principles of Mathematics for Teachers ; Simon Fraser University, 2009
Study Guide: The Math Workshop: Algebra ; Simon Fraser University, 1989 (with Malgorzata Dubiel)
Space Mathematics: A Resource for the Secondary School Teacher; NASA, 1986
Applications of Secondary School Mathematics ; National Council of Teachers of Mathematics, 1978
1979 Yearbook of the National Council of Teachers of Mathematics; Applications in School Mathematics ; NCTM 1979 (Contributing author)
Unifying Concepts and Processes in Elementary Mathematics ; University of Maryland Mathematics Project; Allyn & Bacon, 1978 (Contributing author)

Articles:
“Space Travel Angles”; Quantum , January/February 1992, Springer-Verlag
“Number Sense: The Role of Measurement Applications”; The Arithmetic Teacher ; February 1989
“Decimal Fractions: The Case for Manipulatives”; Vector , BCAMT, Winter, 1988
“Some Applications of Logarithms”; Vector , BCAMT Spring, 1985

Public Information: U.S. School Mathematics from an International Perspective: A Guide for Speakers ; Mathematical Sciences Education Board of the National Research Council. National Academy Press, 1989 (Contributing author)
Dedication
This book is dedicated to my lifelong friend Claire Bernstein, a lawyer, writer ( You Be the Judge ), and now a blogger ( To Life, With Love ) in my home town, Montreal, Quebec, Canada. She kept encouraging me to ‘stick with it’ every time I was ready to abandon this project.
Copyright Information
Copyright © Bernice Kastner (2019)
All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or by any means, including photocopying, recording, or other electronic or mechanical methods, without the prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews and certain other noncommercial uses permitted by copyright law. For permission requests, write to the publisher.
Any person who commits any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages.
Ordering Information:
Quantity sales: special discounts are available on quantity purchases by corporations, associations, and others. For details, contact the publisher at the address below.
Publisher’s Cataloguing-in-Publication data
Kastner, Bernice
The Role of Language in Teaching Children Math
ISBN 9781641825429 (Paperback)
ISBN 9781641825436 (Hardback)
ISBN 9781641825443 (Kindle)
ISBN 9781645369486 (ePub)
The main category of the book — Education / Teaching Methods & Materials / Mathematics
www.austinmacauley.com/us
First Published (2019)
Austin Macauley Publishers LLC
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Acknowledgments
First and foremost, I thank my children – Judith Skillman, Ruth E. Kastner, Joel Kastner – all of whom are writers in their respective fields (literature, philosophy of science, astronomy), for their constant encouragement and assistance as I have tried to make people in mathematics education aware of the importance of language and how it is used in the context of mathematics education. Thanks also to Tom Skillman for invaluable assistance with the diagrams and with format issues.
I am grateful to Malgorzata Dubiel of the Department of Mathematics at Simon Fraser University (Burnaby, British Columbia, Canada) and Melania Alvarez at the Pacific Institute of Mathematical Sciences (Vancouver, British Columbia, Canada), for offering me the opportunity to participate in and look closely at the current preparation offered to elementary school teachers and at what is taught in elementary school mathematics.
I thank Deborah Halperin, recipient of the President’s Award for Excellence in Mathematics Teaching 2014, and Virginia (Gini) Stimpson of the mathematics education group at the University of Washington, Seattle, for some stimulating discussions and for providing me with current copies of elementary school mathematics textbooks.
Thanks also to fellow Horizon House (Seattle, WA) residents, Patricia Henry, Nancy Robinson, and Phyllis Van Orden, for reading early drafts and providing helpful feedback.
Preface
Recent research has shown that some important aspects of human number sense are actually inborn (Dehaene; Carey et al; Buttersworth), and that the language processing capabilities of the human brain are very much involved in mathematical activity. The implications of this research for the teaching and learning of mathematics are profound.
There is also a well-established myth that the verbal and symbolic language of mathematics is clear and unambiguous, but in fact no human language has such properties. If we fear confusing children by showing them that mathematical words and symbols can have different meanings, we should consider whether we might be promoting more serious confusion and misunderstanding by denying or obscuring this reality.
Every school-age child has already become proficient in his or her native language, even though that language has words that have different meanings in different contexts as well as different words for a given object or action. Why do we think children will be unable to handle these same features in the language of math? If we were to address the ambiguities and subtleties, instead of pretending they do not exist, we could avoid creating the kind of self-doubt that can make a learner feel stupid, when the problem actually lies in the language rather than in the student.
We must also be aware that once words have been attached to concepts, there is a tendency for those words to “stick” even after the ideas have been further developed and the words no longer actually describe the new understanding. For example, we talk about “real” and “imaginary” numbers in mathematics; historically, “real numbers” were considered to be properties of concrete aspects of the world. Mathematics has developed far beyond those original ideas, and the Oxford Dictionary now defines mathematics itself as “the abstract science of number, quantity, and space.” All numbers are now recognized as abstractions, and the terms “real number” and “imaginary number” are anachronisms.
In fact, mathematics is so very powerful because it is rooted in abstractions; once a mathematical tool is developed to solve a particular problem in a specific area, it can often be applied in other contexts. For example, the Scottish mathematician and inventor John Napier (1550–1617) developed the idea of the logarithm in response to the need to more efficiently perform the very cumbersome work required for multiplication and division after the invention of the telescope expanded human ability to measure much greater distances in astronomy. He also proposed the use of the decimal point as another way to represent fractions that extends the base-ten aspect of our number system, and he showed that the associated computational procedures would be less tedious than those in use at that time.