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Downloaded by [New York University] at 00:29 01 December 2016 Effective Techniques to Motivate Mathematics Instruction Downloaded by [New York University] at 00:29 01 December 2016 Effective Techniques to Motivate Mathematics Instruction Effective Techniques to Motivate Mathematics Instruction offers pre- and in-service teachers best practices and techniques that can be used to motivate students in the first few minutes of any lesson in mathematics. Veteran teacher educators Posamentier and Krulik show how a bit of creativity and planning up front pays back by enabling a successful lesson on even the most challenging mathematics topic. Organized around eleven different motivational techniques, each chapter includes a variety of illustrative examples of how the technique may be applied. Designed to complement any methods textbook, this updated and expanded version provides an accessible guide that helps future math teachers ease the transition from successful student to successful teacher by developing the tools needed to create motivational introductions in their classes. In-service teachers will also find ideas in this book that could rejuvenate their instruction. Features and updates to the new edition include: ♦♦ Theory to practice focus helps ease future teachers’ tran- sition from mathematics methods courses to actual class- room scenarios. Each chapter offers illustrative examples of how motivational strategies can be applied to various secondary grade levels, from large classes to small group settings. ♦♦ A section on the use of technology for motivating math- Downloaded by [New York University] at 00:29 01 December 2016 ematical relationships, focusing especially on the use of dynamic geometry computer programs and student engagement with technology to discover mathematical phenomena. ♦♦ A new section on the use of practical problems to moti- vate instruction. The authors suggest everyday examples and stories to promote student interest in a wide array of mathematical topics. ♦♦ A new Introduction addresses the challenges of motivat- ing students in the age of standards-based mathematics, especially highlighting the impact of the National Coun- cil of Teachers of Mathematics’ (NCTM) Principles and Standards for School Mathematics and Common Core State Standards (CCSS). Alfred S. Posamentier is currently Chief Liaison for International Academic Affairs at Long Island University, New York. He is for- mer Dean of the School of Education and Professor Emeritus of Mathematics Education at the City College of the City University of New York, and also held the same positions at Mercy College, New York. He was also Distinguished Lecturer at New York City College of Technology of the City University of New York. Stephen Krulik is Professor Emeritus of Mathematics Education at Temple University, where he was responsible for the under- graduate and graduate preparation of mathematics teachers for grades K–12, and for the in-service training of mathematics teachers at the graduate level. Dr. Krulik received the Great Teacher Award from Temple University in 2002, and was given the Lifetime Achievement Award from the NCTM in 2011. Downloaded by [New York University] at 00:29 01 December 2016 Effective Techniques to Motivate Mathematics Instruction Second Edition Alfred S. Posamentier and Stephen Krulik Downloaded by [New York University] at 00:29 01 December 2016 Second edition published 2016 by Routledge 711 Third Avenue, New York, NY 10017 and by Routledge 2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business © 2016 Taylor & Francis The right of Alfred S. Posamentier and Stephen Krulik to be identified as authors of this work has been asserted by them in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. First edition published by McGraw-Hill Education 2011 Library of Congress Cataloging-in-Publication Data Names: Posamentier, Alfred S. | Krulik, Stephen. Title: Effective techniques to motivate mathematics instruction / Alfred S. Posamentier and Stephen Krulik. Description: Second edition. | New York, NY : Routledge, 2016. | First edition published by McGraw-Hill Education, 2011. | Includes index. Identifiers: LCCN 2015046907 | ISBN 9781138640948 (hardback) | ISBN 9781138640955 (pbk.) | ISBN 9781315630854 (e-book) Downloaded by [New York University] at 00:29 01 December 2016 Subjects: LCSH: Mathematics—Study and teaching. | Effective teaching. | Motivation in education. Classification: LCC QA11.2 .P6384 2016 | DDC 510.71—dc23 LC record available at http://lccn.loc.gov/2015046907 ISBN: 978-1-138-64094-8 (hbk) ISBN: 978-1-138-64095-5 (pbk) ISBN: 978-1-315-63085-4 (ebk) Typeset in Palatino by Apex CoVantage, LLC We dedicate this book to mathematics teachers who we hope will enlighten future generations so that they will learn to love mathematics for its power and beauty! To my children and grandchildren, whose future is unbounded: Lisa, Daniel, David, Lauren, Max, Samuel, Jack, and Charles. Alfred S. Posamentier To my children and grandchildren, whose future is unbounded: Nancy, Daniel, Jeffrey, Amy, Amanda, Ian, Sarah, and Emily. Stephen Krulik Downloaded by [New York University] at 00:29 01 December 2016 This page intentionally left blank Downloaded by [New York University] at 00:29 01 December 2016 Contents Introduction ����������������������������������������������������������������������������������xi The Art of Motivating Students for Mathematics Instruction . .1 What Is Motivation? �������������������������������������������������������������������2 1 Indicate a Void in Students’ Knowledge . 11 Topic: The Introductory Lesson on the Tangent Ratio . .12 Topic: Special Quadrilaterals . .14 Topic: Determining the Measure of an Angle Formed by Two Secants to a Circle ���������������������������������������������������15 Topic: Tangent Segments to the Same Circle . .17 Topic: Introducing Heron’s Formula for Finding the Area of a Triangle �����������������������������������������������������������������18 Topic: Introducing the Quadratic Formula ���������������������������19 Topic: The Introductory Lesson on Imaginary Numbers . .20 Topic: Finding the Sum and Product of the Roots of a Quadratic Equation . .22 Topic: The Introduction to Exponential Equations . .23 2 Discover a Pattern �������������������������������������������������������������������25 Topic: Counting Techniques . .27 Topic: Introducing Non-Positive Integer Exponents �����������29 Downloaded by [New York University] at 00:29 01 December 2016 Topic: Caution with Patterns . .30 Topic: The Sum of the Measure of the Interior Angles of a Polygon . .33 Topic: Introduction to Counting Combinations �������������������34 3 Present a Challenge . .37 Topic: Introducing the Order of Operations �������������������������38 Topic: Determining Prime Numbers . .41 viii ◆ Contents Topic: Algebraic Applications �������������������������������������������������42 Topic: Introducing the Concept of π . .44 Topic: Understanding the Value of π �������������������������������������45 Topic: Introducing the Circumference of a Circle . .46 Topic: Finding the Sum of the Interior Angles of a Polygon . .47 Topic: Proving Triangles Congruent . .48 Topic: Introducing Geometric Series . .51 4 Entice the Class with a “Gee-whiz” Amazing Mathematical Result . .53 Topic: Introducing the Nature of Proof ���������������������������������54 Topic: Thales’ Theorem . .56 Topic: Introducing the Nature (or Importance) of Proof . .58 Topic: Considering Division by Zero �������������������������������������60 Topic: The Introductory Lesson on Sample Space in Preparation for Probability ���������������������������������������������61 Topic: Introduction to the Concept of Area, or Looking Beyond the Expected ���������������������������������������63 Topic: Introduction to the Area of a Circle or to Finding Areas of Similar Figures �����������������������������������65 Topic: Infinite Geometric Series . .66 5 Indicate the Usefulness of a Topic �������������������������������������69 Topic: Introduction to Proportions �����������������������������������������70 Topic: Applying Algebra ���������������������������������������������������������71 Topic: Introduction to Similar Triangles . .72 Topic: Introducing Modular Arithmetic . .73 Topic: Introduction to the Concurrency of the Downloaded by [New York University] at 00:29 01 December 2016 Angle Bisectors of a Triangle ���������������������������������������������74 Topic: Determining the Volume of a Right Circular Cylinder ���������������������������������������������������������������������������������76 Topic: Introduction to Probability—Expected Outcomes �������������������������������������������������������������������������������78 Topic: Introducing the Product of the Segments of Two Intersecting Chords of a Circle . .79 Contents ◆ ix Topic: Introduction to the Concurrency of the Altitudes of a Triangle ���������������������������������������������������������80 6 Use Recreational Mathematics ���������������������������������������������83 Topic: Identifying Factors of Numbers . .85
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