• PDF / 6,788,622 Bytes
• 266 Pages / 684 x 864 pts Page_size
• 113 Downloads / 304 Views

DOWNLOAD

REPORT

---

Conceptual Model-Based Problem Solving Teach Students with Learning Difficulties to Solve Math Problems

Yan Ping Xin Purdue University, West Lafayette, USA

A C.I.P. record for this book is available from the Library of Congress.

ISBN: 978-94-6209-102-3 (paperback) ISBN: 978-94-6209-103-0 (hardback) ISBN: 978-94-6209-104-7 (e-book)

Published by: Sense Publishers, P.O. Box 21858, 3001 AW Rotterdam, The Netherlands https://www.sensepublishers.com/

Printed on acid-free paper

All Rights Reserved © 2012 Sense Publishers No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

TABLE OF CONTENTS

Acknowledgements

vii

About the Author

ix

1. Conceptual Model-based Problem Solving: Teach Students with Learning Difficulties to Solve Math Problems Introduction Algebra Thinking in Problem Solving Mathematical Modeling Theoretical Framework: Conceptual Model-based Problem Solving SBI that Emphasizes Semantic Analyses and Representation of the Problem COMPS that Emphasizes Algebraic Expression of Mathematical Relations Summary Program Components The scope and sequence of the program Target Audience and Users of the Program

1 1 2 3 4 4 6 7 7 8

2. COMPS Program Introduction Singapore Bar Models (SBM) to Facilitate the Transition to Mathematical Models Word Problem [WP] Story Grammar (Xin et al., 2008) A Cognitive Heuristic DOTS Checklist (Xin et al., 2008) Additive and Multiplicative Word Problem Structure and its Variations Instructional Phases

13 16

Part 1: Additive Problem Solving Unit 1: Representing Part-Part-Whole (PPW) Problems Lesson 1: Introduction Lesson 2: Part-Part-Whole Problem Representation Unit 2: Solving Part-Part Whole (PPW) Problems Lesson 3: Solving PPW Problems Unit 3: Representing Additive Compare (AC) Problems Lesson 4: Representing AC-More Problems Lesson 5: Representing AC-Less Problems Unit 4: Solving Additive Compare (AC) Problems Lesson 6: Solving Mixed AC Problems

19 21 21 26 35 35 49 49 60 69 69

v

11 11 12 13

TABLE OF CONTENTS

Unit 5: Solving Mixed PPW and AC Problems Lesson 7: Solving mixed PPW and AC Problems

83 83

Part 2: Multiplicative Problem Representation and Solving Unit 6: Representing Equal Groups (EG) Problems Unit 7: Solving Equal Groups (EG) Problems Unit 8: Representing Multiplicative Compare (MC) Problems Unit 9: Solving Multiplicative Compare (MC) Problems Unit 10: Solving Mixed Equal Groups and Multiplicative Compare Problems

141

Part 3: Solving Complex Problems Unit 11: Solving Complex Word Problems Unit 12: Solving Mixed Multi-Step Problems

159 161 173

3

Connection between Mathematical Ideas: Extend Multiplicative Reasoning to Geometry Learning

97 99 107 115 127

183

Appendix A: Student Worksheets

191

Ap