Mathematical Literacy - Heinemann

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Transcript of Mathematical Literacy - Heinemann

Denisse R. Thompson
Janet C. Richards
Patricia D. Hunsader
Rheta N. Rubenstein
H E I N E M A N N • P O R T S M O U T H , N H
Mathematical Literacy
Heinemann 361 Hanover Street Portsmouth, NH 03801–3912 www.heinemann.com
Offices and agents throughout the world
© 2008 by Denisse R. Thompson, Gladis Kersaint, Janet C. Richards, Patricia D. Hunsader, and Rheta N. Rubenstein
All rights reserved. No part of this book may be reproduced in any form or by any elec- tronic or mechanical means, including information storage and retrieval systems, with- out permission in writing from the publisher, except by a reviewer, who may quote brief passages in a review.
The authors and publisher wish to thank those who have generously given permission to reprint borrowed material:
“Day Care Center Problem”from A Collection of Performance Tasks and Rubrics: Middle School Mathematics by Charlotte Danielson. Copyright © 1997. Reprinted with per- mission from Eye on Education.
“Lesson 1-2”from UCSMP Transition Mathematics, Third Edition by the University of Chicago. Copyright © 2005. Published by the Wright Group-McGraw Hill. Repro- duced with permission of The McGraw-Hill Companies.
Cataloging-in-Publication data is on file at the Library of Congress. ISBN-13: 978-0-325-01123-3 ISBN-10: 0-325-01123-0
Editor: Victoria Merecki Production: Vicki Kasabian Cover design: Jenny Jensen Greenleaf Cover photography: Brian Beecher of See Photography, Sarasota, Florida Typesetter: Publishers’ Design and Production Services, Inc. Manufacturing: Steve Bernier
Printed in the United States of America on acid-free paper 12 11 10 09 08 VP 1 2 3 4 5
ch00_4993.qxd 12/20/07 1:56 PM Page ii
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1. Meaning Making in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Communication and Mathematical Literacy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3. Reading and Language Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Section 1 Summary: Learning from Theoretical Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
SECTION 2 Classroom Environments to Facilitate Meaning Making . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4. Toward a Discourse Community . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5. Zoom In–Zoom Out: Using Reading Comprehension to Enhance Problem-Solving Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6. Multiple Representations Charts to Enhance Conceptual Understanding . . . . . . . . . . . . . . . . . 65
7. You Be the Judge: Engaging Students in the Assessment Process . . . . . . . . . . . . . . . . . . . . . . . . 76
Section 2 Summary: Developing Classroom Environments to Facilitate Meaning Making . . . . . . . . . . . 87
SECTION 3 Teaching Practices That Encourage Meaning Making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
8. Building Meanings Through Concept Development and Communication . . . . . . . . . . . . . . . . 91
Models for Mathematical Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Graphic Organizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Comparing and Contrasting Concepts: Venn Diagrams and These Are/These Are Not . . . . . . . . . . . . 96
Illustrating Relationships Among Concepts: Concept Maps and Semantic Feature Analysis Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Concept Development Through Body Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
9. Building Meanings Through Language Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
Contents
Daily Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Venn Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Distinguished Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Invented Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Literature Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Cooperative Learning Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Silent Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Symbol-Language Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
Prereading Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
Brainstorming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
PreP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Anticipation Guides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
During Reading Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Teacher Think-Alouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Pairs Read . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
QAR (Question-Answer-Relationship) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
Strategies That Engage in All Three Phases of Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
SQ3R (Survey, Question, Read, Recite, Review) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
DRTA (Directed Reading-Thinking Activity) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Reading Word Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Mathematics Autobiography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Writing Opportunities for Concept and Language Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Personal Glossaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Symbols-Meanings Writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Notes and Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Test Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Mathematics Bumper Stickers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
Section 3 Summary: Encouraging Meaning Making in Your Classroom . . . . . . . . . . . . . . . . . . . . . . . . 174
Appendix: Sample Middle Grades Mathematics Textbook Lesson . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
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Learning mathematics in the middle grades is a critical compo-
nent in the education of our nation’s youth.The mathematics
foundation laid during these years provides students with the
skills and knowledge to study higher level mathematics . . . ,
provides the necessary mathematical base for success in other
disciplines . . . , and lays the groundwork for mathematically
literate citizens.
Mathematics, and Technology
T his book focuses on the importance of meaning making in middle grades mathematics classrooms. We chose this focus because the middle grades (generally, grades 6–8) are an important period in the mathematical edu-
cation of students. During this time, students solidify their understanding of many concepts they initially studied in elementary school, such as rational numbers and their operations, and begin more formal study of geometric and algebraic concepts. These critical mathematical turning points open doorways to later studies and ca- reers that require mathematics prerequisites. In addition, adolescents are in a stage of development in which they particularly value peer opinions and interactions. Therefore, they need and seek opportunities to communicate with one other. We can capitalize on their need for socialization to build learning communities in which students work with their peers and the teacher to make sense of mathematics.
In this book, we share teaching practices related to communication (reading, writ- ing, speaking, listening) that teachers can use to “establish a communication-rich classroom in which students are encouraged to share their ideas and to seek clarifi- cation until they understand”(National Research Council 2000, 270). In such class- rooms, students are expected to explain their thinking, question and debate responses from their peers, and…