the algebra solution to the mathematics reform completing the equation pdf

www.Technicalbookspdf.com The Algebra Solution to Mathematics Reform Completing the Equation www.Technicalbookspdf.com www.Technicalbookspdf.com The Algebra Solution to Mathematics Reform Completing the Equation FRANCES R SPIELHAGEN Teachers College, Columbia University New York and London www.Technicalbookspdf.com Published by Teachers College Press, 1234 Amsterdam Avenue, New York, NY 10027 Copyright © 2011 by Teachers College, Columbia University All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, or any information storage and retrieval system, without permission from the publisher Library of Congress Cataloging-in-Publication Data Spielhagen, Frances R., 1946The algebra solution to mathematics reform : completing the equation / Frances R Spielhagen p cm Includes bibliographical references and index ISBN 978-0-8077-5231-9 (pbk : alk paper) Algebra—Study and teaching (Middle school)—United States Algebra— Study and teaching (Middle school) —Social aspects I Title QA159.S66 2011 512.9071’2—dc22 2011008527 ISBN 978-0-8077-5231-9 (paper) Printed on acid-free paper Manufactured in the United States of America 18 17 16 15 14 13 12 11 8 7 6 5 4 3 2 www.Technicalbookspdf.com This book is dedicated to the teachers and school administrators who labor daily to create opportunities for the students in their care Especially among them is Gerard Spielhagen, my husband and partner, who has empowered so many to achieve excellence and who has truly been the wind beneath my wings www.Technicalbookspdf.com When you are laboring for others, let it be with the same zeal as if it were for yourself —Confucius www.Technicalbookspdf.com Contents Acknowledgments ix Mathematics Success: Solving the Equation! Algebra as a Civil Right Is 9th Grade Early Enough to Study Algebra? Dissension and Conflict About When to Teach Algebra A Template for Change: Looking at a Model of Success How Did They Do It? The Organization of the Book Understanding the Variables in Mathematics Education 10 15 How Did We Get Here from There?: The History of Mathematics Curriculum Delivery 16 Search for the Identity of the High School in the United States 19 Who Should Study Algebra?: Philosophical and Psychological Foundations 20 Challenging the Status Quo in the Mid-20th Century 21 Reforming the Reform Movement 23 Forward Movement and Backlash to Change in Mathematics Curriculum 25 Redefining the Variables 26 Keeping Track: Setting the Course in Mathematics 27 When Should Most Students Take Algebra? 28 Recent Research on Tracking and Detracking 30 Case Study: Taking Charge of Change in Chesterfield, Virginia 31 Student Voices for Change: “Would Have, Should Have, Could Have Studied Algebra in 8th Grade” 39 Context: The Setting for the Interviews 39 The Interviews: The Students Speak 40 Students’ Views on Social Life in Middle School 41 vii www.Technicalbookspdf.com viii Contents The Relationship of Academics to the Students’ Lives 42 How Were They Selected (or Not) for 8th-Grade Algebra? 42 The Value of 8th-Grade Algebra 43 Long-Term Effects of 8th-Grade Math Classes 44 Lessons Learned from the Students 46 The Value of Student Input 47 Following the Rules: Teachers as Gatekeepers to Advanced Math 51 Input from the Teachers in This Case Study 52 Teacher Talk About Their Students and Math 55 Ready or Not, Here They Come!: Meeting Diverse Algebra Students 56 Redefining Readiness 59 Changing the Rules 61 Changing the Rules: Long-Term Effects of 8th-Grade Algebra 63 Why They Changed the Rules 64 Benefits Derived from Studying Algebra in 8th Grade 65 Effects of 8th-Grade Algebra on High School Math Performamce 66 8th-Grade Math Experiences and the SAT 67 The Effect of 8th-Grade Algebra on College Attendance 67 8th-Grade Algebra for All Students? 68 Mandate for Change in Local Mathematics Policies 70 The Solution: How Educational Policy Changes Mathematics Outcomes 71 Changing the Game Plan for Mathematics Curriculum Delivery 72 Know the Rules 72 Listen to the Experts 74 Review Your Own Data 76 Keep Your Eye on the Prize 78 Courage and Conviction 79 Train the Players 81 Solving the Equation 83 References 85 Index 92 About the Author www.Technicalbookspdf.com 102 Acknowledgments At the turn of the 21st century, the words equity and excellence resounded at all levels of the educational establishment As a career educator with over 30 years’ experience in secondary classrooms, I was as concerned as any teacher who had spent her life trying to connect students to learning and to pave the way for their future success At the same time, I had just begun my doctoral study in educational leadership at Fordham University’s Graduate School of Education Therefore, I resolved that I would explore the ways in which school organization influences student learning and how policy affects the opportunities that are afforded to students In the face of all the rhetoric surrounding the “achievement gap” in education, I was more concerned about opportunity gaps that perpetuated low achievement, especially among underserved populations of students I would like to thank Dr Bruce Cooper, professor of education at Fordham University, for encouraging me to wade boldly into the waters of policy analysis to explore how schools affect student achievement by the structures they create and maintain As my dissertation mentor, Bruce demanded rigor and encouraged me to explore my research questions into hypotheses that produced defensible findings He has continued to offer support throughout all the subsequent stages of this work My initial study resulted in more questions than answers, which I then pursued from 2003 to 2006 as a postdoctoral research fellow, funded by the American Educational Research Association and the Institute for Educational Sciences I am grateful to Felice Levine, executive director of AERA, and members of the Postdoctoral Fellows Advisory Committee, especially Dr Robert Floden and Dr William Trent, for their support and guidance I particularly want to thank Dr Joyce Van Tassel-Baska, professor emerita at the College of William and Mary, who was my mentor during this fellowship Her wisdom and guidance, coupled with her unflagging energy, provided a model of scholarship that continues to inform my work My colleagues and the administration at my home institution, Mount Saint Mary College, in Newburgh, New York, have provided collegial support in countless tacit and overt ways Indeed, this book would not have been possible without the cooperation and vision of the school leaders of Chesterfield County, Virginia, especially Dr Glenn ix www.Technicalbookspdf.com .. .The Algebra Solution to Mathematics Reform Completing the Equation www.Technicalbookspdf.com www.Technicalbookspdf.com The Algebra Solution to Mathematics Reform Completing the Equation. .. www.Technicalbookspdf.com The Algebra Solution to Mathematics Reform: Completing the Equation consideration in their planning during the years that I worked with them Moreover, they also conducted their... www.Technicalbookspdf.com 10 The Algebra Solution to Mathematics Reform: Completing the Equation HOW DID THEY DO IT? THE ORGANIZATION OF THE BOOK The case study in this book chronicles the intricacies