Mathematics teachers at work connecting curriculum materials and classroom instruction dec 2008

Mathematics Teachers at Work Mathematics Teachers at Work is the first collection to compile and synthesize research on teachers’ use of mathematics curriculum materials and the impact of curriculum materials on teaching In response to this rapidly growing field of research, the book places a particular emphasis on – but is not restricted to – those curriculum materials developed in response to NCTM’s Standards Each chapter offers a valuable understanding of teachers’ behaviors, practices, and learning in relation to mathematics curriculum materials Commentaries from both a researcher and a practitioner follow each of the book’s four parts, highlighting insights, questions, and challenges that speak to the significance of the chapters for research and practice Taken together, the chapters in this important new volume not only report empirical research findings, but also offer frameworks and perspectives on the teacher–curriculum relationship that can guide future research Janine T Remillard is Associate Professor of Education and Chair, Foundations and Practices of Education Division, Graduate School of Education, University of Pennsylvania Beth A Herbel-Eisenmann is Assistant Professor of Teacher Education, Michigan State University Gwendolyn M Lloyd is Professor, Department of Mathematics, Virginia Tech Studies in Mathematical Thinking and Learning Alan H Schoenfeld, Series Editor Artzt/Armour-Thomas/Curcio Becoming a Reflective Mathematics Teacher: A Guide for Observation and Self-assessment, Second Edition Baroody/Dowker (Eds.) The Development of Arithmetic Concepts and Skills: Constructing Adaptive Expertise Boaler Experiencing School Mathematics: Traditional and Reform Approaches to Teaching and their Impact on Student Learning Carpenter/Fennema/Romberg (Eds.) Rational Numbers: An Integration of Research Chazan/Callis/Lehman (Eds.) Embracing Reason: Egalitarian Ideals and the Teaching of High School Mathematics Cobb/Bauersfeld (Eds.) The Emergence of Mathematical Meaning: Interaction in Classroom Cultures Cohen Teachers’ Professional Development and the Elementary Mathematics Classroom: Bringing Understandings to Light Clements/Sarama/DiBiase (Eds.) Engaging Young Children in Mathematics: Standards for Early Childhood Mathematics Education English (Ed.) Mathematical and Analogical Reasoning of Young Learners English (Ed.) Mathematical Reasoning: Analogies, Metaphors, and Images Fennema/Nelson (Eds.) Mathematics Teachers in Transition Fennema/Romberg (Eds.) Mathematics Classrooms That Promote Understanding Fernandez/Yoshida A Japanese Approach to Improving Mathematics Teaching and Learning: Lesson Study Kaput/Carraher/Blanton (Eds.) Algebra in the Early Grades Lajoie Reflections on Statistics: Learning, Teaching, and Assessment in Grades K-12 Lehrer/Chazan (Eds.) Designing Learning Environments for Developing Understanding of Geometry and Space Ma Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States Martin Mathematics Success and Failure among African-American Youth: The Roles of Sociohistorical Context, Community Forces, School Influence, and Individual Agency Reed Word Problems: Research and Curriculum Reform Remillard/Herbel-Eisenmann/Lloyd (Eds.) Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction Romberg/Fennema/Carpenter (Eds.) Integrating Research on the Graphical Representation of Functions Romberg/Carpenter/Dremock (Eds.) Understanding Mathematics and Science Matters Romberg/Shafer The Impact of Reform Instruction on Mathematics Achievement: An Example of a Summative Evaluation of a Standards-Based Curriculum Schliemann/Carraher/Brizuela (Eds.) Bringing Out the Algebraic Character of Arithmetic: From Children’s Ideas to Classroom Practice Schoenfeld (Ed.) Mathematical Thinking and Problem Solving Senk/Thompson (Eds.) Standards-Based School Mathematics Curricula: What Are They? What Do Students Learn? Solomon Mathematical Literacy: Developing Identities of Inclusion Sophian The Origins of Mathematical Knowledge in Childhood Sternberg/Ben-Zeev (Eds.) The Nature of Mathematical Thinking Watson Statistical Literacy at School: Growth and Goals Watson/Mason Mathematics as a Constructive Activity: Learners Generating Examples Wilcox/Lanier (Eds.) Using Assessment to Reshape Mathematics Teaching: A Casebook for Teachers and Teacher Educators, Curriculum and Staff Development Specialists Wood/Nelson/Warfield (Eds.) Beyond Classical Pedagogy: Teaching Elementary School Mathematics Zaskis/Campbell (Eds.) Number Theory in Mathematics Education: Perspectives and Prospects Mathematics Teachers at Work Connecting Curriculum Materials and Classroom Instruction Edited by Janine T Remillard University of Pennsylvania Beth A Herbel-Eisenmann Michigan State University Gwendolyn M Lloyd Virginia Tech First published 2009 by Routledge 270 Madison Ave, New York, NY 10016 Simultaneously published in the UK by Routledge Park Square, Milton Park, Abingdon, Oxon OX14 4RN Routledge is an imprint of the Taylor & Francis Group, an informa business This edition published in the Taylor & Francis e-Library, 2008 “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” © 2009 Routledge, Taylor and Francis All rights reserved No part of this book may be reprinted or reproduced or utilized 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 Library of Congress Cataloging-in-Publication Data Mathematics teachers at work: connecting curriculum materials and classroom instruction/editors, Janine T Remillard, Beth A Herbel-Eisenmann, Gwendolyn M Lloyd p cm – (Studies in mathematical thinking and learning) Includes bibliographical references and index Mathematics–Study and teaching–United States Mathematics teachers–Training of–United States Curriculum planning–United States I Remillard, Janine II HerbelEisenmann, Beth A III Lloyd, Gwendolyn M QA13 M1648 510.71–dc22 2008027762 ISBN 0-203-88464-7 Master e-book ISBN ISBN10: 0-415-99010-6 (hbk) ISBN10: 0-203-88464-7 (ebk) ISBN13: 978-0-415-99010-3 (hbk) ISBN13: 978-0-203-88464-5 (ebk) For our sons Alexander, Kaleb, and Owen Contents List of Figures List of Tables Preface Acknowledgments xiii xiv xv xix PART I Introduction Teachers’ Use of Curriculum Materials: An Emerging Field GWENDOLYN M LLOYD, JANINE T REMILLARD, AND BETH A HERBEL-EISENMANN PART II Conceptual and Analytical Frameworks for Studying Teachers’ Use of Curriculum Materials 15 The Teacher–Tool Relationship: Theorizing the Design and Use of Curriculum Materials 17 MATTHEW W BROWN The Role of Mathematics Curriculum Materials in Large-Scale Urban Reform: An Analysis of Demands and Opportunities for Teacher Learning 37 MARY KAY STEIN AND GOOYEON KIM Understanding the Role of the Institutional Context in the Relationship Between Teachers and Text 56 KAY MCCLAIN, QING ZHAO, JANA VISNOVSKA, AND ERIK BOWEN Considerations and Limitations Related to Conceptualizing and Measuring Textbook Integrity KATHRYN B CHVAL, ÓSCAR CHÁVEZ, BARBARA J REYS, AND JAMES TARR 70 Index Abdel-Haqq, I 122 abilities, students 252–6 Ability to Quantitative Thinking subtest 176 access, multiple points of 32 accountability policies 217 action, artifacts in mediating 20 active agents, teachers as 252–62 adaptation 24–6, 28, 96–8; inevitability/difficulty of 199–202 Adaptive Instructional Materials (AIM) 32, 33 Addison Wesley Publishers 72, 81–2 Adler, P S 41 adoption of change 276 agency 61, 63–4, 66–7, 87, 88 Agenda for Action (NCTM) 224 Akers, J 107, 110, 113–14 algebraic activities: methods 155–8; relevant literature 152–5; types of 158–66 Allen, D 126 Amit, M 135, 136 Apple, M W 137, 343 Archer, J Aronsson, K 146 artifacts: analyzing teacher use of 23–6; curriculum materials as 20–1; in extending human capacities 19; influence on instruction 21–2; in mediating action 20; teachers’ interpretation of 22–3 assessment material, CPMP 178–80 assigned activities, algebraic curriculum 160–1 author negotiation, CPMP 178–80 authority 135–6, 194–6 authors, CPMP 175–6 Baker, C D 137–8 Ball, D L 17, 27, 29, 37, 43, 44, 45, 59, 103, 134, 148, 152, 206–7, 226, 229, 305, 322, 335 Banilower, E R 246, 249 Barab, S A 22 base programs 41–4 Bastable, V 116, 350 Becker, G S 40 Bednarz, N 153 Begle, E G 134, 245 Behm, Stephanie L 6, 9, 205–21, 353 beliefs 27 Bell, M 249 Belmont School 283 Ben-Peretz, M 18, 22, 23, 32, 39, 71, 173, 325, 326 Berdot, P 194 Berliner, D C 206 Berne, J 10, 17 Bertoff, Ann 119 Bethea, K A 216 BIFOCAL project 250, 255–6, 258, 259, 260–1, 262–3 Biklen, S 306, 307 Bill, V 251 Bits and Pieces unit 295, 296–8 Blanchard-Laville, C 194 Blanton, M L 57 Bloom, B 147 Bloomfield, K 116 Blunk, M 285 Blythe, T 126 Boaler, J 9, 305 Bogdan, R 306, 307 Bohl, J V 10, 207 Bolin, F 17, 56, 71 book overview 5–7 Borko, H 17, 216 Borman, K 40, 41 Bourdieu, P 40 Bowen, Erik 5, 8, 56–67, 353 Boyd, S E 246, 249 Bretzlauf, J 249 Britzman, D P 218 Brodie, K 115 Bronner, A 194 Brousseau, G 267 Brown, C A 52, 59 Brown, Matthew W 5, 9, 17–34, 334, 353 Bryans, M B 28, 87, 104, 206, 211, 219, 322, 324, 325–6, 335, 350 Bryk, A S 38, 41 Buchmann, M 206 Bugliari, D 305 Bullough, R 223 Burke, K 20 Burt, R S 41 Cai, J 72 Calderhead, J 223 Carmel, enacted task in 163–4 366 • Index Carpenter, T 45, 51, 57, 307 Carroll, W M 249 Castro, A 250 Cazden, C 138 Cebulla, J J 246 Cengiz, Nesrin 5–6, 11, 103–17, 353 Chandler-Olcott, Kelly 6–7, 12, 283–300, 340, 341–3, 344, 347–8, 353–4 Charalambous, Charalambos Y 6, 9, 245–64, 266, 354 Chávez, Óscar 5, 8, 22, 23, 70–83, 354 Chazan, D 134, 148 Children’s Maths Worlds (CMW) 323–6, 335 Cho, J 72 Christie, F 138–9 Christou, Constantinos 6, 95, 223–43, 266, 267–9, 270, 354 Chval, Kathryn B 5, 8, 70–83, 354–5 Circles and Circular Functions unit 180 Clandinin, D J 152, 172–3 Clark, M 309 Clarke, B 152, 173, 174 Clarke D 152, 173, 174, 249, 286 class periods 198–9 classroom management, and use of StandardsBased materials 267–9 Cobb, P 57, 58, 59, 60, 62, 64, 65–6, 67, 103, 134, 148, 285 Coburn, C E 37 Cochran, K 116 Cochran-Smith, M 119 Cockcroft, W 224 coding, tasks 46–7 Cohen, D K 17, 22, 27, 29, 37, 44, 103, 152, 226, 229, 322, 335 Cohen, S 350 Cole, M 168 Coleman, J S 40 collaboration, curriculum adaptation 200–1 Collopy, R 12, 37, 40, 305, 326 Colón, Irma 118–32, 355 commercially-developed textbooks: and textbook integrity 72–3; student teachers’ use of 210–11; studies of 90; and teacher research 118–32 Committee of Primary Mathematics Education, Cyprus 223, 227 communication standard, NCTM 284–5 comparative approach to analysis 45–8 concepts, representations of 26–8 confidence, student teachers 216–17 Confrey, J 57, 64 conjecture testing 60–1 Connected Mathematics Project (NSF) 72, 77, 140–5, 190, 250, 262, 283–300, 302–18 Connelly, F M 172–3 constructs, evolution of 61–5 content knowledge 135–6, 216–17 context and materials 10–11 Cooney, Thomas J 6, 266–72, 345, 355 Cooper, D A 216, 345 Corbin, J 251, 306, 307 Corcoran, T 207 Core-Plus Mathematics Project (CPMP) 190; authors and design principles 175–6; negotiation examples 177–87; teacher negotiation in curriculum development 176–7 Corujo, Raquel 127, 118–32, 355 Costello, R B 171 Crumbaugh, Carol 5–6, 11, 103–17, 355 Cuban, L 17, 168 culturally rooted tools 21 curricular knowledge 305–6 curricular reasoning: foundations for 305–6; implications 316–18; and PDT activities 308–14; research methods 306–8; supporting role of PDT 314–16 Curriculum and Evaluation Standards for School Mathematics (NCTM) 224, 302–4 curriculum change, adoption and implementation 276 curriculum decision-makers perspective: consequences in quest for fidelity 94–5; implications for 98–9; importance of instructional realities 95–6; reconceptualizing operational definition of fidelity 96–8; school level quest for fidelity 93–4 curriculum design, implications of curriculum vision/trust 335–6 curriculum developers, rationales of 44–5 curriculum development: background on second-edition Core-Plus Mathematics 175–7; examples and discussion 177–87; guiding questions 174–5; relevant literature 172–4; summary discussion 187–8 curriculum features, differentiating 90 curriculum implementation: conceptualising 247–50; context of study 250–1; data sources and analysis 251; discussion 262–3; findings 251–62 curriculum materials: analysis from learners’ perspectives 308–10, 315; as artifacts 20–1; comparative approach to analysis of 45–8; confounding nature of teachers’ use of 266–72; design of 32–3; faith in 93–4; general approach to analysis of 41–5; images of teachers learning through 347–51; importance of context 10–11; interaction with organizational Index • 367 features 50–2; interpretation for enacted classroom 345; positioning in relation to 197–8; teachers’ use of 206; type of use 24–6; potential factors influencing student teachers use of 212–19; and preservice teachers 206–7; student teachers’ ways of using 208–12; support for student thinking 109–10, 112–13; teacher learning from 349–50; types of algebraic activity 158–9; in use 212–15; use at points on professional continuum 274–9 curriculum programs: role of materials in change of 277–8; selection of 45–6 curriculum resources 8–9 curriculum strategy changes: developing curriculum vision and trust 332–4; identification of teachers’ strategies 326–7; implications for professional development/curriculum design 335–6; research context 323–6; Year 1/Year strategies 327–32 curriculum trust: defining 325–6; developing 334 curriculum use: meaning of 7–8; as relational 9–10; as support for large-scale teacher learning 39–41; and teacher learning 11–12 curriculum vision: defining 324–5; developing 333–4 customization, supporting 33 Cyprus, beginning teachers adoption of new materials 227–43 Cziko, C 285 Darling-Hammond, L 38, 324 Data Landmarks lessons 209 Davenport, Linda Ruiz 7, 347–52, 355 Davies, B 139 Davis, E A 18, 22, 33, 41, 44–5, 103, 322, 324, 334 De La Cruz, Y 323 Dean, C 59, 60 debriefing 348–9 Department of Education, Cyprus 227 design: of materials 32–3; of professional development 33; teaching as 18–19, 23; of theory 60–1 design capacity for enactment framework (DCE) 26–8, 86, 88 design implications 31–2 design principles, CPMP 175–6 design rationales 44–5 development need areas 89–91 Dewey, J 85, 91, 173, 270 Dialogue Boxes (DBs) 106, 201 dice games 128 differentiating instruction 127–30 Dillard, A 249 Dilworth, Thomas 193 Disappearing Trains lessons 210 DiSessa, A A 57, 58, 64, 65–6, 67 districts, support for teachers 351–2 Dittman, F 173 Doerr, Helen M 6–7, 12, 283–300, 340, 341–3, 344, 347–8, 355–6 doing mathematics (DM) tasks 42–4, 46–52 domino games 128 Donato, R 136 Donovan, B F 11 Dossey, J 302–3, 304 Doyle, W 41, 86 Drake, Corey 7, 12, 152, 299, 321–36, 340–1, 342, 344, 349–50, 356 Duckworth, Eleanor 119 DuFour, R 95 Duke, N K 286 Dunne, M 345 Durkin, D Durkin, K 286 Eaker, R 95 Easley, J 11 Ebby, C B 215 Eco, U 196 Economopoulos, K 116 Edelson, D C 18, 25, 28, 29, 334 education, changes in 224 educational system, Cyprus 227–8 Eisenhart, M 251 Eisenmann, Tammy 6, 152–68, 199, 356 Eisner, E W 18 El Barrio-Hunter College PDS Partnership Writing Collective: as model of collaboration 200; open letter to Everyday Mathematics colleagues 131–2; overview 6, 8; people 118–21; purposes 118; research setting 121–2; teacher action research at PS 112, 122–7; teacher research and differentiating instruction 127–30 eliciting actions 104–17 Eliophotou-Menon, M 224, 226, 235, 266 Elmore, R 40, 62 enacted curriculum: interpreting curriculum and materials for 345; and teachers 197–202; types of algebraic activity 159–66 enacted lessons 11–12, 108–9 enacted tasks 163–6 Enz, B J 206 equivalent algebraic expressions 156–9, 162, 166–7 368 • Index Erickson, J 251 Evans, A E 40 Even, Ruhama 6, 152–68, 199, 356 Everyday Mathematics (University of Chicago Mathematics Project) 39, 45–52, 118–20, 122–5, 129, 131–2, 190, 208–19, 249 Everyone Learns Mathematics 156, 190 extending actions 104–17 Exterior Angle Theorem 181 Factor Pairs from 100 to 1,000 lessons 107–10, 113–14 Fairbanks, C M 218 Fairclough, N 59 Fauvel, J 193, 195 Feiman-Nemser, S 206–7, 218 Fennell, F 208 Fennema, E 307 Fernandez, C 45, 306 Ferreiro, E 193 Ferrini-Mundy, J 208 Fey, J T 140, 144, 172, 175–6, 177, 246, 283, 287, 291, 295, 296, 302, 304, 308, 312 Fi, C 246 fidelity: alternatives to measuring 90–1; of implementation 71–3; and professionalism 64–5; quest for 93–4; reconceptualizing operational definition 96–8; training for 56–7; unintended consequences in quest for 94–5 Fielding, L G 286 Finn, K F 246 Fisher, D 286 FitzGerald, F 3, 140 Fitzgerald, W M 144, 246, 283, 287, 291, 295, 296, 302, 304, 308, 312 Forman, E A 59, 136, 285 Fraivillig, J L 103–4, 105, 107, 108–9, 116 Frank, K 40, 41 Franke, M 40, 57 Freebody, P 137–8 Freedman, D 218 Freeman, D J 3, 22, 39, 152, 168 Frey, N 286 Fried, M N 135, 136 Friedman, T 272 Friel, S N 140, 144, 246, 283, 287, 291, 295, 296, 302, 304, 308, 312 Friere, P 272 front line field testers, teachers as 199–200 Frykholm, J A 218, 220, 269 Fullan, M 37, 56, 72, 226, 246 Fuller, F 225–6 fully-accredited schools 218 Funches, Elaine 118–32, 356 Fuson, K C 104, 105, 108–9, 116, 323 future research, priorities for 342–5 Gallagher, M C 286 Gallas, Karen 119–20 Gallego, M A 168 Gallimore, R 249 Gallucci, C 40 Garnier, H 249 Garry, R F 173 Gattegno, C 193 Gayer, N 147 Gee, J P 284 Geijsel, F 236 Gelinas, Priscilla 121, 127, 118–32, 356–7 Gellert, U 220, 268 general approach to analysis 41–5 generational activities 153–68 geometry, curriculum development 180–3 Ghousseini, Hala 6, 9, 245–64, 266 Gibson, J J 19, 20, 39 Ginsberg, H P 208 Givvin, K 249 Glencoe 72, 81–2 global activities 154–68 goals 27 Goldenberg, M P 22, 270 Goodman, N 17 Goodman, T 8, 10, 152, 168 Gosen, D 251 Grade Level Expectations (GLEs) 310, 311, 312, 315, 316, 318 Grant, Theresa J 5–6, 11, 103–17, 357 Gray, E 194 Greenes, C 129, 208 Greenleaf, C 285 Greeno, J Grossman, P 27, 28, 52, 302, 305 Grouws, D A 71, 72, 78 Grover, B W 10, 37, 154, 248 Guskey, T R 323 Guyton, E 206 Haggarty, L 136 Hall, G E 71, 223, 225, 228, 230–1, 236, 245 Hamilton, L 305 Hamm, J V 136, 145 Hammerness, K 324 Harcourt 72 Hargreaves, A 226, 235–6, 241 Harré, R 139 Hart, A W 40, 41 Hart, Eric W 6, 9, 171–88, 357 Hartfield, R 249 Heaton, Ruth 119–20 Heenan, B 245–6 Heinz, K 62 Index • 369 Hemmings, A 135–6, 140, 147 Henningsen, M 10, 37, 154, 248, 250, 305, 350 Herbel-Eisenmann, Beth A 3–12, 28, 61, 90, 134–49, 153, 168, 198, 285, 357 Hershkowitz, R 168 Hewitt, D 148, 193 Hiebert, J 28, 37, 45, 51, 249, 308, 317, 318 high-level tasks 42–3 high-stakes accountability testing 60, 287–8 Hightower, A M 38 Hill, H 305 Hirsch, C R 172, 175–6, 177 Hjalmarson, M 207 Holland, D Hollingsworth, H 249 Hollingsworth, S 120 Holmes Group 122 Hord, S M 223, 225, 228, 230–1, 236 Horowitz, N 116 Houang, R T 152 Houghton, N 245–6 Houghton Mifflin Publishers 72, 81–2 Howes, E V 120 Howson, G 173, 317, 338 Hubbard, L 38 Huberman, M 226, 235, 241 Hudson, K 323 Hufferd-Ackles, K 323 human capacities, artifacts in extending 19 human capital 40–1, 50–2, 88 Huntley, M 71, 82 Hurwitz, L 285 Hutchins, E 19 Id-Deen, L 10–11, 61, 153, 168 impact concerns 225 implementation of change 276 Implementing Standards-based Mathematics Instruction: A Casebook for Professional Development (Stein et al.) 250 improvisation 24–6, 28, 96–8 Inbar, Y 159 innovations: beginning teachers’ concerns 226–7; teachers’ concerns 225–6 Inquiry Summer 2005 126–7, 131 Inscribed Angle Theorem 181–2 institutional context: data and setting 58–9; designing theory 60–1; evolution of constructs 61–5; orienting framework 65–7; theoretical perspectives 59–60 instruction, influence of curriculum artifacts 21–2 instructional context, teacher adaptation to 198–9 instructional perspective, curriculum implementation 247–50 instructional reality 60–3, 66–7, 87, 94–5; importance of considering 95–6; positioning in three classroom examples 140–5 instructional register 138–9 instructional strategies, teachers repertoire of 256–62 instructional tasks 42–4 instructional triangle 247–50 insubordination 194 integral curriculum programmes 43–4, 46 Investigations in Number, Data, and Space (TERC) 39, 45–8, 103–17, 190, 201, 325–6 Iowa Test of Educational Development 176 Iris Hill 59, 63, 64 Isaacs, A 249 Jackson, P W 147 Jacobs, J 249 Jakwerth, P M 90 Jaworski, Barbara 338–45, 357–8 Jefferson Heights 59, 63, 64 Johansson, M 146 Johnson, S M 206, 219, 226, 227, 231, 239 José Celso Barbosa School (112M) 121–32 K-12 curriculum materials 41, 93–4, 97 Kahan, J A 216 Kahn, C 218 Kaleidoscopes, Hubcaps, and Mirrors unit 295 Kaput, J J 57 Kardos, S M 206, 219, 226, 227, 231, 239 Karhanek, G 95 Kauffman, D 206, 212, 217, 219, 226, 227, 231, 239 Kazemi, E 40 Keble, P 72 Kegan, R 239 Keiser, J M 10 Keitel, C 173, 317 Kelly, A 286–7 Kern, A 168 Kieran, C 153–4, 155, 157, 167, 285 Kilpatrick, J 71, 72, 173, 317 Kim, Gooyeon 5, 37–52, 152, 358 Kim, Ok-Kyeong 5–6, 11, 103–17, 358 Kinzel, M 62 Kirkpatrick, H 168 Kitcher, Zoe 325–6 Klein, S 305 Kliman, M 107, 110, 113–14 Kline, Kate 5–6, 11, 103–17, 358 Knapp, M 38 Knuth, E J 138 Komoski, P K 370 • Index Kong, A 286 Koren, M 159 Krajcik, J S 18, 22, 33, 40, 41, 44–5, 103, 322, 324, 334, 335 Kruse, R A 168 Kruse, S 40 Kuhs, T M Kvatinsky, T 153, 168 Kwon, S 41 Lambdin, D V 10, 71, 72 Lamberg, T 59, 60 Lampert, M 61, 174, 247, 285 Lane, S 248 language choices: lens for interpreting examples 135–40; permutations of positioning 145–7; positioning in three classroom examples 140–5; purposeful positioning 147–8 Lappan, G 140, 144, 246, 283, 287, 291, 293–4, 295, 296, 302, 304, 308, 312 large-scale urban reform: comparative analysis of curriculum materials 45–8; curriculum materials supports for teacher learning 39–41; discussion 48–52; general approach to analysis of curriculum materials 41–5; implications 52 Larson, Matthew R 5, 93–9, 129, 358 Lave, J learners, doing tasks together as 310, 315 learners’ perspective, curriculum materials analysis 308–10, 315 learning trajectories, mapping of 311–12, 315–16 Lee, L 153 Lehrer, R 57, 64 Leinhardt, G 43, 45 Leiva, M 129 Lemke, J 139, 146 Lerman, S 284, 343 Lesh, R 286–7 lesson cycles 288 lessons, selection of 46 Lester, J B 350 Lewis, C 306 light box and mirror activity 311–14 literacy demands: background and theoretical perspectives 284–8; discussion 299–300; and mathematics 289; shift from barrier to opportunity 289–95; shift from opportunity to development 295–9 literacy instruction, framework for 286 literature: algebraic activities 152–5; curriculum intentions/enactment 172–4 Liu, E 206, 219, 226, 227, 231, 239 Livingston, C 216 Lloyd, Gwendolyn M 3–12, 18, 22, 23, 40, 134, 136, 152, 153, 168, 173, 205–21, 305, 317, 326, 358 Lo Cicero, A M 323 Loef, M 307 Lopez, J A 286 Loucks, S F 71, 245 Louis, K S 40 Love, E 137, 138, 148, 191, 195 low-performing schools 217 Lubeinski, S T 10–11, 61, 153, 168, 220, 305 Luehmann, A L 22 Lytle, S L 119 MAC-Glencoe 81–2 McCaffrey, D 305 McCaleb, J 216 McCarthey, S 40 McClain, Kay 5, 8, 56–67, 359 McCormick, D E 136 McIntyre, D J 206 McKinney, M 225 McKnight, C C 152 McLaughlin, M 38, 40 McNeal, B 103, 134, 136 McNight, C C 90 Maiorano, Patricia 118–32, 359 Manaster, A 249 Manouchehri, A 8, 10, 152, 168 Marcus, Robin 6, 9, 171–88, 359 Marks, G 286 Marks, H M 40 Marsh, J A 38 match train assignment 154–5, 163–4 Matese, G 22 Math Thematics (MT) 72, 77 Mathematical Tasks Framework 247–50, 256, 261, 263 Mathematics Counts 224 Mathematics in Context (MiC) 72 Mather, Martha 7, 10, 299, 302–18, 340, 341, 343, 344, 348–9, 359 Matrix Methods unit 183–5 Mauro, L 216 Mayer-Smith, J 220, 227 mediated action 20 mediating agents, teachers as 252–62 Mehan, H 38, 138 Meira, L 56 memorization 46–52 Menon, Maria Eliophotou 6, 223–43, 359–60 mentoring, student teachers 218–19 meta-level activities 154–68 Metz, M H 135 Mewborn, D 305 Index • 371 Meyerson, M J 225 Michigan Merit Curriculum 198 Michigan State University 200 Mills, Valerie 6, 9, 245–64, 266, 360 Mitchell, M 272 Mitchelmore, M 309 Model for Pedagogical Reasoning and Action 305 model readers 195–6 modular learning resources 32, 43, 46 Moon, B 220, 227 Morgan, C 139, 148, 285, 286 Moser, J 51 motivation, students 252–6 Mousley, J 286 Moyer, J C 72 Multiplication and Division Clusters lessons 110–13 multiplicity issue 269–70 Murphy, L A 104, 105, 108–9, 116 Murphy, S 208 Murray, M 107, 110, 113–14, 116 Nacel, Fadwa M 120–1, 118–32, 360 Nathan, M J 138 National Center for Education Statistics 241 National Council of Teachers of Mathematics (NCTM) 3–5, 76, 90, 134, 136, 148, 172, 207, 223–4, 227–8, 245, 247, 266, 270, 284–5, 300, 307, 308, 342; see also Standards-based curriculum materials National Research Council (NRC) 4–5, 70, 71, 72, 172 National Science Foundation (NSF) 3–5, 57, 59, 63, 72, 76–80, 172, 175, 200, 302 negotiators, teachers as: background on secondedition Core-Plus Mathematics 175–7; examples and discussion 177–87; guiding questions 174–5; relevant literature 172–4; summary discussion 187–8 Nelson, B S 59, 224 Nemirovsky, R 200 new mathematics curriculum materials: findings 234–40; implications 240–3; present study 227–9; research method 229–34; theoretical background 224–7 new textbooks, teachers’ responses to 224–5 Newlove, B W 245 No Child Left Behind Act (2002) 4, 70, 93 Norman, D A 19, 20 Northwestern University 323 Ntenza, S P 286 number sense 124–5, 126 Nystrand, M 146 O’Connor, M C 285 Oberman, I 38 offloading 24–6, 28, 96–8 Olson, D R 136–7, 142 ontological innovation 58 ordination 192 organizational conditions: interactions with curriculum materials 50–2; teacher–curriculum material interactions 40–1 orienting frameworks 65–7 Osterlind, S J 22, 23 Oyler, C 146–7 Pace, J L 135–6, 140, 147 Paley, Vivian Gussin 119 Papick, I J 207 Pasch, S H 206 Pasley, J D 246, 249 Passarelli, Christine 130, 118–32, 360 Patterns of Change unit 178 Patterns of Shape unit 178–9 Pea, R D 19, 25, 29 Pearson, P D 286 Peck, C 168 pedagogic intentions 191 pedagogical content knowledge 27 pedagogical design capacity (PDC) 29–31, 87, 88, 89–90, 97–8, 248 pedagogical orientation, textbooks 76–8 pedagogical reasoning 305–6 pedagogy and text authority 137–9 Pepin, B 136 Perry, M 136, 145 Peske, H G 206, 219, 226, 227, 231, 239 Peterson, P 4, 40, 307 Philippou, George 6, 223–43, 266, 360 Phillips, Eileen 6, 140, 144, 246, 274–9, 283, 287, 291, 295, 296, 302, 304, 308, 312 physical objects 26–8 Pimm, David 6, 90–6, 137, 138, 148, 285, 360–1 planning 348–9 plans, revising 312–14, 315–16 Pomfret, A 37, 56, 72 Porter, A C 22, 39, 152, 168 Portes, A 40 Powell, A B 286 Powell, B S 126 pre-service teachers and mathematics curriculum materials 206–7 Prentice Hall Publishers 72, 81–2 Preston, R V 71 primary source, textbooks as 73–4 Principals and Standards for School Mathematics (NCTM) 247 Pritchard, D R 171 Privileging the Teacher 140–7 Privileging the Textbook 140–7 372 • Index Procedure-centric curriculum programs 50–1 procedures with connection (PWC) tasks 42–4, 46–52 procedures without connection (PNC) 46–52 professional continuum, use of materials at points on 274–9 professional development: approach to 306–7; design of 33; implications of curriculum vision/trust 335–6 Professional Development Schools (PDSs) 122–3, 200–1 professional development teams (PDTs): curricular reasoning activities 304, 306–14; supporting role in curricular reasoning activities 314–16 professional identities 8–9 Professional Standards for Teaching Mathematics (NCTM) 224 professional status 64–7, 87, 88 prompting 47 Properties of Circles lessons 180 Pugalee, D K 286 Putnam, R T 17 RAVE 292–3, 298 readiness, students 252–6 Record, Robert 195 regulative register 138–9 relational curriculum use 9–10 Remillard, Janine T 3–12, 18, 22, 23, 28, 38, 39, 40, 42, 44, 49, 56, 65, 70, 71, 72, 85–91, 104, 168, 173, 174, 206, 211, 212, 219, 248, 305, 322, 324, 325–6, 335, 350, 361 research arena 340–2 research teams, roles and relationships 343–5 resource-centric curriculum materials 32–3, 51–2 reusable learning resources 32 reusable resources 33 revisions, CPMP 178 Reys, Barbara J 5, 8, 22, 23, 70–83, 361 Reys, R E 22, 23, 78 Richardson, V 322 Ritsema, Beth 6, 9, 171–88, 361 ritual utterances 142 Robinson, N 153, 154, 156, 159, 162 Robson, M 223 Robyn, A 305 Roehrig, G H 168 Romberg, T 76, 145, 225 Ron, P 323 Rosenthal, Bill 118–32, 361 Roth, Kathleen J 131 Roth McDuffie, Amy 7, 10, 299, 302–18, 340, 341, 343, 344, 348–9, 359 Rowan, B 305 Rowling, J K 190–1 Ruiz-Primo, M A 72 Russell, S J 103, 107, 110, 113–14, 116, 350 Russell, T 135 Rutherford, W L 245 Ryle, G 29 Sabar, N 156 St John, M 245–6 Sanchez, R 43 Saxon Publishers 72, 74–6, 81–2 scaffolding strategies 256–62 Schauble, L 57, 64 Schifter, D 116, 350 Schilling, M 43 Schmidt, W 90, 152 Schneider, B L 38, 40, 41 Schneider, R 18 Schnepp, Marty J 197–202, 361 Schoen, Harold L 6, 9, 171–88, 246, 362 Schoenbach, R 285 Schoenfeld, A H 4, 43, 45, 51, 134, 148 school context, student teachers 217–18 School-master’s Assistant (Dilworth) 193 School Mathematics Study Group (SMSG) 173 Schwarz, B B 168 Sebel, Laura 118–32, 362 Seeley, M 51 self-concerns 225 Senger, S E 59, 224, 241 Senk, S L 71, 245 sequencing, students’ solutions 260–1 Sexton, T 225 Sfard, A 284, 285 Shafer, M C 76 Shaw, J M 129 Sherin, Miriam Gamoran 7, 12, 43, 45, 152, 299, 321–36, 340–1, 342, 344, 349–50, 362 Shih, J 22, 23 Shire, B 286 Shulman, L S 27, 302, 305–6, 307, 322, 340 Sillart, Renée 118–32, 362 Silver, Edward A 6, 9, 40, 245–64, 266, 270, 305, 362 Silver Burdett Ginn (SBG) 210–19 SIMCALC project 200 Simon, M A 59, 62, 306 Skemp, R 135–6 Skott, J 269 Sleegers, P 236 Smith, J P I 22, 40, 45 Smith, M S 4, 71, 78, 90, 248, 249, 250, 251, 305, 306 Smith, S T 323 Smylie, M A 40, 41 Snyder, J 17, 56, 71, 72 Index • 373 social capital 40–1, 50–2, 87, 88, 95–6 social practice, teaching as 59 social settings 342–3 social trust 43–4 solutions: purposeful selection of 259–60; sequencing of students’ solutions 260–1 Sosniak, L A 242 Soto, Esther Robles 118–32, 363 Southwestern 72 Spillane, J P 17, 27, 62, 71, 87, 224 spiral curriculum materials 43–4, 46 Stages of Concern Questionnaire (SoCQ) 230–1 Stake, R E 11 Standards-Based curriculum materials; challenges of 42–4, 302–4; as change agent 37–9; and classroom management 267–9; comparative analysis of 45–52; implementation of 245–64; negotiating literacy demands 283–300; overview 3–5, 11–12; student teachers’ use of 207–10; and student thinking during wholegroup discussions 115–17; studies of 90 Standards-Based Learning Environment (SBLE) index 77–9 Steeby, R 323 Steele, D F 215 Steele, M D 43, 45 Steffy, B E 206 Stein, Mary Kay 4, 5, 10, 22, 23, 37–52, 59, 71, 90, 152, 154, 248, 250, 305, 350, 363 Stephens, M 286 Stephens, W M 11 Stetcher, B 305 Stiff, L 129 Stigler, J 28, 37, 45, 249, 308, 317, 318 Stodolsky, S S 27, 242 Strauss, A 251, 306, 307 Strawhun, B T F 251 Stray, C 137 Stretching and Shrinking unit 289–90, 293–4, 303, 308–18 String Bead Name Collections lessons 209–10 student-centered learning 29–30 student responses, teachers’ anticipation of 45, 258–9 student teachers: adoption of new mathematics curriculum materials 223–43; concerns of 226–7; implications 219–21; and mathematics curriculum materials 206–7; potential factors influencing use of curriculum materials 212–19; research context 207–8; use of textbooks/curriculum materials 206; ways of using curriculum materials 208–12 student teaching, context for 275–6 student thinking: asking questions to support and challenge 261–2; context 104–5; discussion 113–15; implications 115–17; investigation support materials 105–6; supporting efforts to elicit/extend 106–13 students’ solutions, sequencing of 260–1 studies, settings of 338–40 subject matter knowledge 27 subordination 192–4 Sullivan, P 152, 173, 174 supporting actions 104–5 Tabachnick, B R 215 Table-of-Contents Implementation Records 74–5, 78 Taizi, N 154, 156, 162 Talbert, J E 40 Tambe, P 245–6 Tarr, James 5, 8, 23, 70–83, 207, 363 task concerns 225 tasks: coding of 46–7; comfort/discomfort with 278; doing together as learners 310, 315; representations of 26–8 Tate, W 208 Tavor, enacted task in 164–6 Taylor, P 272 teacher authority 135–6 teacher-centered learning 30 teacher–curriculum material interactions 39: need for development 89–91; organizational conditions for 40–1 teacher education coursework 215–16 teacher learning: curriculum materials as supports for 39–41; from curriculum materials 349–50; and curriculum use 11–12; district support for 351–2; images of 347–8; by planning/debriefing 348–9 teacher materials 42–3, 44–5 Teacher Notes (TNs) 106, 201 teacher practice, identifying and sustaining change in 276–7 teacher research: action research 122–7; and differentiating instruction 127–30; open letter to Everyday Mathematics colleagues 131–2; people 118–21; research setting 121–2 Teacher–Student(s) Aligned 140–7 Teacher–Textbook Aligned 140–7 teacher-tool relationship: analyzing teacher use of curriculum artifacts 23–4; curriculum artifacts influence on instruction 21–2; curriculum materials as artifacts 20–1; design implications 31–2; design of materials 32–3; design of professional development 33; facets of 26–8; 374 • Index teacher-tool relationship continued how teaching is design 23; pedagogical design capacity 29–31; teachers’ interpretation/use of curriculum artifacts 22–3; teaching as design 18–19; theoretical background 19–20; types of curriculum use 24–6 teachers 8–9; analyzing use of artifacts 23–4; anticipation of students’ responses 45; conceptions of adequacy of new textbooks 237–40; concerns of adopting new textbooks 225–6, 235–7; confounding nature of use of curriculum materials 266–72; and enacted curriculum 197–202; identification of curriculum strategies 326–7; interpretation of artifacts 22–3; positioning in relation to curriculum materials 197–8; professional status 64–5; repertoire of instructional strategies 256–62; responses to new textbooks 224–5; underdeveloped understanding of role 252–6; use of textbooks 206; Year 1/Year curriculum strategies 327–32 teachers as negotiators: background on secondedition Core-Plus Mathematics 175–7; examples and discussion 177–87; guiding questions 174–5; relevant literature 172–4; summary discussion 187–8 teaching: as design 18–19, 23; student teachers’ confidence 216–17 teaching sets, theoretical perspectives guiding analysis of 59–60 Teddy Bear Game 125 Teitel, L 122 text material change, adoption and implementation 276 textbook authority 137–8 textbook integrity 87–8; conceptualizing 71–3; determining 78–81; operationalizing 73 textbook positioning 197–8; examples 140–5; and language choice 138–40; permutations of 145–7; purposeful positioning 147–8 Textbook Use Diaries 73–4, 76, 78 textbooks: adequacy of 239–40; pedagogical orientation 76–8; regular use 73–4; role in curriculum program change 277–8; significant use 74–6; students’ conceptions of support from 238–9; students’ use of 210–11 theoretical perspectives, analyses of teaching sets 59–60 theory: building 86–9; design 60–1; need for 85–6; in search of 65–7 Thinking Through a Lesson Protocol (TTLP) 251, 256–62 Thinking with Mathematical Models (TMM) 140–5 Tholander, M 146 Thom, R 134 Thompson, A 4, 223 Thompson, D R 71, 245 Thompson, P W 85 Tierney, C 107, 110, 113–14 Tirosh, D 153 Tobin, K 134 Track Game 125 transformational activities 153–68 transparency, teacher materials 44, 46–7, 51, 96 Tuten, Jenny 118–32, 363 Tzur, R 59, 62, 309 University of Chicago Mathematics Project 39, 208; definition of 7–8; materials 17–34; textbooks 73–6, 118–20 Usiskin, Z 153 Valverde, G A 152 Van de Walle, J 313 van den Berg, R 223, 225, 236 van Oers, B 56 Van Zoest, L R 10, 207 Vandenberghe, R 225, 236 Varma, K 18 Veenman, S 226 Visnovska, Jana 5, 8, 56–67, 363 Vogeli, B R 129 Voigt, J 138 Vygotsky, L S 20 Wagner, D 148, 344 Walker, Rebecca K 6, 9, 171–88, 364 Walnut Street Elementary School 208, 268 Wartofsky, M 19, 21 Washington Park 59, 60, 63, 64 Watkins, A 172, 175 Watson, A 286 Waywood, A 286 Wearne, D 249 Weinberg, S 52 Weiss, E M 241, 246 Weiss, I R 246, 249 Wertsch, J V 19, 20, 29, 39, 86 Whatts, Gloria 118–32, 364 Whitehurst, G J 70 Whittington, D 78 whole-class activities, algebraic curriculum 162–6 whole-group discussions, student thinking in 103–17 Wideen, M 220, 227 Index • 375 Wiley, D 18, 32, 152 Wilson, B R 338 Wilson, M 22, 134, 136, 270 Wilson, S M 10, 17, 27 Wisconsin Longitudinal Study 76 Wittenberg, L 116 Wolfe, M P 206 Wood, T 103, 134 Woolworth, S 52 Wooten, W 173 writing-to-learn 286 Wu, H 182 Yackel, E 103, 134, 285 Yaffee, L 350 Year 1/Year curriculum strategies 327–32 Yoshida, M 45 zero enactment 224–5 Zeuli, J S 71 Zhao, Qing 5, 8, 56–67, 364 Zhao, Y 40, 41 Ziebarth, Steven W 6, 9, 171–88, 364 Zumwalt, K 17, 56, 71, 324 .. .Mathematics Teachers at Work Mathematics Teachers at Work is the first collection to compile and synthesize research on teachers use of mathematics curriculum materials and the impact of curriculum. .. Zaskis/Campbell (Eds.) Number Theory in Mathematics Education: Perspectives and Prospects Mathematics Teachers at Work Connecting Curriculum Materials and Classroom Instruction Edited by Janine T Remillard... Use of Curriculum Materials 93 MATTHEW R LARSON PART III Understanding the Relationships Among Teachers, Mathematics Curriculum Materials, and the Enacted Curriculum How Can Curriculum Materials