The Changing Mathematics Curriculum: An Annotated Bibliography Third Edition April 2005 1 2 The K–12 Mathematics Curriculum Center About This Publication The K–12 Mathematics Curriculum Center (K–12 MCC) This publication, an annotated bibliography of articles supports school districts as they build effective mathematics relevant to Standards-based mathematics curriculum education programs using curricula that align with the National reform, is intended as a resource for educators and commu- Council of Teachers of Mathematics’ (NCTM) Curriculum and nities considering the selection and implementation of a Evaluation Standards for School Mathematics (1989) and Standards-based mathematics curriculum. It also may assist Principles and Standards for School Mathematics (2000). individuals who are interested in learning about the student achievement, classroom practices, and implementation The K–12 MCC offers a variety of products and services to challenges associated with the use of Standards-based assist mathematics teachers and administrators. Our seminars materials. address selecting and implementing new curricula, designing professional development and support, aligning curriculum When gathering resources for this publication, the K–12 with assessment, and examining leadership in curricular change. Mathematics Curriculum Center staff reviewed articles that Our other resources include: either addressed important issues in mathematics curricu- lum change or shared experiences, views, and data relevant • Curriculum Summaries to the selection and use of 12 comprehensive mathematics • Perspectives on Curricular Change: Interviews with programs based on the NCTM Standards and developed Teachers, Administrators, and Curriculum Developers with support from the NSF. These programs are listed on who have worked with 12 National Science the back cover of this publication. Foundation (NSF)-funded Standards-based curricula This bibliography does not attempt to be comprehensive • Choosing a Standards-Based Mathematics and certainly does not include every article written about Curriculum, a guide that suggests processes for mathematics curriculum reform. Rather, the goal was to selecting and implementing curricula select articles that would increase readers’ understanding of • a series of Issues Papers that explores contemporary Standards-based mathematics curricula and their use in mathematics education issues classrooms. • Consisdering New Mathematics Curricula DVD Most of the articles are peer-reviewed and were either Information and links to resources about Standards-based published in journals or collections, or presented as papers curricula and their implementation can be found at the K–12 at conferences. They are organized into four categories: Mathematics Curriculum Center website: characteristics of Standards-based mathematics curricula, research regarding the impact of these programs on student http://www.edc.org/mcc achievement, professional development, and issues that arise during implementation. Please contact the K–12 MCC for information on how we can either offer you direct support, point you to relevant Selections beginning with the word “Abstract” were written resources and materials, or connect you with educators by the original authors or publishers. If an article was experienced in curriculum selection and implementation. accessible online at the time of publication, its URL is listed. Some of these articles can be read or downloaded free For more information about our materials and services please of charge; others are available to subscribers and/or can be contact: purchased for a nominal fee. Kim Foster This publication is also available on our website at: K–12 Mathematics Curriculum Center Education Development Center, Inc. http://www.edc.org/mcc 55 Chapel Street Newton, MA 02458-1060 Phone: (800) 332-2429 Fax: (617) 969-1527 E-mail: [email protected] Website: http://www.edc.org/mcc This book was developed by the K–12 Mathematics Curriculum Center at Education Development Center, Inc. The work was supported by National Science Foundation Grant No. ESI-0137826. Opinions expressed are those of the authors and not necessarily those of the Foundation. 3 National Grade-level Implementation Centers In addition to the K–12 Mathematics Curriculum Center, there are three grade- level specific implementation centers supporting these curricula. Alternatives for Rebuilding Curricula (ARC) Contact: Sheila Sconiers The ARC Center is a collaboration between the Consortium for COMAP, Inc. Mathematics and Its Applications (COMAP) and the three NSF- Suite 210 supported elementary mathematics curriculum projects, 57 Bedford Street Investigations in Number, Data, and Space (TERC); Math Trailblazers Lexington, MA 02420 (University of Illinois at Chicago); and Everyday Mathematics Phone: (800) 772-6627, ext. 50 (University of Chicago). The Center promotes the wide-scale and Fax: (781) 863-1202 effective implementation of reform elementary mathematics E-mail: [email protected] curricula. Website: http://www.comap.com/elementary/ projects/arc Show-Me Center (National Center for Standards-based Middle Grades Mathematics Curricula) Contact: Barbara Reys The Show-Me Project is dedicated to providing information and University of Missouri assistance to schools considering and/or in the process of 303 Townsend Hall implementing Standards-based curriculum reform at the middle Columbia, MO 65211 grade levels (grades 6–8). The Project is a partnership of curriculum Phone: (573) 884-2099 developers and professional development staff at: the Show-Me Fax: (573) 882-4481 Center at the University of Missouri–Columbia; the Math in E-mail: [email protected] Context Satellite Center at the University of Wisconsin; the Website: http://showmecenter.missouri.edu Connected Mathematics Project Satellite Center at Michigan State University; the MathScape Satellite Center at Education Development Center; and the MATH Thematics Satellite Center at the University of Montana. Project staff provide assistance to state and district personnel through teacher institutes, curriculum conferences, and teacher leadership conferences. The Project provides information, materials to assist district implementation, and an online curriculum showcase at its website. It also responds to requests for services and information needed by local district personnel. COMPASS (Curricular Options in Mathematics Programs for All Secondary Students) Contact: Eric Robinson The COMPASS project is a secondary school implementation Ithaca College project funded in part by the National Science Foundation. 306 Williams Hall COMPASS consists of six sites: a satellite site for each of the five Ithaca, NY 14850 secondary-level curricula and a generic central site. Phone: (800) 688-1829 (607) 274-1513 The primary function of the central site is to inform schools, Fax: (607) 274-3054 districts, teachers, parents, administrators, state offices, and other E-mail: [email protected] groups about these innovative curricula and aid in the first general Website: http://www.ithaca.edu/compass phase of selection and implementation. It also coordinates requests for additional information and assistance from the satellite sites. Each satellite provides additional information, implementation assistance, and professional development opportunities focused on its curricula to these same constituencies. 4 Table of Contents Characteristics of Standards-Based Mathematics Curricula ...................................... 7 Curricular Implications of the NCTM Standards ............................................................................. 7 Pedagogy........................................................................................................................................ 10 Content ......................................................................................................................................... 13 Evaluating Curricula ...................................................................................................................... 15 Impact Studies ......................................................................................................... 19 Elementary .................................................................................................................................... 19 Middle School ............................................................................................................................... 22 High School................................................................................................................................... 25 Professional Development ........................................................................................ 29 Teacher Learning ........................................................................................................................... 29 Teacher Practice ............................................................................................................................. 34 Teacher Perspectives ....................................................................................................................... 38 Pre-service Learning ....................................................................................................................... 39 Leadership Support ........................................................................................................................ 41 Implementation ......................................................................................................