eric - education resources information centernational grade-level implementation centers...

ED 429 841

TITLEINSTITUTION

SPONS AGENCYPUB DATENOTECONTRACTAVAILABLE FROM

PUB TYPEEDRS PRICEDESCRIPTORS

IDENTIFIERS

ABSTRACT

DOCUMENT RESUME

SE 062 471

Curriculum Summaries, Second Edition.Education Development Center, Inc., Newton, MA. K-12Mathematics Curriculum Center.National Science Foundation, Arlington, VA.1999-01-0035p.

ESI-9617783Education Development Center, Inc., K-12 MathematicsCurriculum Center, 55 Chapel Street, Newton, MA 02458-1060.Reports General (140)MF01/PCO2 Plus Postage.*Academic Standards; Educational Resources; ElementarySecondary Education; *Mathematics Curriculum; ProgramDescriptionsNCTM Curriculum and Evaluation Standards

This document compiles information about 13 comprehensivemathematics curriculum programs that were developed specifically to addressthe recommendations of the National Council of Teachers of Mathematics'(NCTM) Curriculum and Evaluation Standards for School Mathematics. Three ofthe programs are elementary programs, five are for middle school, and fiveare geared towards high school. All of these programs were developed withsupport from the National Science Foundation (NSF) . Each description includesa summary of the program, publisher contact, developer/implementation center,students materials, teacher materials, other support materials, currentavailability of curriculum materials, impact data complied to date, and websites. Programs include: (1) Everyday Mathematics; (2) Investigations inNumber, Data, and Space; (3) Math Trailblazers; (4) Connected Mathematics;(5) Mathematics in Context; (6) MathScape: Seeing and ThinkingMathematically; (7) MATHThematics; (8) Middle-school Mathematics throughApplications; (9) Contemporary Mathematics in Context; (10) InteractiveMathematics Program (IMP); (11) MATH Connections: A Secondary MathematicsCore Curriculum; (12) Mathematics: Modeling Our World (ARISE); and (13) SIMMSIntegrated Mathematics. (ASK)

********************************************************************************* Reproductions supplied by EDRS are the best that can be made *

* from the original document. *

********************************************************************************

PERMISSION TO REPRODUCE ANDDISSEMINATE THIS MATERIAL HAS

BEEN GRANTED BY

V. WI

TO THE EDUCATIONAL RESOURCESINFORMATION CENTER (ERIC)

1

IN/

morIv imm /'

U S. DEPARTMENT OF EDUCATIONOffice of Educational Research and Improvement

E UCATIONAL RESOURCES INFORMATIONCENTER (ERIC)

This document has been reproduced asreceived from the person or organizationoriginating it.

0 Minor changes have been made toimprove reproduction equality.

Points of view or opinions stated in thisdocument do not necessarily representofficial OERI position or policy.

11102 .00

Stallsr:Gisits

Second EditionJanuary 1999

BEST COPY AVAILABLE

About This Publication

Curriculum Summaries compiles information about 13 comprehensive mathematicscurriculum programs that were developed specifically to address the recommendations of theNational Council of Teachers of Mathematics' Curriculum and Evaluation Standards forSchool Mathematics. Three of the programs described here are elementary programs; five arefor middle school; five are for high school. All of these programs were developed withsupport from the National Science Foundation. Many of them are newly available ascomplete and published curricula. Part of our mission at the K-12 Mathematics CurriculumCenter (K-12 MCC), and the intention of this document, is to support teachers, schools,and districts in learning about these new programs and in considering their use.

This publication is intended to be a source of basic information about the mathematicsprograms it describes. We have included information that we think will help the readerunderstand the basic tenets of each of the programs, what distinguishes them fromtraditional curricula, and what distinguishes them from one another. We have also includedinformation that we hope will help you learn more about these programs, through contactwith the publishers, developers, or implementation centers; through print materials and websites; or through continued contact with the K-12 MCC.

We have tried to describe the programs as the developers and publishers would representthem. The information about each of the curriculum programs was obtained from thematerials themselves and was checked by representatives of each of the programs for accuracy.Curriculum Summaries is not, therefore, a source of evaluative data or critical analyses ofthese programs.

The information included in this document is as accurate as we could make it at the time ofpublication. However, since we have included contact information, availability information,and other information that may change over time, we will update the summaries regularly toprovide the most accurate information. For future updates of this publication, contact theK-12 Mathematics Curriculum Center.

Second edition, January 1999.

Cover design by Emily Passman.

Design and Layout by Kristin Winkler.

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-9617783. Opinions expressed are

those of the authors and not necessarily those of the Foundation.

About the K-12 Mathematics Curriculum Center

Established in 1997 by Education Development Center, Inc., the K-12 MathematicsCurriculum Center (K-12 MCC) supports school districts as they build effectivemathematics education programs using curricula that respond to and align with the NationalCouncil of Teachers of Mathematics' Curriculum and Evaluation Standards for SchoolMathematics. The K-12 MCC receives support from the National Science Foundation(NSF) and works with the three NSF-funded grade-level mathematics implementationcenters (see next page).

The K-12 Mathematics Curriculum Center offers a variety of products and services to assistdistrict leadership teams with curriculum selection and implementation. From 1998 through2000, we will offer a series of three seminars repeatedly nationwide; the seminars address theselection and implementation of new curricula, professional development for successfulimplementation, and leadership for curriculum change.

Additionally, the K-12 MCC provides many print resources, including these CurriculumSummaries; a collection of Curriculum Perspectives from teachers and administrators who haveused the 13 reform curricula; Choosing a Standards-Based Mathematics Curriculum, a guidethat suggests a process for selecting and implementing curricula and describes how thesereform curricula differ from traditional materials; a series of short Issues Papers that explorecontemporary issues in mathematics education; Discussion Cases and facilitator guides whichparallel the topics of the seminars; Curriculum Connections, a newsletter produced three timesannually which provides curriculum and resource updates, feature articles, and upcomingseminar information; and a Curriculum Reader, which compiles literature pertaining to theconsideration of reform mathematics programs.

Another offering of the K-12 MCC is our web site (http://www.edc.org/mcc), whichcontains up-to-date information about the Center, the 13 curriculum programs, upcomingevents, and resources; and links to other useful sites.

The K-12 Mathematics Curriculum Center will also assist district administrators andteachers as they consider curricula by making referrals to resources, materials, and othereducators who have experienced the selection and implementation process.

For more information about any of our materials and services, or to receive a brochure orseminar information, please feel free to contact us:

Ki McClennan

K-12 Mathematics Curriculum CenterEducation Development Center, Inc.55 Chapel StreetNewton, MA 02458-1060

phone: (800) 332-2429fax: (617) 969-1527e-mail: [email protected]

Web site: http://www.edc.org/mcc

5BESTCOPY AVAILABLE

National Grade-Level Implementation Centers

Alternatives for Rebuilding Curricula (ARC)Contact: Sheila SconiersCOMAP, Inc.57 Bedford Street, Suite 210Lexington, MA 02420phone: (781) 862-7878 ext. 50fax: (781) 863-1202e-mail: [email protected]://www.comap.com/arc

The ARC Center is a collaboration between the Consortium for Mathematics and Its Applications (COMAP) and the

three NSF-supported elementary mathematics curriculum projects, Investigations in Number, Data and Space (TERC);

Math Trailbkizers (University of Illinois at Chicago); and Everyday Mathematics (University of Chicago). The aim of

the collaboration is to promote the wide-scale and effective implementation of reform elementary mathematics

curricula.

Show-Me Center (National Center for Standards-based Middle Grades Mathematics Curricula)

Contact: Barbara ReysUniversity of Missouri104 Stewart HallColumbia, MO 65211phone: (573) 884-2099fax: (573) 882-4481e-mail: [email protected]://showmecenter.missouri.edu/

The Show-Me Center, in partnership with five NSF-sponsored middle grades curriculum development satellites

(University of Wisconsin, Michigan State University, University of Montana, Institute for Research on Learning,

Education Development Center) and their publishers, provides information and resources needed to support selection

and implementation of standards-based middle grades mathematics curricula.

COMPASS (Curricular Options in Mathematics Programs for All Secondary Students)

Contact: Eric RobinsonIthaca College306 Williams HallIthaca, NY 14850-7284phone: (800) 688-1829

(607) 274-1513fax: (607) 274-3054e-mail: [email protected]://www. i thaca.edu/co m pass

COMPASS is a secondary school implementation project funded in part by the National Science Foundation.The COMPASS implementation center partners with a satellite site for each of the five secondary-level curricula.

The COMPASS project informs schools, districts, teachers, parents, administrators, state offices, and other groups

about these innovative curricula; aids in the first general phases of implementation; and coordinates requests for

additional information and assistance from the satellite sites. Each satellite provides additional information about its

curriculum to these same constituencies as well as professional development opportunities for schools interested in

adopting its curriculum.

6

CONTENTS

Elementary Grades Curricula

Everyday Mathematics TM 6

Investigations in Number, Data and Space® 8

Math Trailblazers TM 10

Middle Grades Curricula

Connected MathematicsTM 12

Mathematics in Context 14

MathScape: Seeing and Thinking Mathematically" 16

MATHThematics 18

Middle-school Mathematics Through Applications 20

High School Curricula

Contemporary Mathematics in Context 22

Interactive Mathematics Program (IMP) TM 24

MATH Connections®: A Secondaty Mathematics Core Curriculum 26

Mathematics: Modeling Our World (ARISE) 28

SIMMS Integrated Mathematics 30

7

EVERYDAY MATHEMATICC

An elementary school curriculum for grades K-6, developed by

the University of Chicago School Mathematics Project

Everyday Mathematics is a K-6 curriculum intended toenrich the mathematical experiences of teachers andchildren. It builds on fundamental mathematical strandssuch as numeration and order, measures andmeasurement, reference frames, operations, patterns,functions, and sequences. It uses more of themathematical spectrum by exploring data and chance,geometry and spatial sense, and algebra and the uses ofvariables.

The curriculum integrates mathematics into other subjectareas; mathematics becomes part of ongoing classroomroutines, outdoor play, and the transitional moments thatoccur every day. Teachers use Everyday Mathematics as acore curriculum during class time. They incorporatemathematical ideas and routines throughout the schoolday and encourage the children to continue the routinesat home with their families.

The Everyday Mathematics curriculum incorporates thebelief that people rarely learn new concepts or skills thefirst time they experience them, but fully understandthem only after repeated exposures. Students in theprogram study important concepts over consecutive years;each grade level builds on and extends conceptualunderstanding.

The instructional model blends exposition anddiscussion, individual and group work, projects,explorations, and investigations. In each grade level of theprogram, students experience hands-on, student-centered,small-group activities which introduce them to variousmathematics concepts. Children also learn and practicebasic facts throughout the curriculum, in the context ofproblem solving, choral drills, and a variety of games.

The program includes cross-curricular projects that letchildren apply mathematics in other subject areas. Ingrades 4 and 5, children participate in the year-longWorld Tour and American Tour projects, in whichstudents apply mathematical concepts to learning aboutthe United States and other countries.

Calculators are an integral part of the program as an aidto concept development and applications. Thecurriculum assumes that each child has a slate, calculator,measuring tools, and drawing tools, and that each teacherhas a classroom set of manipulatives.

Every student in grades 1-6 uses two consumablejournals throughout the school year to recordmathematical ideas and responses to activities andproblems. In grades 1-3, students also have a consumableActivity Book. At grades 4 and 5, student materialsinclude the non-consumable World Tour Guidebook(4th) and the American Tour Almanac (5th). At grade 6,student materials include the non-consumable StudentReference Book. Grades 5 and 6 use the GeometryTemplate for drawing and measuring geometric figures.

Each grade level of Everyday Mathematics has a TeacherResource Package that contains a Teacher's Manual andLesson Guide, Resource Book (with all blacklinemasters), a Teacher's Reference Manual, Towards aBalanced Assessment, and other teacher support items.

Publisher ContactJohn EstradaMarketing DepartmentEveryday Learning Corporation2 Prudential Plaza, Suite 1200Chicago, IL 60601phone: (800) 382-7670

(312) 540-0210fax: (312) 540-5848e-mail: [email protected]

Developer/Implementation CenterAndy IsaacsUniversity of Chicago School Mathematics Project5835 South Kimbark AvenueChicago, IL 60637phone: (773) 702-9639fax: (773) 702-4312e-mail: [email protected]

6 K-12 Mathematics Curriculum Center

Student Materials Teacher Materials

Journals (Grades 1, 2, 3, 4, 5 and 6)

Activity Books (Grades K, 1, 2, 3)

World Tour Guidebook (Grade 4)

American Tour Almanac (Grade 5)

Student Reference Book (Grade 6)

Geometry Template (Grades 5 and 6)

All student materials available in Spanish

(Grades 1, 2, 3, 4, 5 and 6)

Skills Link, cumulative practice sets (Grades 1-6)

Home Links and Math Boxes, consumable studentversions of blackline masters (Grades 1-3)

Teacher Resource Package (K)Program Guide and Activity MastersHome Links 1, 2, 3Teacher's Activity GuideMinute MathClass Number-Grid ChartScope and Sequence Chart

Per-grade Teacher Resources (Grades 1, 2, 3, 4, 5 and 6)Teacher's Manual and Lesson GuideResource Book (blackline masters)Assorted classroom posters and charts

Cross-grade Teacher ResourcesTeacher's Reference Manual (K-3)Teacher's Reference Manual (4-6)Towards a Balanced Assessment (K-3)Towards a Balanced Assessment (4-6)Creating Home-School Partnerships: A Guide for

Administrators and Teachers (K-6)Minute Math+ (1-3)

Manipulative Kits for each grade level

Some teacher materials available in Spanish

Other Support Materials

Everyday Teaching for Everyday Mathematics. Staff Development Kit (K-3)

Grade-Level Videos for Staff Development, Grades 1-5

Evoyday Mathematics: A K-6 Overview for Teachers. Videotape

Everyday Mathematics: An Overview for Parents. Videotape

Technology Guide and Software Correlations

TeacherLink, a newsletter for Everyday Mathematics teachers

Current Availability of Curriculum MaterialsGrades K-6 materials are all available.

Impact Data Compiled to Date

Student Achievement Studies and Student Achievement Studies, Volume 2. Two booklets from the Everyday LearningCorporation presenting results of close to 30 studies and reports on districts using Everyday Mathematics.Everyday Mathematics Success Stories. Cases provided by Everyday Learning Corporation about districts'results from using Everyday Mathematics.A Research Based Curriculum: The Research Foundations of the UCSMP Everyday Mathematics Curriculum. Availablefrom Everyday Learning Corporation or the University of Chicago School Mathematics Project.Additional implementation and achievement papers and information available from UCSMP.

Web Sites

At Everyday Learning Corporation: http://www.everydaylearning.com

At UCSMP: http://ars-www.uchicago.edu/ucsmp-el/

January 1999 7

INVESTIGATIONS IN NUMBER, DATA AND SPACE®

An elementary school curriculum for grades K-5, developed byInvestigations in Number, Data and Space at TERC.

The title of this program, Investigations in Number, Dataand Space, reflects the view that mathematics inelementary school is more than arithmetic. In theelementary grades, students need to develop a foundationin several key content areas of mathematics: number,data, and geometry, or space. The Investigationscurriculum also includes activities based on recentresearch on young children's understanding of themathematics of change.

*Each Investigations unit offers from two to eight weeks ofmathematical work on topics in number, data analysis,and geometry; the number of units per year varies bygrade level. Because of the many interconnections amongmathematical ideas, units may revolve around two orthree related areasfor example, addition andsubtraction or geometry and fractions.

In each unit, students explore the central topics in depththrough a series of investigations, gradually encounteringand using many important mathematical ideas. Ratherthan working through a textbook or workbook doingpage-by-page exercises, students actively engage withmaterials and with their peers to solve largermathematical problems. Students use concrete materialsand appropriate technology, including calculators, as anatural part of their work. They work in a variety ofgroupings: as a whole class, individually, in pairs, and insmall groups.

What all the investigations have in common is studentsworking in depth on a number of problems, activelyusing mathematical tools and consulting with peers asthey find their own ways to solve the problems. Theinvestigations allow significant time for students to think

about the problems and to model, draw, write, and talkabout their work. In addition to the investigations, thecurriculum also includes games and classroom routinesthat support mathematical thinking.

Investigations looks quite different from a traditionalelementary program. While it provides all theinformation teachers need to implement a completemathematics curriculum, there are no student textbooks.The main teaching tool is a single teacher resource book,called a curriculum unit, for each unit in a grade level.Each curriculum unit provides lesson plans, materialslists, reproducible student sheets for activities and games,assessment activities, and other support materials forteaching the unit. Some units at each grade level includecomputer software. Optional Student Activity booksprovide the reproducible unit pages from the TeacherResource book in a booklet for each student.Investigations at Home booklets for every unit aredesigned to provide extra practice and to inform andinvolve families in this kind of mathematics.

Publisher ContactLorraine GroffProduct Manager, MathematicsDale Seymour PublicationsP.O. Box 5026White Plains, NY 10602

Developer/Implementation CenterLorraine BrooksAdministrative AssistantTERC2067 Massachusetts AvenueCambridge, MA 02140

phone: (800) 872-1100 phone: (617) 547-0430

fax: (914) 997-8115 fax: (617) 349-3535

e-mail: [email protected] e-mail: [email protected]


Student MaterialsStudent Activity Booklets

One per unit, Grades K-5

Student Materials Kit, Grades K-5

Student Activity Sheets are also available in Spanish

Investigations at Home: family involvement booklets

One per unit, Grades K-5

Teacher Materials

Curriculum UnitsKindergarten: 6 units Grade 3: 10 unitsGrade 1: 6 units Grade 4: 11 unitsGrade 2: 8 units Grade 5: 9 units

Implementing the Investigations in Number, Dataand Space Curriculum, Grades K-2

Implementing the Investigations in Number, Dataand Space Curriculum, Grades 3-5

Teacher Resource PackageManipulativesOverhead transparenciesBlackline masters

Family Letters: explain the mathematics of each unit.Available in English, Spanish, Vietnamese,Cantonese, Hmong, and Cambodian.


Recommendations for a SuccessAl Implementation of Investigations in Number, Data and Space. Two-pagetipsheet based on notes from a Math Supervisor. Available from Dale Seymour Publications.

Beyond Arithmetic. A handbook for educators who are transforming mathematics learning and teachingthrough programs such as Investigations, by Mokros, Russell, and Economopoulos. Available from Dale SeymourPublications.

Mathematics Curriculum Implementation: Not a Beginning, Not an End, by Russell. An article available in the Spring1998 issue of Hands On! Available from TERC.Changing the Elementary Mathematics Curriculum: Obstacles and Challenges, by Russell. Available from TERC.


Impact Data Compiled to DateHow Do We Know These Programs Work? Available from Dale Seymour Publications.

Results of pilot studies and other data available from TERC:Full Year Pilot Grades 3 and 4, Investigations in Number, Data and Space, by Mokros, Berle-Carman,

Rubin and Wright.Learning Operations: Invented Strategies That Work, by Mokros, Berle-Carman, Rubin and O'Neil.

Web Sites

At Dale Seymour Publications: http://www.awl.com/dsp/MainPages/Invest.html

At TERC: http://www.terc.edu/investigations

January 19991 1

9

MATH TRAILBLAZERST"

An elementary school curriculum for grades K-5, developed byTeaching Integrated Mathematics and Science (TIMS).

A fundamental principle of Math Trailblazers is thatmathematics is best learned through active solving of realproblems. Lessons are grounded in everyday situations, soabstractions build on experience. Students' skills,procedures, and concepts emerge and develop as theysolve complex problems. The curriculum introduceschallenging content at every grade level, includingcomputation, measurement, data collection, statistics,geometry, ratio, probability, graphing, simple algebra,estimation, mental arithmetic, and patterns andrelationships. Each grade level has 16-20 units; unitsrange from one to three weeks long.

A central tenet of Math Trailblazers is that real problemsare naturally interdisciplinary. Accordingly, thecurriculum integrates mathematics with many disciplines,especially science and language arts.

Scientific investigations embedded in many units use theTIMS Laboratory Method, an organized method ofinvestigation appropriate for elementary school childrento use. Students explore a situation by drawing a picture,gathering and organizing data, graphing the data, andanalyzing their results. The science content in MathTrailatzers is intended to supplement, rather thanreplace, a school's existing science curriculum.

Math Trailblazers also makes strong connections tolanguage arts. As part of every lesson, students discussand write about mathematics. Many lessons use tradebooks to launch or extend mathematical investigations.The curriculum itself contains original stories, calledAdventure Books, that show applications of conceptsbeing studied or episodes from the history ofmathematics and science.

Many of the assessment activities in Math Trailblazers areincorporated into daily lessons; others are included informal assessment units. Assessments include a mix ofshort, medium-length, and extended activities. Beginningin third grade, Math Trailblazers provides a scoring rubricfor assessing students' work. An adaptation of this rubricallows students to assess their own work using the samecriteria.

Components of the Math Trailblazers curriculum varyacross grade levels. For grades 1 and 2, student materialsare consumable, and consist of a Student Guide and aDiscovery Assignment Book (containing student activityand homework pages) and an Adventure Book. Forgrades 3-5, Student Guides are hardcover, non-consumable texts and Adventure Books are spiral-bound,non-consumable texts; the Discovery Assignment Bookfor grades 3-5 is still consumable. Kindergarten studentmaterials are reproducible pages contained in the teachermaterials.

For every grade level, Math Trailblazers includes a TeacherImplementation Guide that provides backgroundinformation and support for teachers on the pedagogyand content of the program. Teacher materials for grades1-5 consist of Unit Resource Guide Files, which containteacher support materials organized for each unit of thecurriculum. Teacher materials for kindergarten alsoinclude a Teacher Resource Book.

Math Trailblazers requires the use of manipulatives.Calculator use is also integrated into the program, and isrequired for some activities.

Publisher ContactDennis Jaeger (ext. 1056)or John Barbee (ext. 1123)Kendall/Hunt Publishing Company4050 Westmark DriveDubuque, IA 52004-1840phone: (800) 542-6657fax: (800) 228-0720e-mail: [email protected]

or [email protected]

Developer/Implementation CenterJoan Bieler and Cathy KelsoCo-DirectorsTeaching Integrated Mathematics and Science ProjectInstitute for Mathematics and Science Education950 South Halsted, Rm. 2075 SEL m/c 250Chicago, IL 60607phone: (800) 454-TIMS


101 ) K-12 Mathematics Curriculum Center

Student Materials

Student Guide, Grades 1-5

(consumable, Grades 1-2)

Discovery Assignment Book, Grades


Adventure Book, Grades 1-5


Math Manipulative Kit, Grades K-5

Teacher Materials

Unit Resource Guides, Grades 1-5

Individual Replacement Unit Guides, Grades 1-5

1-5 Teacher Resource Book, K

Teacher Implementation Guides, Grades K-5

Quick Start, Grades K-5Unit summary, scope and sequence table of contents

Letter Home in Spanish translation, Grades 1-5

Generic Page: blackline masters, Grades 1-5

Transparency Packages, Grades K-5

Individual Assessment Record Sheets, Grades 1-3

Answer Keys, Grades 1-2

Wall Charts

Other Support MaterialsA Look Inside Math Mailblazers. Videotape


Spanish editions of student materials expected to be available in Fall, 1999.


Preliminary results of Math Trailblazers implementation are available from the TIMS Implementation Center.

Web Sites

At Kendall/Hunt Publishing Company: http://www.kendallhunt.com

At the TIMS project at UIC: http://www.math.uic.edu/IMSE/timsmath.html

January 1999 11

1 3

CONNECTED MATHEMATICS'A middle school curriculum for grades 6-8, developed bythe Connected Mathematics Project (CMP).Connected Mathematics strives to develop student andteacher knowledge of mathematics that is rich inconnections and deep in understanding and skill.Connected Mathematics' goals can be summarized into asingle standard: all students should be able to reason andcommunicate proficiently in mathematics. This includesknowledge and skill in vocabulary use, forms of represen-tation, materials, tools, techniques, and intellectualmethods of the discipline of mathematics including theability to define and solve problems with reason, insight,inventiveness and technical proficiency.

Connected Mathematics defines skill as much more thanjust proficiency with computation and symbolmanipulation. Skill in Connected Mathematics means thata student can use the mathematical tools, resources,procedures, knowledge, and ways of thinking developedover time to make sense of new situations.

The curriculum is structured around "big ideas inmathematicsclusters of important, related concepts,processes, ways of thinking, skills, and problem solving

strategies. The curriculum emphasizes significantconnections among various mathematical topics and toapplications in other disciplines. These connections alsooffer opportunities to revisit and deepen understanding ofmathematical ideas.

Mathematical concepts are embedded in the context ofinteresting problemsreal applications, whimsicalsettings, or mathematical problem situations. As studentsexplore a series of connected problems they develop skilland deep understandings of mathematical ideas. Problemcontent becomes a vehicle for understanding andremembering concepts. The curriculum develops sixmathematical strandsnumber, geometry, measurement,probability, statistics, and algebra.

Connected Mathematics is organized into units thatinvestigate important mathematical ideas. Each unitcontains four to seven investigations; each investigationexplores one to five major problems in class to developstudents' understanding and reasoning. The problem-centered teaching model consists of three phases: launch-ing the problem, exploring the problem, and summariz-ing the problem. Extensive problem sets, called Applica-tions, Connections, and Extensions (ACE), help studentspractice, apply, connect, and extend these understandings.Investigations culminate in Mathematical Reflections,helping students articulate their understandings andconnect "big" mathematical ideas and applications.

Connected Mathematics gives students many ways todemonstrate how they make sense of the mathematics inthe units. The Assessment Resources include check-ups,partner quizzes, projects, unit tests, self-assessments, andquestion banks. Connected Mathematics also suggests thatstudents keep notebooks and journals for mathematicalreflections, vocabulary, assessment, and other class work.

Students need access to calculators at all times. In the sixthgrade, students use a standard scientific calculator. Ingrades 7 and 8, students need access to a graphingcalculator. Optional computer software programs aresuggested to enhance some of the units.

Each grade consists of eight units. Student materials areavailable in softcover, non-consumable modular form. ATeacher Guide accompanies each unit, and contains a dis-cussion of the mathematics underlying the investigationswithin a unit and the instructional role of the teacher inorchestrating the classroom investigations. For each unit,the Guide gives a list of the materials needed, suggestedtimelines, homework assignment choices, and essentialvocabulary. Teacher materials include blackline masters ofconsumable student pages and overhead transparencies.

Publisher ContactLorraine GroffProduct Manager, MathCuisenaire Dale Seymour PublicationsP.O. Box 5026White Plains, NY 10602phone: (800) 872-1100fax: (800) 551-7637e-mail: [email protected]

Developer/Implementation CenterElizabeth PhillipsSenior Academic SpecialistConnected Mathematics ProjectMichigan State UniversityMathematics Department, A715 Wells HallEast Lansing, MI 48824-1050phone: (517) 353-3835

(517) [email protected]

fax:

e-mail:

12 1 4K-12 Mathematics Curriculum Center

Student MaterialsStudent Editions of each unit, Grades 6-8

Grade 6: 8 unitsGrade 7: 8 unitsGrade 8: 8 units

Student Materials Kits, Grades 6-8

Some student materials available in Spanish at eachgrade level.

Teacher Materials

Teacher Guide Packages, Grades 6-8Grade 6: 8 unitsGrade 7: 8 unitsGrade 8: 8 units

Getting To Know Connected Mathematics

Teacher Resource Kit, Grades 6-8TransparenciesBlackline MastersAssessment Resources

Other Support MaterialsScope and Sequence, Grades 6-8

Consultant Overview Sessions: Successful implementation suggestions from administrator/teacher consultants.

Current Availability of Curriculum MaterialsGrades 6-8 materials are all available.

Impact Data Compiled to DateHow Do We Know These Programs Work? Available from Cuisenaire Dale Seymour Publications.

A Study of Proportional Reasoning of Seventh Grade Students, by Ben-Chaim, Fey, Fitzgerald, Benedetto, andMiller. Connected Mathematics and non-Connected Mathematics students. Available from Cuisenaire DaleSeymour Publications.

Effects of the Connected Mathematics Project on Student Attainment, by Hoover, Zawojewski, and Ridgway.Available from Cuisenaire Dale Seymour Publications.

Web Sites

At Cuisenaire Dale Seymour Publications: http://www.awl.com/dsp/MainPages/CMP.html

At Michigan State University: http://www.math.msu.edu/cmp

Januaty 1999 13

1 5

MATHEMATICS IN CONTEXTT"

A middle school curriculum for grades 5-8, developed bythe Mathematics in Context (MiC) project.

Mathematics in Context is a comprehensive middle schoolmathematics curriculum for grades 5 through 8. It wasdeveloped by the Wisconsin Center for EducationResearch, School of Education, University of Wisconsin-Madison and the Freudenthal Institute at the Universityof Utrecht, The Netherlands.

Connections are a key feature of the programconnections among topics, connections to otherdisciplines, and connections between mathematics andmeaningful problems in the real world. Mathematics inContext emphasizes the dynamic, active nature ofmathematics and the way mathematics enables studentsto make sense of their world.

In traditional mathematics curricula, the sequence ofteaching often proceeds from a generalization, to specificexamples, and to applications in context. Mathematics inContext reverses this sequence; mathematics originatesfrom real problems. The program introduces conceptswithin realistic contexts that support mathematicalabstraction.

Mathematics in Context consists of mathematical tasksand questions designed to stimulate mathematicalthinking and to promote discussion among students.

*Students are expected to explore mathematicalrelationships; develop and explain their own reasoningand strategies for solving problems; use problem-solvingtools appropriately; and listen to, understand, and valueeach other's strategies.

The complete Mathematics in Context program contains40 units, 10 at each grade level. The units are organizedinto four content strands: number, algebra, geometry, and

statistics. Every Mathematics in Context unit consists of aTeacher Guide and non-consumable, softcover studentbooklet.

The Teacher Guides contain the solutions to the exercises;a list of unit goals; and objectives, comments, andsuggestions about the approach and the mathematicsinvolved in the unit. The guides include assessment piecesfor each unit, including tests, quizzes, and suggestions forongoing assessment. The guides also provide blacklinemasters for exercises requiring students to have copies ofthe text page.

Also available are two supplementary packets for teachers:the Teacher Resource and Implementation Guide (TRIG)and Number Tools. The TRIG manual is acomprehensive guide for the implementation ofMathematics in Context. It addresses topics such assuggested sequence of units, preparation for substituteteachers, preparing families, assigning homework, andpreparing students for standardized achievement tests.Number Tools, Volumes I and II, give students furtherexposure to number concepts, including fractions,decimals, percents, and number sense. The activity sheetsare supported by a context similar to those in thecurriculum units and can be used as homework andquizzes on classroom activities.

Manipulatives used in the program are items commonlyfound in the classroom, such as scissors, coordinate paper,string, and integer chips. As students progress to laterunits, the need for a personal calculator increases. Theeighth grade units were written with the expectation thatstudents would have access to graphing calculators.

Publisher ContactBill GasperMiC Product ManagerEncyclopedia Britannica, Inc.310 South Michigan AvenueChicago, IL 60604phone: (800) 554-9862, ext. 7927fax: (312) 347-7225e-mail: [email protected]

Developer/Implementation CenterMeg MeyerStaff DeveloperMathematics in Context Satellite CenterWisconsin Center for Education Research1025 W. Johnson StreetMadison, WI 53706phone: (608) 263-1798fax: (608) 263-3406e-mail: [email protected]


Student Materials

Student Booklets for each unit,

Plan A (5-8)Grade 5,10 unitsGrade 6,10 unitsGrade 7,10 unitsGrade 8,10 units

Plan B (6-8)

Grade 6,10 unitsGrade 7,10 unitsGrade 8,10 units

Student Booklets also available in Spanish

Teacher Materials

Teacher Guide for each unit includes:Black line MastersAssessment Packages

Teacher Resource and Implementation Guide

Number Tools, Volumes III

News in Numbers

Other Support MaterialsMiC Internet Support Group. Designed for teachers to ask questions about MiC implementation throughout theschool year; the MiC Consulting Group will respond within 48 hours.

MiC Parent Brochure.

Optional Manipulative Kits available through ETA: (800) 445-5985.

Suggested Software Integration to MiC Units.

Mathsphere and Mathsense videos. May be used to introduce concepts and help students make additionalmathematical connections.

Pacing Strategies for Each MiC Unit. Provides pacing suggestions and highlights Core Ideas of each unit.

MiC Scope and Sequence. (Plan A, 5-8) and (Plan B, 6-8).

Current Availability of Curriculum MaterialsAll materials for Grades 5-8 are currently available.

Half of the student materials are currently available in Spanish. The remainder will be available later in the 1999-2000 school year.


The Impact of the Mathematics in Context Curriculum. Impact data, shared with the Mathematics in Contextproject staff, from three districts which used the curriculum for at least two years. Available from the Mathematicsin Context Satellite Center.

Data from a National Science Foundation-funded three year longitudinal and cross-sectional study of the impact ofMathematics in Context on student mathematics performance will be made available in early 1999 from the MiCSatellite Center.

Web Site

At Encyclopedia Britannica, Inc.: http://www.ebmic.com

January 1999

1 715

MATHSCAPE: SEEING AND THINKING MATHEMATICALLim

A middle school curriculum for grades 6-8, developed bythe Seeing and Thinking Mathematically project at EDC.

MathScape is a comprehensive, three-year middle schoolmathematics curriculum that focuses on mathematics inthe human experience. Throughout the 21 units of thiscurriculum, students experience mathematics asfundamental to human endeavors throughout the worldand through historyendeavors such as planning,predicting, designing, creating, exploring, explaining,coordinating, comparing, and deciding.

The curriculum focuses on four mathematical strandsthat develop across the three grade levels: number;algebra; geometry and measurement; and statistics andprobability. MathScape supports students in learningmathematics by having them do mathematics, use andconnect mathematical ideas, and actively construct theirown understandings.

There are seven MathScape units at each grade level. Eachunit provides about 5-6 weeks of material and exploresseveral mathematical topics in depth, such as "what is afunction?" or "how do you interpret information onCartesian graphs?" The mathematics is presented incontexts designed to appeal to middle school students,such as music, sports, and architecture, as well as inpurely mathematical contexts. The curriculum engages

*students in hands-on investigations that involvemathematical concepts, skills, and processes, and providesopportunities for practice and application of basic skills.Lessons prompt students to work collaboratively withtheir classmates, communicate about mathematics in classdiscussions and writing, and reflect on their thinking andlearning.

Each unit of the program features an assessment packagewith options that allow teachers to choose when and how

to assess students. Resources include embeddedassessment tasks with detailed rubrics and sample studentwork; skill quizzes; final projects; pre-assessment tasks;and suggestions for using portfolios.

MathScape teacher materials support teachers in using thematerials flexibly to meet the needs of their students. TheTeacher's Guides include detailed lesson plans;reproductions of the student pages; sample student work;homework options; reproducibles; and From theClassroom comments and tips from teachers who havetaught the materials. Each guide also provides MathBackground pages where teachers can find informationabout the mathematics of the unit.

Calculators are used throughout the curriculum. Eachunit identifies Technology Options, appropriate juncturesfor the use of spreadsheets and other optional computersoftware programs. Suggestions for using graphingcalculators are provided throughout the eighth gradeunits.

Each of the MathScape units consists of a Teacher's Guideand a non-consumable student book. The student booksare also available as a hardcover consolidated text (one pergrade). The units are supplemented by a skills resourcebook called Hot Words, Hot Topics (one student book andone teacher's book per grade level). Most of the unitsinvolve the use of manipulative materials.

Publisher ContactBernard TurnerProduct Manager, Core ProductsCreative Publications2 Prudential Plaza, Suite 1175Chicago, IL 60601phone: (312) 540-4510fax: (312) 540-4581e-mail: [email protected]

Developer/Implementation CenterSusan JanssenAssociate Project DirectorMathScape/STM Curriculum CenterEducation Development Center, Inc.55 Chapel StreetNewton, MA 02458-1060phone: (617) 969-7100, ext. 2553fax: (617) 969-1580e-mail: [email protected]


Student MaterialsStudent Editions of each unit.

Grade 6: 7 modular unitsGrade 7: 7 modular unitsGrade 8: 7 modular units

OR

Bound Student Text: 1 per grade

Hot Words, Hot 7bpics Math User's Handbookfor Students

Grade 6: 1 bookGrade 7: 1 bookGrade 8: 1 book


Current Availability of Curriculum MaterialsGrades 6-8 materials are all available.

Teacher Materials

Teacher Editions of each unit.Grade 6: 7 modular unitsGrade 7: 7 modular unitsGrade 8: 7 modular units

Hot Words, Hot Topics Math User's Handbookfor 7eachers

Grade 6: 1 bookGrade 7 : 1 bookGrade 8: 1 book

Manipulative Kits available for each module

Impact Data Compiled to DateResearch Done During Field-Thsting of the MathScape Curriculum. Available from the MathScape/STMCurriculum Center at EDC.

Web Sites

At Creative Publications: http://www.creativepublications.com/mathScape/mathscape_frameSet.html

At Education Development Center: http://www.edc.org/mathscape

BESTCOPYAVAILABLE

January 1999 1 9 /7

M AT H THEMATICS

A middle school curriculum for grades 6-8, developed bythe STEM Project: Six Through Eight Mathematics.

MATH Thematics is a complete three-year mathematicscurriculum for students in grades 6 to 8. This programpresents mathematics in relevant and meaningfulcontexts; each module focuses on a theme that extendsthroughout the module. The goals of this program are tohelp all students develop their abilities to reason logically,apply mathematical skills to real-life activities,communicate mathematically, and feel confident in usingquantitative and spatial information to make decisions.Major mathematical strands of the program include:number concepts, measurement, probability, statistics,algebra, geometry, and discrete mathematics.

The instructional approach engages students in doingmathematics in a variety of settings. It encourages activelearning, and students work both independently and incooperative groups to investigate mathematics and solvereal-life problems. Not all instruction, however, isthrough discovery learning; the program includes directinstruction in concepts and skills as well. The curriculumincludes practice, review, and extension exercises thatreinforce and extend learning.

Assessment is an integral part of the MATH Thematicsmaterials. Each grade-level course begins by introducing

*students to assessment criteria that are used for assessingproblem solving and mathematics communication onopen-ended problems and projects throughout themodules. Other assessment tools include "checkpoint"questions that check students' understanding as they areexploring mathematics; reflection exercises that askstudents to describe, summarize, and extendmathematical ideas; module assessments that ask studentsto reflect on a module as a whole; and portfolio projects

that can be used to assess whether students can applywhat they have learned.

MATH Thematics assumes that students have access to ascientific calculator. Graphing calculators can benefitstudents in the eighth grade modules, but are notrequired.

Each of the three grade levels of MATH Thematicsincludes eight modules; each module requires about fourweeks of instruction. The modules are available as aconsolidated text for each grade level. Accompanyingeach grade level is a Teacher's Resource Package, whichincludes an annotated Teacher's Edition (with warm-upactivities, closure questions, and answers to all studenttext exercises and questions), a Professional DevelopmentHandbook (which outlines program philosophy,assessment, and scoring rubrics) and Teacher's ResourceBooks (which provide module-by-module teachingstrategies, classroom management tips, and blacklinemasters).

Publisher ContactDenise McDowellMath Products Manager, 6-8McDougal Littell1560 Sherman AvenueEvanston, IL 60204phone: (800) 323-5435; Customer Service, Schools


Developer/Implementation CenterRick BillsteinDirectorSTEM Project: Six Through Eight MathematicsDepartment of Mathematical SciencesUniversity of MontanaMissoula, MT 59812phone: (406) 243-2603fax: (406) 243-2674e-mail: [email protected]


Student Materials

Pupil's EditionsBook 1: Grade 6Book 2: Grade 7Book 3: Grade 8

Student Manipulative Kits


Real MathReal Careers laserdisk series (6 disks).

Teacher Materials

Teacher's Resource Packages (each grade level)Annotated Teacher EditionResource Book, Modules 1 & 2Resource Book, Modules 3 & 4Resource Book, Modules 5 & 6Resource Book, Modules 7 & 8Professional Development Handbook

Teacher Overhead Manipulatives

Glossary for each book available in Spanish.

Current Availability of Curriculum MaterialsPupil's Editions of all books are currently available.

Teacher's Editions and Resource Packages for all grades are currently available.


Field test and materials evaluation results available from McDougal Littell.

Web Sites

At McDougal Littell: http://www.mlmath.com

At the University of Montana: http://www.math.unmedu/-stem

January 1999 2 I 19

MIDDLE-SCHOOL MATHEMATICS THROUGH APPLICATIONS

A middle school curriculum for grades 6-8, developed by theMiddle-school Mathematics Through Applications Project

Middle-school Mathematics through Applications (MMAP)is a flexible middle-school mathematics curriculum whichintegrates computer technology and interdisciplinarylinks. The MMAP program is composed of three kinds ofunits: Applications, Extensions, and Investigations.Applications units form the core of the curriculum. Eachunit places students in an extended role play based onreal-life work and problem solving. In the role play,students "work" for a design company, creating codes,floor plans, maps, or biological models. Mathematicalconcepts and skills are integrated and developed along theway; the design context provides grounded reasons andresources for developing the mathematics. Applicationsunits integrate mathematical software developed for usewith MMAP; the developers estimate that 40-60 percentof students' work in these units requires the use ofcomputers.

Extensions units build directly on the mathematicalinsights and skills students have developed within theApplications units. They introduce students to standardmathematical notations associated with concepts such asproportion, help students develop specific skills such asmanipulating algebraic expressions, and deepen their

*conceptual understanding.

Investigations units introduce other mathematicalconcepts, within more fanciful contexts or from a puremathematics point of view. In these units, students learnsuch things as geometric vocabulary in the context ofquilting or methods of proof while exploringrelationships between even and odd integers.Investigations units emphasize mathematics concepts,common notations, and vocabulary, along with

mathematical practices such as making conjectures,coming up with counter-examples, and writing proofs.

A variety of assessment tools are provided and techniquesare recommended for incorporating assessment into theactivities of each unit. Assessment pages exist at thebeginning of each section within the units. Additionalresources include an Assessment Sampler that describesMMAP's assessment philosophy and provides resourcepages, and an Assessment Supplement that offers acollection of tips for using assessment in MMAP units.

The MMAP program requires student access to a set ofmathematical tools that includes calculators andmeasuring tools. MMAP software runs on any Macintoshcomputer that has a hard drive and uses System 7.0 ornewer. A word processing and spreadsheet program arerecommended for use with the program as well.

MMAP units combine to create a comprehensiveprogram for grades 6 through 8. Units may be usedflexibly or integrated with other instructional materials tocustomize a program to meet local needs.

Publisher ContactCommercial publisher to be announced.

Developer/Implementation CenterJennifer KnudsenDirector, MMAP Implementation CenterThe Institute for Research on Learning66 Willow PlaceMenlo Park, CA 94025phone: (650) 687-7918fax: (650) 687-7957e-mail: [email protected]

202 2

K-12 Mathematics Curriculum Center

Student MaterialsReproducible handouts and software containedwithin the Teacher Editions.


A Guide to MMAP, October 1997.

Teacher Materials

Applications Units: Teacher's Guides with software.Programs include: Architech, Habitech, Mapper,CodingToolbox

Grades 6/7: 7 Applications UnitsGrades 7/8: 6 Applications Units

Extensions for each Applications UnitGrades 6/7: 7 ExtensionsGrades 7/8: 10 Extensions

Investigations UnitsGrades 6/7: 6 InvestigationsGrades 7/8: 4 Investigations

Current Availability of Curriculum MaterialsDrafts of materials are available from the MMAP Implementation Center.

Impact Data Compiled To Date

Some impact data available upon request from the Institute for Research on Learning.

Web Site

At the Institute for Research on Learning: http://www.irl.org/mmap/

BESTCOPY AVAILABLE

January 1999 212 3

CONTEMPORARY MATHEMATICS IN CONTEXT

A high school curriculum for grades 9-12, developed bythe Core-Plus Mathematics Project

Contemporary Mathematics in Context is a four-year,integrated mathematics program that includes a three-year core curriculum for all students, plus a flexiblefourth-year course that continues to prepare students forcollege mathematics. The curriculum builds on the themeof mathematics as sense making.

Each year-long course of the curriculum features fourinterwoven strands: algebra and functions, geometry andtrigonometry, statistics and probability, and discretemathematics. The program emphasizes mathematicalmodeling and modeling concepts, including datacollection, representation, interpretation, prediction, andsimulation. The modeling perspective permits students toexperience mathematics as a means of making sense ofdata and problems through the investigation of real-lifecontexts. Graphics calculators are an integral tool used bystudents in every unit.

Lessons are organized in a four-phase cycle: Launcha whole-class discussion establishing a context for thelesson; Exploresmall-group investigation of morefocused real-world problems; Share and Summarizea whole-class discussion enabling groups to summarizeresults of investigations and construct a sharedunderstanding of important concepts, methods andapproaches; and Applya task to be completedindividually to assess understandings gained in the lesson.

In addition to the classroom investigations, the programprovides sets of MORE tasks, which engage students inModeling with, Organizing, Reflecting on, andExtending their mathematical knowledge. These tasks areintended for individual work outside of class. Theprogram also includes opportunities to assess studentlearning in whole-group "Checkpoint" discussions, and"On Your Own" tasks.

Each course of the curriculum consists of seven units anda capstone experience. Each unit has four to six multi-daylessons which develop major ideas through investigationsof applied problems. The time needed to complete unitsvaries from four to six weeks. The final element of eachcourse, the Capstone, is a thematic, two-week, project-oriented activity that enables students to synthesize andapply the important mathematical concepts and methodsdeveloped in the course.

Student materials for Courses 1, 2, and 3 of thecurriculum are available in two parts, A and B, both inhardcover. (The fourth year course is still underdevelopment.) For each course of the publishedcurriculum, there are also two hardcover Teacher'sGuides, in parts A and B, that correspond to the students'texts. The Teacher's Guides contain fiill-size student textpages with facing pages containing answers, suggestedstudent responses, points for discussion, suggestions forpromoting student investigation and collaborative work,and background information. Also available is anImplementation Guide that supports teachers in usingthe program effectively.

Other teacher support materials include AssessmentResources (which include quizzes, exams, and projects foreach unit) and Teaching Resources (which includeblackline masters that support classroom activities) foreach course. Software developed for the TI-82, TI-83,and TI-92 graphing calculators supports studentinvestigations, and is required for some activities.

*Publisher ContactGreg McRillProduct ManagerEveryday Learning Corporation2 Prudential Plaza, Suite 1200Chicago, IL 60601phone: (800) 382-7670


Developer/Implementation CenterBeth RitsemaProfessional Development CoordinatorCore-Plus Mathematics ProjectDepartment of Mathematics and StatisticsWestern Michigan UniversityKalamazoo, MI 49008phone:fax:

e-mail:

(616) 387-4562(616) [email protected]

22 2 4 K-12 Mathematics Curriculum Center

Student MaterialsStudent Text, Courses 1-3

Part A (Units 1-4)Part B (Units 5-7 plus Capstone)

Teacher Materials

Teacher's Guide, Courses 1-3, Parts A & B

Teaching Resources, Courses 1-3, Parts A & B

Assessment Resources, Courses 1-3, Parts A & B

Calculator Software and Guide, Courses 1-3


Implementing the Core-Plus Mathematics Curriculum

A Balanced Approach to Mathematics Education

The Core-Plus Mathematics Project Contemporary Mathematics in Context: An Overview. A 30-minute video.

Current Availability of Curriculum MaterialsCourses 1-3 are currently available.

Course 4 is in development and undergoing field tests.

Impact Data Compiled to DateAssessments of Students' Mathematical Performance: A Core-Plus Mathematics Project Field Test ProgressReport. EI . Schoen & S. Ziebarth, January 1998. Available from the Core-Plus Mathematics Project.

Mathematical Achievement on Standardized Tests: A Core-Plus Mathematics Project Field 7.st ProgressReport. H. Schoen & S. Ziebarth, January 1998. Available from the Core-Plus Mathematics Project.

An Emerging Profile of the Mathematical Achievement of Students in the Core-Plus Mathematics Project. H. Schoen,C. Hirsch & S. Ziebarth, April 1998. Available from the Core-Plus Mathematics Project.

Contemporary Mathematics in Context Field 7i,st Results. Available from Everyday Learning Corporation.

Contemporary Mathematics in Context Student Achievement Results, Volume I. Available from Everyday LearningCorporation.

Web Sites

At Everyday Learning Corporation: http://www.everydaylearning.com

At Western Michigan University: http://www.wmich.edu/cpmp

January 1999 23

2 5

INTERACTIVE MATHEMATICS PROGRAM

A high school curriculum for grades 9-12, developed bythe Interactive Mathematics Program (IMP).

The Interactive Mathematics Program (IMP) is a four-yearcurriculum of problem-based, integrated mathematicsdesigned to replace the traditional Algebra I, Geometry,Algebra II/Trigonometry, Pre-Calculus sequence. IMPintegrates traditional mathematics with additional topicsrecommended by the NCTM Curriculum and EvaluationStandards, such as statistics, probability, discretemathematics, and matrix algebra. By combiningtraditional concepts and newer material in an integratedsetting, and by placing these ideas in meaningfulcontexts, the IMP curriculum meets the needs of bothcollege-bound students and those headed directly into theworkforce.

Most units begin with a central problem that studentsexplore over the course of six to eight weeks. Some ofthese central problems are based on practical, real-worldsituations, such as maximizing profits for a business orstudying population growth. Others are more fanciful,involving situations like a pennant race or a circus act. Asstudents work through smaller problems in the unit, theydevelop the mathematical concepts and techniques theyneed to solve the central problem. A particular unit maycombine several branches of mathematics so that studentssee how important ideas are related to one another.

There are three main types of student assignments inIMP: in-class activities, daily homework, and Problems ofthe Week (POWs). Students examine new conceptsthrough in-class activities, working in groups andindividually. Homework assignments reinforce andextend concepts introduced in class. POWs are open-ended problems, often mathematical classics, that cannotbe solved easily in a very short period of time. In POW

write-ups, students describe how they worked on theproblem and explain their reasoning.

Each unit also includes a collection of supplementalproblems, both to reinforce concepts and skills and toextend ideas beyond the basic curriculum. Theseproblems provide a way to tailor the curriculum to meetthe needs of individual students.

IMP requires the use of a graphing calculator duringclass. There are many IMP activities in which computerprograms could provide valuable enrichment, but thereare no activities that require computer use.

Teachers assess individual students in IMP using a varietyof tools, including daily homework assignments, oralpresentations, contributions to the group or whole-classdiscussions, Problems of the Week, in-class and take-home unit assessments, end-of-semester examinations,self-assessments, and portfolios.

Student materials for IMP are available in one hardcovertextbook for each of the four years of the program.Accompanying Teacher's Guides are published insoftcover for each of the units in a grade level. Additionalteacher support materials include Introduction andImplementation Strategies for the Interactive MathematicsProgram; the 7eaching Handbook for IMP: A Teacher-to-Teacher Guide-, Baker's ChoiceA Unit of High SchoolMathematics; It's All Write: A Writing Supplement for HighSchool Mathematics; and the Guide to Using TI Calculatorswith IMP.

Publisher ContactKelvin Taylor, National Sales ManagerKey Curriculum PressP.O. Box 2304Berkeley, CA 94702phone: (800) 338-7638fax: (800) 541-2442e-mail: [email protected]

Developer/Implementation CenterLynne Alper, Dan Fendel, Sherry Fraser, Diane Resek,Directorsphone: (415) 332-3328Janice Bussey, Outreach Coordinatorphone: (888) 628-4467Interactive Mathematics ProgramP.O. Box 2891Sausalito, CA 94966fax: (415) 332-3381e-mail: [email protected]

24

2K-12 Mathematics Curriculum Center


Student Texts, Grades 9-12Year 1, Grade 9Year 2, Grade 10Year 3, Grade 11Year 4, Grade 12

Modular Teacher's Guides, Grades 9-125 units, Year 15 units, Year 25 units, Year 35 units, Year 4

Other Support MaterialsIntroduction and Implementation Strategies for the Interactive Mathematics Program: A Guide for Teacher-Leaders and Administrators

Baker's ChoiceA Unit of High School Mathematics. Student Text, Teacher's Guide and student blacklinemasters for this three-week unit.

Itc All Write: A Writing Supplement for High School Mathematics Classes. Teacher's Guide and studentblackline masters for this one-week unit.

Teaching Handbook for IMP: A Teacher-to-Teacher Guide

Guide to Using TI Calculators with IMP Year 1, Guide to UsingTI Calculators with IMP Year 2, and Guide to Using TICalculators with IMP Year 3

Years 1 and 2 Student Texts in Spanish are currently available from IMP.

Years 1 and 2 Student Texts in French are currently available from Cheneliere/McGraw Hill, 7001 bouf Saint-Lauren, Montreal, (Quebec), Canada H2S 3E3.

Years 1 and 2 Student Texts in Hawaiian are currently available from Kathy Nishimura, Office of InstructionalServices, 189 Lunalilo Home Road, 2nd floor, Honolulu, HI 96825.

Current Availability of Curriculum MaterialsYears 1-3 (Grades 9-11) are currently available.

Year 4 (Grade 12) is currently available in pre-publication draft and will be published in August 1999.

Guide to Using TI Calculators with IMP Year 4 will be published in August 1999.

Impact Data Compiled to DateEvaluation Update, No. 1, Spring 1995 available from the Interactive Mathematics Program.

Evaluation Update, No. 2, Fall /996available from the Interactive Mathematics Program.

Evaluation Update, No. 3, Fall 1997 available from the Interactive Mathematics Program.

Web Sites

At Key Curriculum Press: http://www.keypress.com

At Interactive Mathematics Program: http://www.mathimp.org

January 19992 7

25

M AT H CONNECTION&A SECONDARY MATHEMATICS CORE CURRICULUM

Three years of high school mathematics curriculum.

The vision of MATH Connections is that all students canlearn mathematics. MATH Connections is a completethree-year high school curriculum for all students that hasas its mission the conceptual development of the learner.Using the NCTM Standards as a guideline and replacingtraditional Algebra I, Geometry, Algebra II, MATHConnections blends the mathematics of algebra, geometry,trigonometry, probability, statistics, and discretemathematics. As its name suggests, the curriculumbridges connections of all sorts: those between differentmathematical areas; mathematics and science;mathematics and other subject areas; and mathematicsand the real world of people, business and everyday life.

MATH Connections is concept driven. That is, conceptsare introduced in the context of real world applications,problems and projects. Rather than teaching a singletopic, MATH Connections uses broader concepts to linktopics together in a unified, interconnected approach.

MATH Connections is designed to provide students withexperiences that excite their curiosity, stimulate theirimagination, and challenge their skills. The pedagogicalapproach of MATH Connections is flexible. It is intendedto meet the needs of all students by making a concertedeffort to accommodate a variety of student learning stylesand levels. The materials support a combination ofteacher-student and student-student interaction, handson investigations with prompts for class discussion,individual activities and student writing and justificationof results.

Student assessment in MATH Connections includeswritten, oral, and demonstration formats that assess

higher order thinking skills. In this way, studentsdemonstrate their mathematical skills, their approach tonon-routine, real world problems, and theirunderstanding of mathematics concepts and how theyrelate to one another.

The curriculum integrates technology through the use ofgraphing calculators and computers, which students useto make conjectures; validate findings; and investigateconcepts, problems, and projects in greater depth. Theprogram encourages students to use these tools whenappropriate. Discussions of how the tools work, why theywork, and whether or not they are appropriate for aparticular task occur throughout the course.

The Student Edition is published in six half-year,hardbound textbooks. The Teacher Edition is organizedin half-year sections in binders to accommodate differentteaching styles and traditional and block scheduling. TheTeacher Resource Pack includes the Teacher Edition, areplica of the Student Edition, a Teacher Commentarywhich is correlated to the Teacher Edition and providesprofessional development; Blackline Masters for use asoverheads or classroom handouts; and a full set of FormA MATH Connections Student Assessments with SolutionKeys and Scoring Guides.

Publisher ContactLaurie KreindlerIt's About Time, Inc., Publisher84 Business Park Drive, Suite 307Armonk, NY 10504phone: (888) 698-TIME (8463)fax: (914) 273-2227e-mail: [email protected]

Developer/Implementation CenterJune Ellis, Ph.D., Principal InvestigatorMATH Connections Implementation CenterMathconx, LLC750 Old Main Street, Suite 303Rocky Hill, CT 06067-1567phone: (860) 721-7010fax: (860) 721-7026e-mail: [email protected]

26

2 8K-12 Mathematics Curriculum Center


Student Edition (3 years)

6 half-year hardbound color textbooks

Teacher Resource Pack (3 years)

Teacher Edition, replica of the Student Edition

(6 half-year texts in binders)

Teacher Commentary, correlated to theTeacher Edition

Black line Masters

Form A MATH Connections Student Assess-ments with Solution Keys and Scoring Guides

Other Support MaterialsForm B MATH Connections Student Assessments with Solution Keys and Scoring Guides

Extensions. Correlated to the text, for students interested in exploring topics in greater depth and breadth.

Supplementary materials for reinforcement learning for students to improve their proficiency as well as toaccommodate students who have been absent or who are entering the program midstream.

The User-Friendly Booklet Introducing MATH Connections to Students and Their Families

Videos for teachers and administrators

Current Availability of Curriculum MaterialsStudent Textbooks and Teacher Resource Packs for all grades are now available from It's About Time, Inc.

Introductory Pack, available from the MATH Connections Implementation Center:Video (11 minutes of classes in action)Sample Lessons and AssessmentsCareers, Professions & Real Life Applications in MATH Connections Problems, Explorations, Simulations &

Situations Fact SheetNCTM Standards (9-12) Exemplified in MATH Connections

Impact Data Compiled to DateSee "Evaluation Summary" at the MATH Connections web site for student results of standardized testsincluding the Scholastic Aptitude Test (SAT), student confidence in learning mathematics, student perception ofthe usefulness of mathematics, and external evaluation of cognitive discourse in the classroom.

"Evidence of Effectiveness and Success" available from the MATH Connections Implementation Center.Data showing the success of MATH Connections students in college and university attendance. Furtherinformation is available from the MATH Connections Implementation Center.

Data showing that MATH Connections has been recognized by the NCAA for sports eligibility requirements.Further information is available from the MATH Connections Implementation Center.

Web Site

At the MATH Connections Implementation Center: http://www.mathconnections.com

January 1999

2 9BESTCOPYAVAILABLE

27

MATHEMATICS: MODELING OUR WORLD

A high school curriculum for grades 9-11, developed by theConsortium for Mathematics and Its Applications (COMAP), Inc.

Mathematics: Modeling Our World is an integrated corecurriculum for high school that is based on the premisethat students learn best when they are actively involved inthe process. In this program students do not first learnmathematics and then apply what they've learned. Rather,important questions about the real world come first.Students analyze situations and apply the mathematicalconcepts needed to solve problems. Contextual questionsdrive the mathematics. In each unit, students build, test,and present models that describe a real-world situation orproblem, such as deciding where to build a fire station.Mathematical modeling is a central focus throughout thecurriculum.

Each course covers the mathematical content found inthe NCTM Standards. Each of the first three courses ofMathematics: Modeling Our World contains seven or eightunits. Units are divided into four to seven lessons; eachmay take several days to complete. Each lesson contains aLesson Opener, which provides the context for the lesson;Activities, which students work on in pairs or smallgroups using hands-on mathematical investigation; andIndividual Work, items that review, reinforce, extend,practice, and foreshadow concepts developed in thelesson.

Assessment is an integral part of Mathematics: ModelingOur World. Both Activities and Individual Work offerembedded opportunities to assess student progress. TheTeacher's Resources provide Assessment Problems for usewith each unit, as well as unit projects. A "Wrapping Up"problem set at the end of each unit provides moreopportunities for students to review what they havelearned.

The units of Mathematics: Modeling Our World beginwith a real situation or problem to be solved during thecourse of the unit. A short video segment may be used tointroduce the theme or problem. Students use bothgraphing calculators and computers extensivelythroughout the curriculum to assist in carrying outcomputations of real problems and to enhance conceptdevelopment. While it is strongly recommended thatstudents use computers with this curriculum, material isprovided to teach the lessons without computers as well.However, use of the graphing calculator is essentialthroughout the program.

Student materials for Mathematics: Modeling Our Worldare available in three hardcover texts, one each forCourses 1, 2, and 3. Teachers materials include, for eachcourse, an Annotated Teacher's Edition, a SolutionsManual, and Teacher's Resources, which containsadditional teaching suggestions, background readings,reproducible handouts, assessment problems,supplemental activities, and transparencies. Othermaterials include a video with segments for each unit anda CD-ROM with calculator and computer programswritten specifically for Mathematics: Modeling Our World.

Course 4, geared for grade 12, is currently underdevelopment and is being field-tested.

Publisher Contact*Customer SupportSouth-Western Educational PublishingAn International Thomson Publishing Company5101 Madison RoadCincinnati, OH 45227-9985phone: (800) 824-5179fax: (800) 539-1623

Developer/Implementation CenterLinda VaheyMarketing Director, Special ProjectsConsortium for Mathematics and Its Applications(COMAP) Inc.57 Bedford Street, Suite 210Lexington, MA 02420phone: (800) 772-6627


283 0

K-12 Mathematics Curriculum Center

Student MaterialsStudent Editions, Courses 1-3 (Grades 9-11)


Current Availability of Curriculum Materials

Courses 1-3 are currently available.

Course 4 (Grade 12) is under development.


Teacher Materials

Included for each course:

Annotated Teacher's Edition

Teacher's Resources: a binder containing a teacher'sguide with additional notes and background reading,Supplemental Activities, Assessment Problems,Handouts, and Transparencies.

Solutions Manual

Video with a documentary for each unit

CD-ROM with programs for graphing calculators andcomputers

Web Sites

At South-Western Educational Publishing: http://www.swep.com

At COMAP: http://www.comap.com

January 1999 31 29

SIMMS INTEGRATED MATHEMATICS

A high school curriculum for grades 9-12, developed by the SystemicInitiative for Montana Mathematics and Science (SIMMS).

SIMMS Integrated Mathematics (SIMMS IM) is acomplete 9-12 mathematics curriculum that uses real-world contexts in an integrated approach for all students.It is designed to replace all secondary mathematicscourses, with the possible exception of advancedplacement courses. SIMMS IM considers mathematicaltopics in a different order than in a traditionalcurriculum, and teaches some mathematical topics notusually encountered at the high school level. Thecurriculum includes work in algebra, geometry,trigonometry, analysis, statistics, probability, matrices,and data analysis, as well as less traditional high schooltopics such as graph theory, game theory, and chaostheory.

SIMMS IM materials are partitioned into six levels; eachlevel is a year's worth of material. All students take Levels1 and 2 as a core curriculum. In the third and fourthyears, SIMMS IM offers a choice of options. Level 3 issuitable for all students; Level 4 is intended for thoseplanning careers in mathematics or science. Levels 5 and6 offer options for students in the fourth year: Level 5focuses more specifically on applications from businessand the social sciences; Level 6 materials continue thepresentation of mathematics through applied contextswhile embracing a broader mathematical perspective.Each year-long level contains 13-16 modules; eachmodule takes between two and three weeks.

SIMMS IM invites the use of a variety of instructionalformats, including individual and cooperative groupwork, whole-class discussions, and individual and groupprojects. Each module has a central theme, and includes3-4 activities. The activities use hands-on explorations,discussions, and assignments to guide students to a

common understanding of the mathematics within it."Mathematics Notes" sections in the text furnish studentswith definitions, symbolism, and appropriate examples.Additional features of the curriculum include researchprojects and brief sets of problems called "flashbacks" foradditional practice of procedural skills.

Assessment materialsincluding alternative assessmentsthat emphasize writing and logical argumentare anintegral part of the curriculum. Suggested assessmentitems for use with a standard rubric are identified in allteacher editions. Assessment is an integral part of theExploration, Discussion, Assignment, and Flashbacksections of every module. In addition, each module has aSummary Assessment that is open-ended and oftenproject-oriented, as well as a Module Assessment.

Technology is an important part of the SIMMS IMcurriculum. Students must have ready access to thefunctionality of a graphing utility, spreadsheet-likefeatures, geometric visualization, a statistics program, asymbolic manipulator, and a word processor (a graphingcalculator such as the TI-92 has all of these functions). Inaddition, students should have access to a science-interface device (such as Texas Instruments' CBL(Calculator-Based Laboratory)Tm) that allows forelectronic data collection from classroom experiments.

SIMMS IM student materials are available in three non-consumable, softcover volumes for each grade level.Teachers' editions correspond to the student materials:three softcover, non-consumable volumes at each gradelevel.

Publisher Contact*Lynette FelixSIMMS Integrated Mathematics(Simon & Schuster Custom Publishing)401 Linfield HallBozeman, MT 59717-2810phone: (888) 339-0529 (textbook orders)

(800) 693-4060 (curriculum information)fax: (406) 994-3733e-mail: [email protected]

Developer/Implementation CenterGary Bauer, DirectorSIMMS Integrated Mathematics Dissemination401 Linfield HallMontana State University-BozemanBozeman, MT 59717-2810phone: (800) 693-4060fax: (406) 994-3733e-mail: [email protected]

30

3K-12 Mathematics Curriculum Center

Student MaterialsStudent Editions of each volume, Levels 1-6

Level 1 (9th grade): 3 volumesLevel 2 (10th grade): 3 volumesLevel 3 (3rd Year): 3 volumesLevel 4 (3rd Year): 3 volumesLevel 5 (4th Year): 3 volumesLevel 6 (4th Year): 3 volumes

Teacher Materials

Teacher Editions of each volume, Levels 1-6Level 1 (9th grade): 3 volumesLevel 2 (10th grade): 3 volumesLevel 3 (3rd Year): 3 volumesLevel 4 (3rd Year): 3 volumesLevel 5 (4th Year): 3 volumesLevel 6 (4th Year): 3 volumes

Other Support MaterialsSIMMS Resource Guide for Administrators, Counselors and Other Educators

Restructuring Mathematics Assessment: Suggestions from the Classroom

SIMMS in the Classroom. Videotape: Levels 1-6

Curriculum Sampler

Objectives/Content Outline

Content Matrix

Materials List

Current Availability of Curriculum MaterialsAll materials for Levels 1-6, 1st Edition, are currently available.

Impact Data Compiled to DateSIMMS Monograph 4: Assessment Report 1. A collection of articles summarizing research pertaining to SIMMS,available from the SIMMS Implementation Center

SIMMS Monograph 5: Assessment Report II. A collection of articles summarizing research pertaining to SIMMS,available from the SIMMS Implementation Center.

Web Sites

At Simon 86 Schuster Custom Publishing: http://www.simmsnet.com

At Montana State University-Bozeman: http://www.montana.edu/wwwsimms

BEST COPY AVAILABLE

January 19993 3

31

Other Resources and Services available fromthe K-12 Mathematics Curriculum Center

'Print MaterialsCurriculum Connections newsletter

Choosing a Standards-Based Mathematics Curriculum guide to selection and implementation

Curriculum Perspectives from teachers, administrators, and developers

Discussion Cases to provoke reflection on a variety of issues

A series of Issues in Mathematics Education papers

Mathematics education and curriculum reform Reader

Seminars

The K-12 MCC offers the following three seminars about selection and implementation, professionaldevelopment, and building leadership for curricular change:

Considering New Curricula

March '99 April '99 July '99 September '99 December '99 March '00 July '00

Making Your New Curriculum a Success for Teachers

February '99 (pilot) July '99 February '00 July '00

Building Support for Curricular ChangeMay '99 (pilot) July '99 November '99 May '00 July '00

For more information, contact:

Ki McClennan

K-12 Mathematics Curriculum CenterEducation Development Center, Inc.55 Chapel StreetNewton, MA 02458-1060

phone: (800) 332-2429fax: (617) 969-1527e-mail: [email protected]

Web site: http://www.edc.org/mcc

BESTCOPY AVAILABLE 3 4

Everyday Mathematics (K-6)

Investigations in Number, Data and Space (K-5)

Math Trailblazers (TIMS) (K-5)

Connected Mathematics (6-8)

Mathematics in Context (5-8)

MathScape: Seeing and Thinking Mathematically (6-8)

MATHThematics (STEM) (6-8)

Middle-school Mathematics through Applications Project II (6-8)

Contemporary Mathematics in Context(Core-Plus Mathematics Project) (9-12)

Interactive Mathematics Program (IMP) (9-12)

MATH Connections:A Secondary Mathematics Core Curriculum (9-11)

Mathematics: Modeling Our World (ARISE) (9-11)

SIMMS Integrated Mathematics:A Modeling Approach Using Technology (9-12)

111:1Nalogikuill4K-12 Mathematics Curriculum CenterEducation Development Center, Inc.

(800) 332-2429http://www.edc.org/mcc

e-mail: [email protected]

05/28/99 11:15 /T617 969 1527

05/27/1999 09:46 6142920263

EDC LITERIC CSMEE

U.S. Department of EducationOffice of Educabonal Research and Improvement (OERI)

National Library of Education (NLE)Educational Resources Information Center (ERIC)

REPRODUCTION RELEASE

Q002/002PAGE 83

, ERIC I

(Specific Document)

DOCUMENT IDENTIFICATION:

CwMCsuluirn, Swramosie_s Wier-v)Authorm: 11/4ko)-ine-iu N-rticuAuxn Con..61.

C Publication Date:4trixrate Sourcerietin '12A) ei vY1e44 CeAer, bite- Scutugunj cl,c1a1

II. REPRODUCTION RELEASE:In on:Ier to dissamlnete es widely as possible timely and eIgnificant materials of interest to the educadanal community, document& sitihouncad in themonthly abstract *mud of the ERIC aymern, Resources hi Education (RIE), ere usually made available to users in microfiche. reproducad paper asp,and electronic media, and sold through the ERIC Document Reproduction Service (MRS). Credit is gtven to the source of each document, and, It

rePreeeeflon reieeoe je granted, one Of the Mewing notelet ia ofiked to the document_

0T:emission is granted to nwtoduce and disseminate the Identifieddocument, please CHECK ONE Of the following three optima and sign at the bottomof the Me.

The wale sassier shown below aitsMal to all Laser, claimants

PERMISSION TO REPRODUCE ANDDISSEMINATE THIS MATERIAL HAS

BEEN GRANTED EY

VD

secTO THE EDUCATIONAL RESOURCES

INFORMATION CENTER (ERIC)1..

The nalrade iiaker ahapn as be The swept* Oder shom bete. eel bedbed te en Lewd 2A dectenento Wind in ell Laim aosaiont

PERMISSION TO REPRODUCE ANDDISSEMINATE THIS MATERIAL IN

MICROFICHE, AND IN ELECTRONIC MEDIAFOR ERIC COLLECTION SUBSCRIBERS ONLY.

HAS BEEN GRANTED BY

\eP

TO THE EDUCATIONAL RESOURCES:NFORMATION CENTER (ERIC)

PERMISSION TO REPROOLIOS ANDDISSEMINATE THIS MATERIAL IN

MICROFICHE ONLY HAS BEEN GRANTED BY

2A 2Leeel I Level 2A

Meek ewe Ihr Leael 1 edam samIttlho notosocilenali trissaninaftn In ntltadWm at cane ERIC enalloni

media (as. alackalc) sad pips. cm,.

Signhere,please

'3 THE EDUCATIONAL RESOURCES:NFORMATION CENTER (ERIC)

Level 20

Chat:Rhea For Levet 2A rolatss, woman* remoduallanend diebeneletellon in wenn:inch. am in elemburoc memo

for ERIC archives collodion suheatase only

on.* nano rw Loud 20 naease. swathingrasnaluaSen and ellommInglon hi tnismilithe city

Deaenents Me be metes's! ea Indinebee ueided raroctuasti am* tenni*ft ShethIssiell te Wham= ta arintai, ha no Dem 13 cheeks!. danneenfteivAll be processesi ei Laval

111hereby met to the Educational Resources Intimation Center (ERIC) nonexctushre pannission to reproduce end disseminate this doorman

as Indicated above. Reproductidn hem the ERIC microfiche or electronic merle by persons other than ERIC employees arstile systemocintiectors roe/antePeffnission born the craVtight holder. Exception is made for nonprofit raprodudien by librariesend other saMos agendasto satisfy information needs of educators M response to discrete Inquiries.

eric - education resources information centernational grade-level implementation centers...

Documents