ED 403 126

TITLE

INSTITUTIONSPONS AGENCYPUB DATENOTEAVAILABLE FROM

PUB TYPE

EDRS PRICEDESCRIPTORS

IDENTIFIERS

ABSTRACT

DOCUMENT RESUME

SE 059 454

The University of Chicago School Mathematics Project,Autumn 1996.Chicago Univ., IL. School Mathematics Project.Amoco Foundation, Inc., Chicago, IL.9621pUniversity of Chicago School Mathematics Project,5835 S. Kimbark Avenue, Chicago, IL 60637.Reports Descriptive (141)

MF01/PC01 Plus Postage.Academic Ability; *Educational Resources; ElementarySecondary Education; Instructional Materials;*Mathematics Curriculum; *Professional Development;*Relevance (Education); Student Evaluation;Telecommunications*University of Chicago School Mathematics Project

This document discusses a variety of aspects of theUniversity of Chicago School Mathematics Project (UCSMP). Extensivehistorical background of the project, including key personnel andfunding sources at various stages, is provided. The goals of theproject are to upgrade the mathematics experience of the averagestudent, connect the real world with the mathematics curriculum, andgarner international support for UCSMP. This report containsdescriptions of the scope of the project; the UCSMP Online Service;the resource development component; the elementary and secondarycomponents including materials development, teacher development, andevaluation; and a listing of available materials related to thedifferent aspects of the project. Resources are also noted throughoutthe report that are appropriate for elementary and secondarymathematics instruction. (DDR)

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

Reproductions supplied by EDRS are the best that can be madefrom the original document.

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

UCSMP

PERMISSION TO REPRODUCE ANDDISSEMINATE THIS MATERIAL

HAS BEEN GRANTED BY

TO THE EDUCATIONAL RESOURCESINFORMATION CENTER (ERIC)

S

BEST COPY AVAILABLE

2

S

111

U S DEPARTMENT OF EDUCATIONOffice or Edo al Researcn and improvement

EDUCATIONAL RESOURCES INFORMATIONCENTER (ERIC)

This document nas oeen reproduCed ascoved Isom the Person or oroanaetion

Or mating itO Minor cnanoes nave been made 10 improve

reproduction Duality

Penni! Of wow or opruons1111O on ma 42OCurnent do not necessarily reptesem officialOERI position or polCY

UCSMP

ContentsThe University of Chicago School Mathematics Project

Overview 3

UCSMP Online 6

Resource Development Component 7

Elementary Component

Materials Development 9

Teacher Development 11

Evaluation 13

Secondary Component

Materials Development 14

Teacher Development 16

Evaluation 17

Available Materials 19

UCSMP Funding SourcesAmoco Foundation

supporting all components & project administration

National Science Foundationsupporting Elementary Materials & Teacher Development, Resource Development

Ford Motor Companysupporting Elementary & Secondary Teacher Development

Carnegie Corporation of New Yorksupporting Secondary Evaluation

General Electric Foundationsupporting Secondary Materials Development

GTE Corporationsupporting Primary Materials Development

Citicorp/Citibanksupporting Elementary Teacher Development

Exxon Education Foundationsupporting Elementary Teacher Development

UCSMP Secondary Curriculum Royaltiessupporting Elementary & Secondary Evaluations, Administration

32 THE UNIVERSITY OF CHICAGO SCHOOL MATHEMATICS PROJECT

UCSMP

The University of ChicagoSchool Mathematics ProjectZalman Usiskin, DirectorUCSMP officially began in 1983 when, throughthe work of Izaak Wirszup at the University ofChicago and Keith McHenry of the Amoco Cor-poration, the departments of mathematics andeducation at the University received a generoussix-year grant from the Amoco Foundation for amultifaceted project to improve mathematicseducation for the vast majority of students ingrades K-12.

The project brought together several fac-ulty whose research laid the groundwork forUCSMP. They were:

Paul Sally, UCSMP's first director. Profes-sor Sally had created special summer programsto teach higher mathematics to bright highschool students and had taken a special interestin educating inner-city schoolchildren.

Zalman Usiskin, UCSMP's current directorand co-director of the Secondary Component.Professor Usiskin had researched the teachingof mathematics through real-life applicationsand had developed textbooks for all four yearsof high school incorporating contemporary math-ematical thinking. His work had shown thatmany students enter high school with insuffi-cient knowledge of arithmetic, algebra, and ge-ometry to enable them to succeed.

Max Bell, UCSMP's Elementary Compo-nent director. Professor Bell was a pioneer inthe desire to teach applications of mathematicsand had shown in his research that most childrenentered school with far greater mathematicalknowledge than teachers and textbooks assumed.

Izaak Wirszup, UCSMP's Resource Devel-opment Component director. Professor Wirszuphad collected a vast library of educational mate-rials and research from the Soviet Union andEastern European countries, from which he hadtranslated some of the best non-text materials.This work led him to alert senior governmentofficials about the low standards of mathemat-ics education in the United States compared tothose in other countries.

Later, UCSMP would bring in as directorsof portions of its work Sheila Sconiers, a 7th-and 8th-grade science and mathematics teacherwho had worked with Professor Bell on devel-

4

oping materials for teachers; Larry Hedges, aprofessor of education with expertise in quanti-tative analysis and meta-analysis; Susan Stodolsky,a professor of education with expertise in quali-tative analysis and classroom observation; andSharon Senk, a professor of mathematics educa-tion who, before UCSMP began, had workedwith Professor Usiskin on the development ofgeometry and proof.

UCSMP began by examining the curriculaof other countries for proven ideas and methods,creating textbooks and training programs at boththe elementary and secondary level, and engag-ing in extensive evaluations of its own work.Essential to this work was the participation ofschool administrators and teachers, who wereclosely involved in the planning, writing, andevaluation. Activities during this period weresupported by grants from the first seven fundingsources listed on page 2.

In 1989, recognizing the need for UCSMPto continue its work, the Amoco Foundationgranted funding for five more years. This grant.followed by additional grants from the CarnegieCorporation of New York and the National Sci-ence Foundation (NSF), allowed the project tocomplete its K-3 materials, finish the last twobooks of its secondary curriculum, and continuework on its program for mathematics specialistsin grades 4-6.

In 1992, the project undertook three newmultiyear initiatives: the publication of UCSMPtranslations of foreign textbooks, the extensionof the K-3 curriculum to grades 4-6 with thehelp of a five-year NSF grant, and the develop-ment of a second edition of the 7-12 curriculum.

The past year has seen the publication ofSixth Grade Everyday Mathematics by Every-day Learning Corporation and the second edi-tion of Geometry by Scott Foresman/AddisonWesley. For educators and researchers, theAmerican Mathematical Society (AMS) haspublished UCSMP translations of four Japanesetexts for grades 10 and 11. UCSMP and itspublishers continue to run conferences for teachers.

Work continues on an NSF-funded initia-tive to help implement Everyday Mathematics

OVERVIEW 3

and other innovative curricula by orienting teachersto recent changes in elementary school math-ematics. Work is also being done on the secondeditions of Functions, Statistics, and Trigonom-etry and Precalculus and Discrete Mathematicsto complete the second editions of UCSMP's 7-12 curriculum, an effort supported by royaltiesfrom Scott Foresman/Addison Wesley sales ofthe first editions.

The most fundamental featureof UCSMP is its focus on

upgrading the mathematicsexperience of the average student.

These royalties also generate funds for re-search in mathematics educationfor UCSMPevaluations and other university research onteaching and learning mathematics.

Upgrading the School Mathematics Experiencefor the Average StudentWhy has UCSMP undertaken such a massiveeffort, and why have so many supported us?One reason is that the information explosion andadvances in technology have widened the scopeand multiplied the methods of applied math-ematics. More and more, mathematical ideasare important to the activities and well-being ofthe average citizen.

Improving the current situation requires ef-fort at all levels from kindergarten through col-lege. The typical first-grade student today canexpect to work through the first half of the nextcentury. Yet in many American schools, thisstudent still encounters a variant of the elemen-tary school curriculum designed for the pupil ofa hundred years ago. The secondary curriculumin many schools is likewise out of date, withalmost all of its content oriented towards calcu-lus, ignoring the vast majority of students whoeither will not take calculus or require prepara-tion for other college mathematics as well. Atall levels, curricula need to be modified to takeadvantage of today's widely available technol-ogy.

Teaching in the elementary grades oftenilluminates only one band of the mathematicalspectrum, calculation. Even where studentsreceive other mathematics instruction, the cur-ricula do not expect competence or fully de-

4 OVERVIEW

velop the concepts presented. In contrast, theUCSMP Everyday Mathematics curriculum en-courages teachers and students to explore moreof the spectrum by investigating, informally butsystematically, the basics of data gathering andanalysis, probability, geometry, and algebra,and by taking advantage of the young child'sability and desire to explore and learn.

Most primary teachers, though willing totake students as far as possible with languagearts and reading, feel insecure about stretchingstudents' mathematical experiences. A mathe-matics-rich atmosphere in the classroom is pos-sible, but requires sensitivity to the subject andknowledge of a variety of pedagogical tools.UCSMP's Everyday Teaching for EverydayMathematics gives K-3 teachers breadth of math-ematics knowledge and a full complement ofinstructional strategies. A more extensive pro-gram for grades 4-6 concentrates on upgradingteachers to become mathematics specialists.

A major UCSMP strategy has been to evenout the pace of instruction. In the past, seventh-and eighth-grade mathematics courses offeredonly counterproductive, dulling review. Al-though some might feel the UCSMP secondarycurriculum accelerates students, it is more accu-rate to say that it avoids deceleration. The firstcourse, Transition Mathematics, is designed forstudents at the seventh-grade level mathemati-cally, regardless of age; it consolidates thearithmetic of previous grades while preparingstudents for the next two courses, Algebra andGeometry. The fourth course, Advanced Alge-bra, should be taken by all who graduate highschool. Those who will attend college needFunctions, Statistics, and Trigonometry to pre-pare them for the wide range of mathematicsfound in virtually all college majors today. Pre-calculus and Discrete Mathematics, the finalcourse, covers the content and mathematicalthinking that mathematical and physical sciencemajors and engineers require. With a strength-ened K-5 curriculum, increasing numbers ofstudents are starting this curriculum in sixthgrade and taking advanced placement courses.

The Real World and the MathematicsCurriculumAnother reason for UCSMP's work is to counterthe practice of many existing mathematicscourses, which avoid the real world and useinstead contrived word problems. Real data arevirtually absent.

In contrast, applications are a hallmark ofall UCSMP materials. Project curricula explorethe questions many students ask: "How doesthis relate to the world I know? How canmathematics help me understand my world andwhat people do?" All UCSMP materials viewand teach mathematics as a tool for life. Ele-mentary-level materials explain how teacherscan integrate mathematics with other subjects,sensitizing teachers to seize opportunities forthinking mathematically throughout the schoolday. And at the secondary level, applicationsabound. The reading in lessons highlights theseapplications and introduces students to the his-tory and cultural presence of mathematics.

The real world affects process as well ascontent. In some traditional classrooms, stu-dents learn one way to do a problem and areprohibited from using the tools that might makesolving it easier. On the job, the opposite oc-curs: the goal is to be flexible, to consider manyways to accomplish a task, and to use the besttools available. For this reason, UCSMP iscommitted to using calculators and computertechnology. The calculator and computer affectnot only the approaches to content, but alsocontent itself. Some topics are no longer essen-tial; other topics become accessible to morestudents; still other topics must enter the cur-riculum. Evidence from UCSMP evaluationsand from the research of others shows that theappropriate use of technology enhances stu-dents' mathematical understanding and improvesproblem-solving skills.

Beginning in kindergarten, therefore, weencourage the use of four-function calculatorsto explore mathematical concepts. In the fourththrough sixth grades, separate time for calcula-tor work is no longer necessary, and studentsshould use calculators at their own discretion.By the seventh grade, students need scientificcalculators because common numbers are oftentoo big or too small to be handled by simplercalculators. Beginning with UCSMP Algebra,we recommend the use of graphing calculators.Automatic graphers are required for the last twosecondary courses in the first edition, and thelast three in the second edition.

With adequate software, the computer solvesproblems and allows teachers and students toconsider variations on a problem, to test conjec-tures, to process a large amount of data, and tograph in a variety of modes. Software thatsupports UCSMP's secondary-level courses is

6

available from Scott Foresman/Addison Wesley.

Support Within UCSMPA project of this magnitude requires many ideas.From its inception, UCSMP has scoured theworld for the best ideas available. By surveyingand translating materials from Europe and Ja-pan, UCSMP has broadened its perspective re-garding what can be done in the classroom. Thiswork raises the proficiency levels we think stu-dents can achieve, for it is clear that foreigneducators (and parents) work from the premisethat mathematical success is based more onopportunity to learn, interest, and diligence thanon ability, and that the abilities of most studentsdo not differ enough to warrant a different cur-riculum.

These ideas and beliefs need to be commu-nicated to a broader audience. To this end, theResource Development Component sponsored

From its inception, UCSMPhas scoured the world

for the best ideasavailable.

international conferences in 1985, 1988, and1991. UCSMP translations and a large collec-tion of foreign materials are accessible for scholarlyresearch through the International MathematicsEducation Resource Center. Some translationshave been published (see p. 19).

Other countries look to the United States forleadership. No curriculum in any country isperfect, and changes in mathematics and its useshave occurred worldwide. Our attention to ap-plications and technology has generated greatinterest in the project throughout the world.

As schools and educators look to UCSMPfor leadership, we realize the importance ofself-examination. Evaluation has been integralto UCSMP from the start, providing a regularsource of feedback. UCSMP evaluators use thelatest qualitative and quantitative methods toassess the impact and implementation of projectcurricula. Rather than assume that students andteachers work with the materials uniformly andaccording to project intentions, evaluators ex-amine actual use. Studies focus equally on theunique characteristics of classes, schools, and

OVERVIEW 5

districts, and on broader generalizations aboutthe effectiveness of project programs.

While curriculum materials are being de-veloped, evaluations are formative. They indi-cate how we are doing and where we need to

Since 1983, we have seen many ofour beliefs accepted by the

education community. Still,much work remains to be done.

improve. After the materials are final or near-final, evaluations demonstrate the achievementdifferences educators can expect from UCSMPmaterials and ideas. These evaluations then be-come available to the public.

How Far Have We Come?In 1996-97, we estimate that over three millionstudents are using UCSMP elementary and sec-ondary materials; teachers of many other stu-dents, along with teacher educators, have par-ticipated in UCSMP teacher development pro-grams or attended our conferences.

It was never UCSMP's goal to create anational curriculum. No project should aim forsuch a goal. We need a diversity of ideas toenable us to improve what we do, and the workof everyone involved in schooling is required toimplement change on the necessary scale. Ourgoal continues to be the creation of exemplarymodels and materials that will challenge othersto work to improve school mathematics in gradesK-12.

Change does not occur quickly, but since1983 we have seen many of our beliefs accepted

by the education community. Applications havebecome a feature of most course materials at alllevels from K-12. When we began, we werebold in requiring calculators in our courses;now calculators are a mainstay in most secon-dary school classrooms. That all children canlearn significant amounts of mathematics isnow a widely held belief. And in many schoolsthe curriculum in grades 7 and 8 is no longerconcerned primarily with review; national datasuggest that since 1981 the number of studentstaking a full algebra course in eighth grade hasapproximately doubled.

UCSMP has also influenced national pol-icy. We had a hand in creating the Mathemati-cal Sciences Education Board, and our workinfluenced the standards established by the Na-tional Council of Teachers of Mathematics(NCTM). After some fifteen years during whichcurriculum projects were thought not to influ-ence what goes on in more than a handful ofschools, the existence and wide use of UCSMPmaterials encouraged NSF to fund a dozen multiyearprojects at all levels from K-12 (including ourown 4-6 curriculum efforts). Last year, wehosted the Gateways Conference, bringing to-gether these projects.

Still, much work remains to be done. Thereare very few specialist teachers in elementaryschools, and the mathematical preparation ofmost elementary school teachers is pitifullyweak. Many educators still view the develop-ments of recent years as a fad, and they arewaiting for it to pass. We must be especiallyconcerned about urban public schools because.as before in the history of U.S. education, theyare changing with the times more slowly thansuburban and small-town public, private, andparochial schools. Those who do not keep upnow are likely to be even further behind whenthe next changes come.

UCSMP OnlineGetting in touch with the project...To inquire about project activities or materials, you may contact the UCSMP office directly.

e-mail ucsmp@cicero.uchicago.edu

Getting in touch with other UCSMP users...To subscribe to the UCSMP forum and receive all of its messages

e-mail ucsmp-request@spclists.spc.uchicago.edutype the word subscribe in the body (not the subject line) of your message

To participate in the forum once you are a subscribersend messages to ucsmp@spclists.spc.uchicago.edu

6 OVERVIEW

UCSMP

Resource Development ComponentIzaak Wirszup, DirectorBy translating outstanding school mathemat-ics publications from around the world, theUCSMP Resource Development Componentoffers a first-hand look at expectations, ap-proaches, and methodologies differing fromthose in the United States. Primary schooltexts and workbooks from the former SovietUnion, for example, introduce multidigit num-bers, variables, and equations, together withan abundance of word problems, starting ingrade 1 (our grade 2); by mandate, intuitivegeometry comprises at least 20% of the mathe-matics curriculum in grades 1-5. The spec-tacular achievement of elementary and sec-ondary school students in Japan led UCSMP totranslate a major Japanese textbook series. Inaddition to translating foreign publications,the Resource Development Component moni-tors the latest international literature on mathe-matics education, has organized internationalconferences, and maintains an InternationalMathematics Education Resource Center. WhatUCSMP has learned of mathematics educationand achievement standards in other countrieschallenges Americans to expect more of ourown students and has been a valuable resourcefor developing UCSMP materials.

Translation and Publication of ForeignMathematics Education MaterialsFor the first time in 1992, UCSMP translatedand made available a number of foreign mate-rials, including three Japanese textbooks forgrades 7-9, three Russian textbooks for grades1-3, and two Russian research monographs. Inaddition, as a result of an agreement betweenUCSMP and AMS, in 1996 AMS published thefollowing UCSMP translations as part of its"Mathematical World" series: Mathematics 1:Japanese Grade 10; Mathematics 2: Japa-nese Grade 11; Algebra and Geometry:Japanese Grade 11; and Basic Analysis:Japanese Grade 11. These books (and thetexts for grades 7-9 published by UCSMP) arepart of the leading high school series in Japan,edited by Kunihiko Kodaira, Professor Emeri-tus of Mathematics at the Institute for Ad-vanced Study in Princeton. All the books

8

reflect Japan's sophisticated national curricu-lum. In the future, we hope to publish more ofour translations.

These publications are among more than40 outstanding mathematics textbooks, includingthe entire compulsory curriculum of the formerSoviet Union, translated by the Resource De-velopment Component. The Russian materialscomprise standard textbooks for every gradelevel, as well as supplements for both teachersand students.

Other elementary textbooks and workbooksfrom Bulgaria, Czechoslovakia, Germany, andHungary have been translated. These textsfeature a lively presentation coupled with dif-ferent emphases, such as coding and histo-grams in the Bulgarian books and combina-torics in the Hungarian texts. The component'stranslations are accessible to a wider audiencethrough the International Mathematics Educa-tion Resource Center (see p. 8).

The component translated the 200th issueof Kvant, a popular monthly Soviet mathemat-ics and physics magazine for secondary schoolstudents (grades 6-10). Founded in 1970,Kvant is published by the Russian Academyof Sciences and the Russian Academy of Peda-gogical Sciences. Following UCSMP's trans-lation, in 1989 the National Science TeachersAssociation and Quantum Bureau of the SovietAcademy of Sciences, with the American As-sociation of Physics Teachers and NCTM, be-gan joint publication of a bimonthly English-language version of Kvant, which is entitledQuantum.

Survey of Foreign Mathematics EducationLiteratureIn cooperation with the NSF-funded Survey ofApplied Soviet Research in School Mathemat-ics Education (1985-91), UCSMP has translat-ed and published leading Soviet research in thepsychology and methodology of mathematicseducation, material previously unavailable inthe United States. The first six translations inthe new series "Soviet Studies in MathematicsEducation" were published in 1991 by NCTM;two additional volumes were published in 1992

RESOURCE DEVELOPMENT COMPONENT 7

by UCSMP. These studies continue to haveapplications both within UCSMP and in math-ematics and science curriculum initiatives else-where.

The library of the NSF Survey of RecentEast European Mathematical Literature(1958-83) was available to the project at itsoutset. The collection has since expanded toinclude similar publications from Belgium,France, Germany, Great Britain, Israel, Japan,and Sweden.

The Resource Development Componentcontinues to monitor foreign journals and re-search monographs for significant develop-ments in mathematics education around theworld. Awareness of foreign successes andinnovative approaches is essential if Ameri-can mathematics education is to be competi-tive with the best foreign programs.

International Conferences on MathematicsEducationThe component has organized three UCSMPInternational Conferences on MathematicsEducation. Held in 1985, 1988, and 1991, eachfeatured prominent U.S. and foreign math-ematics educators. NCTM published the pro-ceedings of these conferences in three vol-umes titled Developments in School Mathe-matics Education Around the World.

The first conference focused on applica-tions-oriented curricula and innovative instructionalstrategies, and the second conference on schoolmathematics reform and national standards inFrance, Great Britain, Japan, Sweden, and theUnited States.

The proceedings of the third conferenceappeared in 1993, comprising 31 papers byleading scholars from the United States, Bra-zil, Canada, the People's Republic of China,Denmark, France, Germany, Great Britain, Is-rael, Japan, the Netherlands, and Sweden. Thevolume is organized into four sections discuss-ing the goal of mathematics for all, analyzinghistorical and contemporary reforms, examin-ing current projects and proposals for reform,and making international comparisons.

Proceedings from all three conferences havebeen distributed internationally and are fre-quently cited in the United States and abroad.These volumes represent some of the best thinkingof the mathematics education community world-wide and are a valuable resource for Americanscholars and teachers, especially those inter-

8 RESOURCE DEVELOPMENT COMPONENT

ested in setting world-class school mathemat-ics standards.

International Mathematics EducationResource CenterIn 1988, the Resource Development Compo-nent opened a unique center to house the UCSMPtranslations, to complement the two NSF sur-veys kept elsewhere on campus. The purposeof the three collections is to help U.S. educa-tion leaders further improve mathematics andscience instruction. The International Mathe-matics Education Resource Center serves as apermanent exhibit, clearinghouse, and researchfacility containing original and translated ma-terials related to school mathematics, offeringaccess to a broad range of hard-to-find foreignsources and providing research assistance tovisitors.

Holdings of the three collections includethe following:

Russian-language publication in mathe-matics and science education and educationalpsychology. This collection comprises text-books and workbooks, teacher's manuals,teacher training materials, extracurricularliterature, and research monographs in mathe-matics education and psychology. It wasassembled primarily by the two NSF surveys.Also available are 57 published survey trans-lations of outstanding Soviet materials; addi-tional unpublished translations may also beexamined.

All UCSMP translations of mathematicstextbooks, workbooks, and teacher's manualsfrom the former Soviet Union, Japan, Bul-garia, and Hungary.

Some 500 recent mathematics textbooksfrom Belgium, Bulgaria, Czechoslovakia, Ger-many, France, Great Britain, Hungary, Japan,Poland, and Sweden, selected from the NSFsurvey collection.

The center is continuously expanding itsholdings. It has hosted teachers, scholars, andgraduate students from all over the nation andseveral foreign countries. Those who wish tovisit the center may set up appointments bywriting to the director of the component.

Translations and other documents are availableas indicated on page 19.

9

UCSMP

Elementary CornMax Bell, Director

Materials DevelopmentUCSMP began developing its elementary cur-riculum in the summer of 1985 by working withteachers on the material that became Kinder-garten Everyday Mathematics. By then, theneed for richer curriculum resources had beenmade clear by the results of our studies of K-3children in a broad range of schools. Theseresults clearly showed that the early school mathe-matics experience in the United States ignoredmany of the actual capabilities of young chil-dren. At the same time, reports from interna-tional studies showed U.S. students learningmuch less mathematics in grades K-6 than stu-dents in many other countries.

Principles for Building a New CurriculumResearch with children and teachers led us to anumber of principles for developing the Every-day Mathematics curriculum:

From their own experience children con-struct an understanding of mathematics andacquire knowledge and skills. Teachers andother adults are a very important part of thatexperience.

Children begin school with quite a lot ofknowledge and intuition on which to build. Oneimportant task for the K-6 curriculum is to helpchildren make the gradual transition from intui-tion and concrete operations to abstractions andsymbol processing skills.

Excellent instruction is very important. Itshould provide rich contexts and accommodatea variety of learning styles.

Reforms often fail because they do not takeinto consideration the working lives of teachers.The new curriculum should be practical andmanageable, and it should include suggestionsand procedures that make teachers' lives easier,at least in the long run.

The new curriculum should include practi-cal routines to help build the arithmetic skillsand quick responses that are essential for build-ing number sense, estimation skills, and flexi-bility in a problem-rich environment.

orient

The structure of the UCSMP curriculum is thatof a helix (three-dimensional spiral), with everyimportant concept or skill recurring with varia-tions throughout the curriculum. Hence, ourdevelopment principles include a two-year rule(e.g., anything dealt with seriously in grade 3has been introduced by grade 1) and a five-exposures rule (once introduced, a concept is

Thinking with mathematicsbecomes as natural as

thinking withlanguage.

revisited in at least five different ways, eachwith considerable practice).

Features of Everyday MathematicsThe Everyday Mathematics curriculum estab-lishes a framework for dialogue about mathe-matics between teachers and children and amongchildren themselves. Thinking with mathemat-ics becomes as natural as thinking with lan-guage. Calculators are an integral part of theprogram as an aid to concept development andapplications. Estimation and a variety of strate-gies for problem-solving are emphasized through-out.

The curriculum assumes that each child hasa slate, a calculator, measuring tools, and draw-ing tools, and that each teacher has a classroomset of manipulatives. This requires an initialinvestment, without which genuine reform can-not be successfully implemented.

Kindergarten Everyday MathematicsThe first year of the curriculum supports about100 hours of mathematics activities. The pro-gram emphasizes playful, verbal interactionsand manipulative activities while laying the

10

BEST COPY AVALABLE

ELEMENTARY COMPONENT 9

groundwork for symbolic understanding. Theactivities encompass a variety of mathematicsstrands, including simple and complex count-ing, numeration, operations, measurement, ge-ometry, clock and calendar use, graphs, pat-terns, attributes, and function ideas. Common-life applications are a feature of each strand.Kindergarten Everyday Mathematics includesthese parts:

The Teacher's Manual and Lesson Guidepresents the core of the program. In addition, itsuggests a variety of ongoing daily routines, tobe carried out mostly by the children, whichoffer many opportunities for teaching meaning-ful mathematics. Children keep daily atten-dance and weather records, maintain a job chartand daily schedule, and are involved in a varietyof daily activities, including counting, numera-tion, measurement, geometry, data collectionand display, money, operations, time, patterns,and sequences.

Minute Math offers many suggestions for"fillers" for odd moments of the day. Activitiesparallel and reinforce the Lesson Guide activi-ties. They present much of the problem-solvingstrand of the program as brief verbal problems.

A set of Student Activity Aids providesgames and other playful activities in support ofthe lessons.

Kindergarten Home Links is a series ofbooklets (in English and Spanish) sent homethree times during the year with many sugges-tions for playful activities related to the curricu-lum that parents can do with their children.

Everyday Mathematics for Grades 1-3Materials for grades 1-3 build on and extend theconcepts begun in the preceding grades, withprogressively increasing attention to mental andsymbolic arithmetic, measurement, geometry,the collection and use of data, and the begin-nings of algebra. Strong emphasis is placed onformulating and solving "number stories" withinformation from day-to-day life, science, ge-ography, and other curriculum areas.

Each course provides complete teacher guidesand student materials for a full year of work.Every curriculum package has four parts:

The Teacher's Manual and Lesson Guideincludes these main components: 1) daily les-son plans supporting the program's mathemat-ics strands; 2) a reference on mathematics andthe program for first-time users and for consul-tation by experienced users; 3) explorations

10 ELEMENTARY COMPONENT

and projects that support the mathematics strandsand also include cross-curricula work in sci-ence, health, geography, and other areas; 4)math boxes to provide continuous review ofconcepts and skills: 5) blackline masters forreproducing forms, reports, and letters.

Minute Math Plus provides more of thekinds of activities described for kindergarten.

Student Materials include student jour-nals, Numbers About Me and Numbers In MyWorld booklets, and books of activity sheets.

Home Links provides for follow-up andenrichment activities that may be done withsomeone at home.

An assessment booklet, a bridging module(for schools new to the Everyday Mathematicscurriculum), and a parent handbook are beingdeveloped.

Everyday Mathematics for Grades 4-6Extension of the Everyday Mathematics seriesthrough sixth grade was assured in September1992, when NSF awarded the University ofChicago a five-year grant to support the prepa-ration of materials for grades 4-6. With publi-cation of the sixth-grade materials for the 1996-97 school year, UCSMP has completed its cur-riculum for elementary and secondary schools.

Input from field test teachers has played acrucial role in developing the program for grades4-6. UCSMP field test teachers met regularly fortraining, review of materials, and discussion ofexperiences. Frequent contact was maintainedthrough staff visits and through phone calls, and anInternet link with many field test teachers wasestablished.

As the sequel to Everyday Mathematics forgrades K-3, the 4-6 program builds on theexperience with K-3, which has demonstratedthat students of average ability can succeed in amore ambitious mathematics curriculum andmaintain a high level of interest and enthusiasm,regardless of gender, race, community, or socio-economic status.

The 4-6 curriculum emphasizes "mathemati-cal modeling" of situations from everyday life andother school subjects. It blends mathematical strands(numeration, operations, geometry, measurement,data, and so on) with themes such as science,geography, sports, and architecture. For example,a fourth-grade unit on mammals develops skillsand concepts of measurement, estimation, rates,and data analysis. In a year-long project for thesame grade called World Tour, students "visit" a

variety of countries and collect and analyze infor-mation about them. Instruction blends expositionand discussion, individual and group work, andprojects and investigations.

Calculators, manipulatives, and other tools arean integral part of the curriculum in grades 4-6.UCSMP recommends and provides materials formid-unit, end-of-unit, cumulative, and ongoingassessment. Techniques include observation, port-folios, scoring rubrics, self-assessment, oral-and-slate questioning, and written assessments.

Each grade level includes a Teacher's Manualand Lesson Guide plus a Teacher's ReferenceBook with detailed information on mathematicalcontent, classroom management, and other usefultopics. Student materials include journals, book-lets that provide lesson information, instruction,questions, and a permanent place to record conjec-tures and results; MathLinks, follow-up activitiesto be done in the classroom or at home; and areference book and student record book for each

of the year-long projects.Our goal is that at least half of the students

who complete Everyday Mathematics 4-6 beprepared to begin an algebra course in seventhgrade, such as the second edition of UCSMPAlgebra. The remainder will be well preparedfor a course such as Transition Mathematics.

Everyday Learning CorporationIn 1989, Everyday Learning Corporation (ELC)in Evanston, Illinois, undertook commercialpublication of Everyday Mathematics andMathTools for Teachers. To date, some 600,000students across the country are using the K-5materials already on the market.

ELC provides inservice training for users ofEveryday Mathematics. Seven conferences heldin the summer of 1995 provided inservice forabout 2,400 people.

ELC also provides financial support for avariety of UCSMP development activities.

Teacher Development Sheila Sconiers, Director

With over 37 million students and 1.5 millionteachers in U.S. elementary schools this year, staffdevelopment programs must expand beyond tradi-tional limits. Addressing this "scale problem" forelementary mathematics education reform is a prin-cipal concern of UCSMP.

Over the past ten years, UCSMP has takenseveral approaches to this problem. One is apackage of monthly workshops, first developedduring the late 1980s and early 1990s, that enablesclassroom teachers to conduct staff developmentworkshops for their colleagues and reduces theneed for outside experts. Another approach is theUCSMP Mathematics Specialist Program, whichprepares specialist teachers for mathematics ingrades 4-6 and thus reduces the number of teachersneeding staff development. A third approach to thescale problem is through teacher preparation pro-grams. Over the years, UCSMP has surveyed theseprograms, sponsored conferences, and issued re-ports. Together, the Mathematics Specialist Pro-gram and the workshops provide plausible near-term solutions to the scale problem, while theinvestigations into teacher preparation programsseek answers for the longer term.

1.2

To date, UCSMP efforts have been aimed atteachers working with any elementary mathemat-ics curriculum. Now, with the completion andwidespread implementation of the EverydayMathematics curriculum, UCSMP's elementarycurriculum and teacher development efforts aremore closely linked. Two UCSMP programs, onerecently completed and the other currently underway, illustrate this linking of staff development andcurriculum. Another project, not related to Ev-eryday Mathematics, continues the investiga-tions into teacher preparation programs.

Everyday Teaching for EverydayMathematics K-3UCSMP has recently completed Everyday Teach-ing for Everyday Mathematics K-3, a series ofseven workshops, each about three hours long, forprimary teachers of Everyday Mathematics. Theseworkshops are designed to introduce the goals,philosophy, and mathematical foundations of Ev-eryday Mathematics in a collaborative and reflec-tive workshop setting. The Everyday Teachingseries supersedes MathTools for Teachers.

Everyday Teaching is self-contained and trans-

ELEMENTARY COMPONENT I I

portable, so that a school district's own trainingstaff can conduct the program. The program isdesigned to be flexible: any subset of the work-shops can be presented in any sequence. Theworkshops can be used as after-school workshops,as part of an inservice day, or as a week-longsummer course. The Everyday Teaching packageincludes a Staff Developer's Guide, Station Ac-tivity Sets, and a Mathematics Handbook, a col-lection of six background essays for workshopparticipants.

The topics for the Everyday Teaching work-shops are numeration and counting, plane geom-etry, measurement, operations, data analysis, solidgeometry, and applications. Everyday Teachingfor Everyday Mathematics K-3 is published bythe Everyday Learning Corporation.

Bridges to Classroom MathematicsBridges to Classroom Mathematics, a four-yearNSF-funded project now in its second year, alsoaddresses the problem of how to provide intensivestaff development to thousands of teachers. Bridgesis a collaboration between UCSMP and two Bos-ton-area educational research and developmentorganizations, the Consortium for Mathematicsand Its Applications (COMAP) and TERC.

Bridges has two principal components: 1) thedesign of a staff development program and 2) theorganization of two implementation centers forinitial testing of that program.

Staff Development Program. Bridges aimsto create materials that local school personnel canuse to conduct staff development workshops forelementary school mathematics teachers. The ma-terials will eventually support 90 hours of teacherworkshops; the first 30 hours have already beenwritten and field tested and are being revised. Thematerials will be arranged in 45 two-hour sessions.This modular arrangement will give teacher lead-ers and other staff developers the flexibility totailor the program to their local needs and re-sources.

Some Bridges materials address the math-ematics and pedagogy underlying all innovativeprograms based on the NCTM standards; otherBridges materials focus on the philosophy, goals,lesson formats, and so forth of a particular curricu-lum. Initially, two sets of curriculum-specificmaterials are being developed, one for UCSMP'sEveryday Mathematics and one for TERC' s Inves-tigations in Number, Data, and Space.

Schools can use the generic Bridges materials

12 ELEMENTARY COMPONENT

even if they are not using Everyday Mathematics orInvestigations. Other curriculum projects may findthat they can create staff development programs bysupplementing the generic materials with their owncurriculum-specific materials.

The Bridges package for staff developers willinclude a Staff Developer's Guide, Teacher'sHandbook, and Video Library. Both UCSMP'selementary materials publisher, the EverydayLearning Corporation, and TERC's publisher, DaleSeymour Publishing, will publish the Bridges ma-terials.

Implementation Centers. To aid in the de-velopment, testing, and dissemination of theBridges staff development units, the project hasorganized two implementation centers, one in LasVegas and the other in Oakland County, Michigan.Each center has a Director and a group of SiteFacilitators who are reform-oriented classroomteachers interested in providing staff developmentfor their colleagues.

Over the next three years, the Site Facilitatorswill lead summer and academic-year pilot testworkshops for teachers who are preparing to useeither UCSMP's Everyday Mathematics orTERC's Investigations. During the summer of1996, Oakland Site Facilitators conducted 30hours of Bridges workshops for more than 50elementary school teachers, and Las Vegas SiteFacilitators conducted Bridges workshops for 90teachers. During the 1996-97 school year, therewill be follow-up workshops with many of theseteachers and initial workshops for other teachers.

Several other school districts are also using thepilot Bridges materials. These secondary sites,together with the Implementation Centers, are thebeginnings of a Bridges to Classroom Mathematicsnetwork that we hope will spread across the coun-try, thus enabling new users to find experiencedBridges staff developers nearby and providing aneffective response to the scale problem.

Study of the Mathematics Preparation ofElementary School TeachersUCSMP and COMAP recently received a grantfrom NSF to examine the current state of elemen-tary teacher preparation in mathematics. Thisgrant, one in a series extending back to the early1990s, will characterize preservice programs forelementary school mathematics teachers and willidentify directions for future projects to help col-lege mathematics faculty develop more effectiveprograms for their own institutions.

13

Evaluation

Completed reports of many of these evaluationsare available and may be ordered directly fromUCSMP (see p. 19).

Materials DevelopmentKindergarten Everyday Mathematics was pi-loted in 1985-86 and revised prior to field test-ing in 1986-87. A formative study involving 17classrooms in the inner city and suburbs ofChicago showed that students substantially im-proved their mathematics skills, with studentperformance comparing favorably to that in aprevious study of counting, numeration, andoperations abilities. Improvement was particu-larly apparent in urban classes. Inner-city chil-dren who did about half as well as suburbanchildren on a variety of mathematics tasks at thebeginning of the year did 80% as well as theirsuburban counterparts at the end of the year.

Field test teachers reported that their stu-dents took more responsibility for their ownmathematics learning, that small-group activi-ties encouraged cooperative learning, and thatprojects and explorations provided challengesfor children of varying abilities in the sameclassroom. Developers revised KindergartenEveryday Mathematics again on the basis offield test results prior to publication.

Evaluation of subsequent years of the Eve-ryday Mathematics curriculum has proceededsimilarly. Formative evaluation of field testmaterials was the basis for the publishedversions of the curriculum for grades 1-5.

Results from the grades 4 and 5 field testsand related studies indicate that EverydayMathematics students do as well on computa-tion and much better in areas traditionallyunderrepresented in the elementary school cur-riculum, such as mental computation, geometry,data and graphing, and fractions.

Study teachers indicate that students aremuch better at reasoning, problem-solving, andcommunication, and show a better mathemati-cal understanding than students of previous years.Teachers also rate the curriculum highly onmeeting the goals of the NCTM standards.

In October 1993, NSF authorized adding alongitudinal study of K-4 Everyday Mathemat-ics to the project. Researchers have been inter-viewing and testing a cohort of Everyday Math-

14

ematics students since first grade. Along withcollecting data on the students, in the third gradein 1995-96, researchers observed classroomsand interviewed teachers to help identify waysof implementing, supporting, and sustaining re-form.

Teacher DevelopmentMathTools for Teachers, the UCSMP programfor primary teachers, was systematically andextensively evaluated in 1985-86. The studyfound that teachers responded positively to theworkshops, increasing their mathematics instructiontime incrementally during a period of heavyinformation accumulation and assimilation.Teacher networks were less successful due tofactors such as lack of time. In 1986-87, UCSMPevaluated one aspect of the program, calculatorusage by the K-3 teachers after their workshoptraining. Students and teachers enjoyed usingcalculators, and nearly half the teachers reportedusing them often. Teachers saw improvementsin student achievement, motivation, mathematicalconfidence, attitudes, and accuracy.

In 1987-88, UCSMP conducted a study ofthe Mathematics Specialist Program in grades4-6. To describe and document the implemen-tation of math specialists in the six participatingelementary schools, teacher development staffobserved classes, while evaluation staff focusedon the structural, organizational, and social im-plications of the program. In 1988-89, evalua-tors surveyed participants in the program infor-mally, assessing their adjustment to the special-ist role. Of interest was the reorganization ofeach school to allow for content specializationand its impact on the students, teachers, andadministrators.

Although many organizations have recom-mended the use of calculators in mathematicsclasses from kindergarten on, there has beenvery little research to determine the effects ofcalculator use on students in grades K-2. In1988-89, a calculator study was conducted in 36first- and second-grade classes in the Chicagoarea. Experimental classes used the UCSMPcalculator curriculum materials. Pretests andposttests were administered and were supple-mented by classroom observations and inter-views with teachers and students.

ELEMENTARY COMPONENT 13

UCSMP

Secon ary ComponentZalman Usiskin & Sharon Senk,

Materials DevelopmentSince 1980, reports from national commissionshave identified major problems in performanceand curriculum in pre-college mathematics: highschool students currently are not learning enoughmathematics; school curricula have not keptpace with changes in mathematics, its applica-tions, and technology; all students need to learnsignificant amounts of mathematics. These re-ports have produced a broad consensus on thechanges needed in mathematics instruction, aconsensus reflected in the NCTM standardsdocuments.

From 1983 to 1991, the UCSMP SecondaryComponent developed a six-year mathematicscurriculum for students in grades 7-12 in linewith this consensus. Since 1992, the componenthas worked on the second editions of thesematerials. The UCSMP curriculum transformshigh school mathematics into a mathematicalsciences curriculum, covering a much greaterrange of material important for life in a techno-logical society while maintaining consistencywith recent developments in college-level mathe-matics. This curriculum targets the generalschool populationstudents who will graduatehigh schooland conveys the essential role ofmathematics in everyday life by teaching stu-dents to use mathematics effectively.

Elements of the Secondary CurriculumSeveral basic elements distinguish UCSMP textsfrom most existing texts:

Wider Scope Geometry, algebra, and somediscrete mathematics occur in all courses. Sta-tistics and probability are integrated into thestudy of algebra and functions. All coursesdiscuss the history of major ideas and recentdevelopments in mathematics and mathematicalapplications.

Reading and Problem-Solving Each lessonincludes selections for students to read and con-tains questions and problem sets applying thereading. The text informs students about theselection of problem-solving methods, the his-tory and application of ideas, and the relationsbetween concepts.

14 SECONDARY COMPONENT

Co-Directors

Applications Students study each mathe-matical idea through its application to practicalproblems, providing many opportunities for thedevelopment of skills and an understanding ofthe importance of mathematics in everyday life.

Every high school graduateshould take the first fourcourses in the UCSMPsecondary curriculum,

all college-bound studentsthe first five, and all students

who might study technicalsubjects all six courses

or their equivalent.

Use of Technology The emphasis on every-day mathematics applications extends to theapproaches for solving problems. Students areexpected to have scientific calculators in allcourses. Automatic graphers are used begin-ning in UCSMP Algebra and assumed to beavailable daily in the last three courses. Auto-matic drawers are recommended for use withUCSMP Geometry. Calculators or computersoftware that does statistics is required for thefifth course.

Multidimensional Approach to Under-standing All texts emphasize skill in knowinghow and when to use various algorithms, prop-erties and mathematical relationships, realisticuses of ideas encountered, and the representa-tion, or picturing, of mathematical concepts.This is the SPUR approachemphasizing Skills,Properties, Uses, and Representations.

Instructional Format The materials maxi-mize learning by featuring continual review,combined with a modified mastery learningstrategy. The questions at the end of each

15

lesson include review of previous lessons. Atthe end of each chapter are a summary, a self-test to assess progress toward mastery, and re-view questions keyed to objectives.

Projects In the last two courses of the firstedition and in all second-edition courses, a se-lection of student projects is offered for eachchapter. These projects offer the opportunityfor students to spend a few hours or days explor-ing a topic in depth and writing about it forothers to see or hear.

Secondary Curriculum OutlineExtensive testing verifies that the average toabove-average student can begin this curricu-lum in the seventh grade and proceed with onecourse a year through twelfth grade. Schoolsthat have a strong K-5 curriculum like UCSMPEveryday Mathematics have found that they canbegin this curriculum in the sixth grade.

By starting earlier or later, or taking the firsttwo courses at a somewhat slower pace, thecurriculum sequence can accommodate a widerrange of students. It was originally thought thatTransition Mathematics would be used only ingrades 6-9, but in actuality, classes in grade 5through developmental courses at the collegelevel are currently using the text. A student maytake Transition Mathematics in ninth grade andstill complete a high school mathematics se-quence through Advanced Algebra. UCSMP'sgoal is to have every high school graduate takethe first four courses, all college-bound studentstake the first five, and all students who maystudy technical subjects take all six courses, ortheir equivalents.

Transition Mathematics (Year 1) This courseweaves together three themesappliedarithmetic, pre-algebra, and pre-geometrybyfocusing on arithmetic operations in mathemat-ics and the real world. The course introducesalgebra by examining three uses of variables(pattern generalizers, abbreviations in formu-las, and unknowns in problems) and variablerepresentation on the number line and coordi-nate plane. The course also introduces basicalgebra skills and connects geometry to arith-metic, measurement, and algebra.

Algebra (Year 2) UCSMP Algebra has a scopefar wider than traditional algebra books, high-lighting applications, using statistics andgeometry to develop the algebra of linear

1.6

equations and inequalities, and including prob-ability concepts in conjunction with algebraicfractions. Applications motivate virtually alllessons. Considerable attention is given tographing. Manipulation with rational algebraicexpressions is delayed until later courses.

Geometry (Year 3) UCSMP Geometry, diver-ging from the order of topics in most geometrytexts, presents coordinates, transformations, meas-urement formulas, and three-dimensional fig-ures earlier in the year. To teach writing proofsand other mathematical arguments more effec-tively, the course lays a foundation of prerequi-site understanding step by step. Again, applica-tions abound throughout.

Advanced Algebra (Year 4) This course em-phasizes facility with algebraic expressions andforms, especially linear and quadratic forms,powers and roots, and functions based on theseconcepts. Students study logarithmic, trigono-metric, polynomial, and other special functionsas tools for modeling real-world situations. Thecourse applies geometrical ideas learned in theprevious years, including transformations andmeasurement formulas.

Functions, Statistics, and Trigonometry(Year 5) Students study descriptive and infer-

ential statistics, combinatorics, and probability,and do further work with polynomial, exponen-tial, logarithmic, and trigonometric functions.Enough trigonometry is available to constitute astandard precalculus background in trigonom-etry and circular functions. Algebraic and sta-tistical concepts are integrated throughout, andmodeling of real phenomena is emphasized.Students use a function grapher and a statisticalutility to study functions, explore relationshipsbetween equations and their graphs, analyzedata, and develop limit concepts.

Precalculus and Discrete Mathematics(Year 6) Precalculus topics include a review ofthe elementary functions, advanced propertiesof functions (including special attention to poly-nomial and rational functions), polar coordi-nates, complex numbers, and introductions tothe derivative and integral. Discrete mathemat-ics topics include recursion, induction, combi-natorics, vectors, graphs, and circuits. Manipu-lation of rational expressions is discussed here.Mathematical thinking, including specific at-tention to formal logic and proof and comparingstructures, is a unifying theme throughout.

SECONDARY COMPONENT 15

DevelopmentThe Secondary Component developed each first-edition course in stages spanning four or fiveyears. During the planning stage, UCSMPcreated overall goals, both in consultation witha national advisory board of distinguished mathe-matics educators and through discussion withclassroom teachers, school administrators, anddistrict and state mathematics supervisors.

At the pilot stage, UCSMP selected au-thors to write first drafts of the courses. Half ofall UCSMP authors currently teach mathemat-ics in secondary schools, and all of the authorsand editors for the first five courses have hadsecondary teaching experience. Authors or theirsurrogates taught the first drafts of the textsthemselves, so their subsequent revision ben-efited from first-hand classroom experience.

After revision by the authors and editors,materials entered the formative stage of coursedevelopment. More classes used the books andindependent evaluators closely monitored stu-dent achievement and attitudes, as well as issuesrelated to implementation. Teachers met peri-odically at the university to provide feedback to

the UCSMP staff for a second revision.For the first three books, the Carnegie Cor-

poration of New York funded large nationalstudies assessing student and teacher perfor-mance and comparing UCSMP courses withtraditional mathematics curricula; final revi-sions were based on the findings of these stud-ies. The last three books went through forma-tive evaluations.

Planning, writing, and field testing of UCSMPsecond editions began with Transition Mathe-matics and UCSMP Algebra in 1992 and contin-ued with UCSMP Geometry and UCSMP Ad-vanced Algebra in 1993. The second edition ofTransition Mathematics appeared in 1994,UCSMP Algebra and Advanced Algebra in1995, and UCSMP Geometry in 1996. Workis underway on the second editions of Func-tions, Statistics, and Trigonometry and Precal-culus and Discrete Mathematics, and publica-tion is expected in 1997. See p. 18 for some ofthe changes made in the second editions.

All secondary textbooks and a complete setof supporting materials are available from ScottForesman/Addison Wesley.

Teacher DevelopmentThe elements distinguishing UCSMP texts frommost otherswider scope, an emphasis on readingand problem-solving, many more applications,the use of technologyhave obvious implica-tions for the way mathematics should be taught.The Secondary Component has engaged in in-tensive efforts in the area of teacher develop-ment.

InstitutesThe project received funding in 1989 from theFord Motor Company for five UCSMP Second-ary Summer Institutes, held in 1989-92. For twoweeks each institute brought together 25 univer-sity educators, secondary supervisors, and teachersin leadership positions chosen from a nation-wide pool of applicants. They attended sessionsfocusing on new content (including applica-tions, modeling, statistics, discrete mathemat-ics) and new approaches (problem-solving andunderstanding, careful development of geome-try and proof), as well as technology workshopsand discussion groups.

To facilitate the transmission of new ideas

16 SECONDARY COMPONENT

to teachers across the country, while at theUniversity of Chicago participants developedplans for further dissemination tailored to theparticular situation in their own districts.

WorkshopsHeld annually in August since 1989, these day-long workshops are open to all those who will beteaching or supervising the teaching of UCSMPsecondary materials during the upcoming aca-demic year. Participants register for an entireday devoted to one of the texts. Following anoverview of the secondary curriculum, the dayconsists of sessions led by UCSMP authors andexperienced teachers, who provide detailed in-formation about teaching from the text, offeradvice, and answer questions. In 1996, over 400teachers attended these workshops.

ConferencesSince 1985, the Secondary Component has hosteda November conference at which both currentand prospective users of project materials canlearn more about UCSMP. The conference

17

includes users' sessions offering teachers anopportunity to share experiences and ideas withtheir peers, overviews of each text presented byUCSMP authors and experienced teachers, ses-sions on teaching each book as described for theworkshops, and many other sessions on issues

related to using UCSMP materials. In 1995,over 600 people attended. The 1996conferenceis being held November 9-10. Scott Foresman/Addison Wesley sponsors several regional userconferences. For more information, contactUCSMP.

Evaluation

There is room here for only a brief summary ofthe evaluations of secondary materials. A longersummary is found in the Teacher's Edition ofeach book. Full reports of some of these evalu-ations are available (see p. 19). Final reports forthe second editions should be available in thenear future.

First EditionsIn 1985-86, a large matched-pair, nationwidestudy compared Transition Mathematics withstandard texts used in 7th-, 8th-, and 9th-gradeclasses. UCSMP students significantly outper-formed comparison students in geometry andalgebra readiness and became effective calcula-tor users with no loss of arithmetic skills. Teachersreported that although at first many students didnot do the desired reading, the situation im-proved as the year went on.

In 1987-88, a similar study was conductedon UCSMP Algebra. UCSMP and comparisonstudents did equally well on a standardizedalgebra posttest. UCSMP students outper-formed comparison students in every area ontwo other tests of nontraditional and traditionalconcepts and skills. Algebra teachers, enthusi-astic about its applications, rated the text highlyand were successful in getting students to read.

National field testing of Geometry began in1987-88. UCSMP students scored significantlyhigher than comparison students on a content-specific test of reasoning, transformations, vi-sualization, coordinates, applications, and stan-dard geometry. A second national field study in1988-89 focused on Geometry students withprevious UCSMP experience. One new findingwas that teaching such students was easier; classesin which 80% of the students had taken previousUCSMP courses began the year expecting to doa lesson a day, completing all the questions andengaging actively in class discussion.

The last three texts in the secondary cur-

18

riculum went through two years of pilot testingfollowed by a formative evaluation. Studiesincluded observations, interviews, and testingwith multiple-choice and open-ended items. In1987-88, UCSMPAdvancedAlgebra underwentformative evaluation. Analyzed according toUCSMP's SPUR dimensions of understanding,the posttest showed UCSMP students answer-ing correctly 15.6% more questions than com-parison students and outperforming their counter-parts by more than 20% on a variety of commonadvanced algebra problems.

During 1988-89, Functions, Statistics, andTrigonometry underwent a formative evalua-tion, and in 1991 the multiple-choice part of theposttest was repeated in the same schools. Inboth cases, UCSMP students outperformed theU.S. sample of precalculus students in the Sec-ond International Mathematics Study (SIMS)on items involving statistics and probability,with the sample outperforming UCSMP stu-dents on items covering polynomial and rationalfunctions. The text was revised to include moreon polynomial functions.

During 1989-90, Precalculus and DiscreteMathematics underwent formative evaluationin nine schools across the country. Part of theposttest was repeated in 1991 in six of theseschools. On standard precalculus content, suchas functions, trigonometry, and limits,UCSMP students significantly outperformed theSIMS precalculus students. UCSMP studentswere quite successful at proving trigonometricidentities, moderately successful with numbertheory proofs, and not very successful at proofsusing mathematical induction.

A longitudinal study of the first cohort tocomplete the first four UCSMP texts was donein 1989-90 at two suburban and one urban site.UCSMP students significantly outperformedcarefully-matched comparison students.on tra-ditional tests at two of the three sites and on

SECONDARY COMPONENT 17

applications at all sites. At one suburban site,UCSMP students significantly outperformedstudents a year older (in comparable courses) onapplications and did as well on traditional tests;at the other, older comparison students did aswell as UCSMP students on applications andsignificantly better on traditional tests.

Second EditionsThe evaluations that led to the second editionscan be said to have begun before their writing. Alarge sample of users was selected for eachcourse and asked for comments about each les-son in the student text and about the variousmaterials available with the text.

Their recommendations led to several ma-jor revisions in all the books. Projects werewritten for each chapter. Also included werereading heads to organize each lesson, in-classactivities to introduce selected lessons, and ac-tivities within lessonsall making it easier forstudents to read the lessons and become moreactive learners. A double set of Lesson Masterswas made available.

Recommendations relevant to specific coursesalso were made, often motivated by the desire toensure that material in the books' last few chap-ters would be reached. First-edition as well asnew authors were brought in to write. Thematerials, edited by UCSMP, were distributedto schools during the next school year.

Evaluations were directed by an experi-enced researcher brought in expressly for thispurpose. Schools and classes were chosen fromaround the nation to reflect the wide range ofstudents using UCSMP materials and for theirlikelihood of obtaining matching comparisonclasses. In every matched pair, the two classeshad to be from the same school. Most compari-son classes used first-edition UCSMP materials.We believe this is the first time a curriculum hasbeen carefully compared with a previous ver-sion of itself. Other comparison classes usednon-UCSMP materials, providing a replicationof first-edition studies.

Transition Mathematics was so well likedby teachers that no major changes were made inits structure. Still, large numbers of smallerchanges were made. Although teachers in theseclasses who had taught both first- and second-edition materials unanimously preferred the secondedition, there were no statistically significantdifferences between the performance of first-and second-edition students. All four UCSMP

I$ EVALUATIONS. CONTINUED

second-edition classes were equal to their non-UCSMP counterparts on general mathematics,two classes outperformed their non-UCSMP coun-terparts on the algebra posttest, and three classesoutperformed their non-UCSMP counterpartson the geometry posttest. These results confirmthe results of the first-edition studies.

A major change in the structure of UCSMPAlgebra for the second edition was to shortenthe review of ideas found in the preceding bookand to begin equation-solving with equations ofthe form ax = b rather than with equationsinvolving addition. Other changes included anearlier introduction of quadratic equations and amore intense development of factoring. Therewere no significant differences among studentsin the sixteen pairs of classes in which thecomparison class used first-edition UCSMPmaterials. In the four pairs of classes in whichthe comparison classes used non-UCSMP mate-rials, the UCSMP students were equal on astandardized algebra test and significantly out-performed their counterparts on tests of a widerrange of algebra and problem-solving.

No major changes were made in the struc-ture of UCSMP Geometry for the second edi-tion, although some chapters were reordered.Second-edition UCSMP students outperformedtheir first-edition counterparts on both a stan-dardized geometry test and a second test withbroader geometry content. This may be becausethey were more likely to find their textbook easyto read and interesting or because the moreactive approach and projects benefit geometrystudents more than students in other courses.Second-edition UCSMP students performed aswell as their non-UCSMP counterparts on thestandardized test and scored much higher on thebroad-based test.

A major change in the second edition ofUCSMP Advanced Algebra was to require theuse of automatic graphers and begin the study offunctions in the first chapter. This enabled newlessons on modeling using linear, quadratic, andexponential functions. Content in other chap-ters was reordered. Standardized tests appropri-ate to the content of this book do not exist, so wedesigned multiple-choice and problem-solvingposttests. On these tests, there were no signifi-cant differences between first- and second-edi-tion students. There were large significant dif-ferences favoring second-edition UCSMP stu-dents over their non-UCSMP counterparts onboth tests.

19

UCSMP

Available MaterialsElementary Materials available from EverydayLearning CorporationKindergarten Everyday MathematicsFirst Grade Everyday MathematicsSecond Grade Everyday MathematicsThird Grade Everyday MathematicsFourth Grade Everyday MathematicsFifth Grade Everyday MathematicsSixth Grade Everyday MathematicsEveryday Teaching K-3Do Elephants Eat Too Much?If I Walk in the Woods, Will I Run into a Bear?From the Seas to the StarsFrom Your Backyard to the Great WallCalculator Mathematics 1Calculator Mathematics 2

Secondary Materials available from ScottForesman/Addison Wesley*Transition MathematicsUCSMP AlgebraUCSMP GeometryUCSMP Advanced AlgebraFunctions, Statistics, and TrigonometryPrecalculus and Discrete MathematicsGeoExplorerGraphExplorerStatExplorerWide World of Mathematics*Each text has student and teacher editions, ancillarymaterials, and software.

Resource Materials available from the UCSMPDirector's OfficeSoviet Studies in Mathematics Education,

vols. 7-8Japanese Grade 7 MathematicsJapanese Grade 8 MathematicsJapanese Grade 9 MathematicsRussian Grade 1 MathematicsRussian Grade 2 MathematicsRussian Grade 3 Mathematics

Resource Materials available from the AmericanMathematical SocietyMathematics 1: Japanese Grade 10Mathematics 2: Japanese Grade 11Algebra and Geometry: Japanese Grade 11Basic Analysis: Japanese Grade 11

Resource Materials available from the NationalCouncil of Teachers of MathematicsDevelopments in School Mathematics Education

Around the World, vols. 1-3Soviet Studies in Mathematics Education,

vols. 1-6

Evaluation Reports available from the UCSMPDirector's OfficeElementaryAn Evaluation of the Teacher Development

Project, 1985-86Formative Evaluation of Kindergarten Everyday

MathematicsA Follow-up of Kindergarten Everyday Math-

ematics UsersThe Ray School Computer Lab: Evaluation

Report, 1985-86Calculator Usage in the Teacher Development

ProjectMathematical Knowledge of Kindergarten and

First-Grade Students in Everyday MathematicsClassroom Implementation and Impact of

Everyday Mathematics K-3: Teachers' Per-spectives on Adopting a Reform Curriculum

A Field Test of Fourth Grade Everyday Mathem-atics, 1993-94 (complete & summary reports)

Third Grade Everyday Mathematics Students'Performance on the 1993 and 1994 IllinoisState Mathematics Test

Report on the Field Test of Fifth Grade EverydayMathematics

SecondaryTransition Mathematics Field StudyTeaching and Learning Algebra: An Evaluation

of UCSMP Algebra

Evaluation Reports available from. UMI Disserta-tion ServicesAn Evaluation of a New Course in Precalculus

and Discrete MathematicsImplementation of the First Four Years of the

University of Chicago School MathematicsProject Secondary Curriculum

See back cover for addresses.

20BEST COPY AVAOLABLE

AVAILABLE MATERIALS 19

UCSMP DirectoryAt 5835 S. Kimbark Avenue, Chicago, IL 60637:Director's OfficeZalman Usiskin, DirectorCarol Siegel, Assistant to the Director

Elementary ComponentMax Bell, DirectorSheila Sconiers, Director ofTeacher Development

COMAP, Inc., 57 Bedford St., Suite 210,Lexington, MA 02173

Secondary ComponentZalman Usiskin, Co-DirectorSharon Senk, Co-Director

Mathematics Department, Wells Hall,Michigan State University, East Lansing, MI 48824

(773) 702-1560(773) 702-9770

(773) 702-1563(617) 862-7878

(773) 702-1560(517) 353-4691

Evaluation ConsultantLarry Hedges (773) 702-1589

At 5734 S. University Avenue, Chicago, IL 60637:Resource Development ComponentIzaak Wirszup, Director (773) 702-7397

UCSMP Past Director, 1983-87Paul Sally (773) 702-7388

Publishers of UCSMP MaterialsEveryday Learning Corporation (800) 382-7670P.O. Box 812960Chicago, IL 60681

Scott Foresman/Addison Wesley (800) 554-44111900 E. Lake AvenueGlenview, IL 60025

National Council of Teachers of Mathematics (703) 620-98401906 Association DriveReston, VA 22091

UMI Dissertation Services (800) 521-0600300 N. Zeeb RoadAnn Arbor, MI 48106

American Mathematical Society (800) 556-7774P.O. Box 6248Providence, RI 02940-6248

Other materials are available directly from the UCSMPDirector's Ofice.

21

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

Educational Resources Information Center (ERIC)

REPRODUCTION RELEASE(Specific Document)

I. DOCUMENT IDENTIFICATION:

Title:

....... 1.4e ... V11-1.4 6g 6 114 0-4.ar, I

Author(s):

Corporate Source:

CsmePublication Date:

nibki** taPiL

IL REPRODUCTION .RELEASE:

In order to disseminate as widely as possible timely and significant materials of interest to the educational community, documents announcedIn the monthly abstract journal of the ERIC system, Resources in Education (RIE), are usually made available to users in microfiche, reproducedpaper copy, and electronic/optical media, and sold through the ERIC Document Reproduction Service (EDRS) or other ERIC vendors. Credit isgiven to the source of each document, and; if reproduction release is granted, one of the following notices is affixed to the document

If permission is granted to reproduce and disseminate the identified document, please CHECK ONE of the following two options and sign atthe bottom of.the page.

xiCheck here

For Level 'I Release:Permitting reproduction Inmicrofiche (4' x 6' film) orother ERIC archival media(e.g.. electronic or optical)and paper copy.

Signhere)please

The sample iticker shown below will beaffixed to all Leve11' docUmenti

PERMISSION TO REPRODUCE ANDDISSEMINATE THIS MATERIAL

HAS SEEN GRANTED BY

TO THE EDUCATIONAL RESOURCESINFORMATION CENTER (ERIC)

Level

The sample sticker shown below will beaffixecito all Leve1.2 documents

PERMISSION TO REPRODUCE ANDDISSEMINATE THIS

MATERIAL IN OTHER THAN PAPERCOPY HAS BEEN GRANTED BY

TO THE EDUCATIONAL RESOURCESINFORMATION CENTER (ERIC)

Level 2

Documents will be processed as indicated provided reproduction quality permits. If permissionto reproduce is granted, but neither box is checked, documents will be processed at Leval 1.

Check hereFor Level 2 Release;Permitting reproduction inmicrofiche (4" x 6' film) orother ERIC archival media(e.g., electronic or optical),but not in paper copy,

. .

hereby grant to the Educational Resources Information Center (ERIC) nonexclusive permission to reproduce and disseminatethis document as indicated above. Reproduction from the ERIC microfiche or electronic/optical media by persons other thanERIC employees and its system contractors requires permission from the copyright holder. Exception is made for non-profitreproduction by libraries and other service agencies to satisfy information needs of educators in response to discrete inquiries."

Tynature2

alia7KIERZ:

The University of Chicago5835 S. Kimbark AvenueChicago, IL 60637

---157IWtion e:

779- 741,z'`I 7 7e 7 7, -762ebtstefe

4111r.r0.1

EMail Address: Date:

(over)