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MATHEMATICS IN CONTEXT

MATHEMATICS IN CONTEXT 2001, Education Development Center, in Contextis a comprehensive middle school MATHEMATICS curricu-lum for grades 5 through 8. It was developed by the Wisconsin Center forEducation Research, School of Education, University of Wisconsin Madison andthe Freudenthal Institute at the University of Utrecht, The Netherlands. Connections are a key feature of the program connections among topics, con-nections to other disciplines, and connections between MATHEMATICS and mean-ingful problems in the real world. MATHEMATICS in Contextemphasizes the dynam-ic, active nature of MATHEMATICS and the way MATHEMATICS enables students tomake sense of their world. In traditional MATHEMATICS curricula, the sequence of teaching often proceedsfrom a generalization, to specific examples, and to applications in in Contextreverses this sequence; MATHEMATICS originates from realproblems.

The third strand is geometry. Geometry, from the Dutch point of view, and from the work we’ve done, has much more focus on spatial visualization skills than on learning to identify properties of plane figures—which is the singular focus for geometry in so many curricula. The final strand of work is in statistics and probability.

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Transcription of MATHEMATICS IN CONTEXT

1 MATHEMATICS IN CONTEXT 2001, Education Development Center, in Contextis a comprehensive middle school MATHEMATICS curricu-lum for grades 5 through 8. It was developed by the Wisconsin Center forEducation Research, School of Education, University of Wisconsin Madison andthe Freudenthal Institute at the University of Utrecht, The Netherlands. Connections are a key feature of the program connections among topics, con-nections to other disciplines, and connections between MATHEMATICS and mean-ingful problems in the real world. MATHEMATICS in Contextemphasizes the dynam-ic, active nature of MATHEMATICS and the way MATHEMATICS enables students tomake sense of their world. In traditional MATHEMATICS curricula, the sequence of teaching often proceedsfrom a generalization, to specific examples, and to applications in in Contextreverses this sequence; MATHEMATICS originates from realproblems.

2 The program introduces concepts within realistic contexts that supportmathematical in Contextconsists of mathematical tasks and questions designed tostimulate mathematical thinking and to promote discussion among are expected to explore mathematical relationships; develop and explaintheir own reasoning and strategies for solving problems; use problem-solving toolsappropriately; and listen to, understand, and value each other s strategies. The complete MATHEMATICS in Contextprogram contains 40 units, 10 at each gradelevel. The units are organized into four content strands: number, algebra, geometry ,and statistics (which also includes probability). Every MATHEMATICS in Contextunitconsists of a Teacher Guideand a non-consumable, softcover student booklet. The Teacher Guidescontain the solutions to the exercises; a list of unit goals;and objectives, comments, and suggestions about the approach and the mathe-matics involved in the unit.

3 The guides include assessment activities for eachunit, including tests, quizzes, and suggestions for ongoing assessment. Theguides also provide blackline masters for activities requiring students to havecopies of the text page. Also available are two supplementary products for teachers: the Teacher Resourceand Implementation Guide(TRIG) and Number Tools. The TRIG manual is a com-prehensive guide for the implementation of MATHEMATICS in CONTEXT . It addressestopics such as suggested sequence of units, preparation for substitute teachers,preparing families, assigning homework, and preparing students for standardizedachievement tests. Number Tools, Volumes I and II give students further exposureto number concepts, including fractions, decimals, percents, and number activity sheets are supported by a CONTEXT similar to those in the curriculumunits and can be used as homework and/or quizzes on classroom used in the program are items commonly found in the classroom, suchas scissors, graph paper, string, and integer chips.

4 As students progress to laterunits, the need for a personal calculator increases. The 8th-grade units were writtenwith the expectation that students would have access to graphing IN CONTEXTA middle school curriculum for grades 5 8, developed by theMathematics in CONTEXT (MiC) ContactBriana VillarrubiaEncyclopaedia Britannica310 S. Michigan AvenueChicago, ILphone: (800) 554-9862, ext. 7961fax:(312) CenterMeg MeyerStaff DeveloperMathematics in CONTEXT Satellite CenterWisconsin Center for Education Research1025 W. Johnson StreetMadison, WI 53706phone: (608) 263-1798fax:(608) 2001, Education Development Center, A. Romberg is the SearsRoebuck-Bascom Professor ofEducation at the University ofWisconsin Madison andPrincipal Investigator and pastDirector of the National Centerfor Improving Student Learningand Achievement inMathematics and Science(NCISLA) and the NationalCenter for Research inMathematical SciencesEducation (NCRMSE).

5 Dr. Romberg has a long historyof involvement with mathematicscurriculum reform. In particular,he chaired the NCTM groupsthat produced the Curriculumand Evaluation Standardsandthe Assessment Standards. Hisresearch has focused on threeareas: young children s learningof initial mathematicalconcepts1; methods of evaluat-ing both students andprograms2; and an integrationof research on teaching, curricu-lum, and student thinking3. Thomas A. RombergDeveloping MATHEMATICS in CONTEXT (MiC)There were several influences on why and how we developed MATHEMATICS inContext. First, I was chairman of the NCTM Commission on Standardsthat pro-duced the 1989 NCTM Curriculum and Evaluation Standards. We had laid out avision in the Standardsfor a changed MATHEMATICS curriculum. At the time, I wasalso the director of the National Center for Research on Mathematical SciencesEducation, funded by the Department of Education.

6 The research done overthe last 20 years made it very clear that there were some features of teaching andlearning that needed to be incorporated into the way materials were were only a necessary part of a reform strategy necessary, but not suf-ficient to produce reform on their own. In order to change MATHEMATICS teachingand learning, you needed to provide a lot of professional development for teach-ers, and you needed to change the assessment systems that are used in schools tojudge progress, as well as make other changes. About that time, as a part of the background work we had been doing in the devel-opment of the Standards, I became familiar with the work of the Dutch at theFreudenthal Institute in Utrecht. The Dutch had been, for the previous 20 years,implementing what they refer to as a realistic MATHEMATICS program in program is based on the ideas of Hans Freudenthal and others, and is cen-tered on the notion that MATHEMATICS is a sense-making device.

7 Students need toengage in trying to make sense out of real problems, and the development of math-ematics needs to be from that point of view. As part of our research, we worked with the Dutch, trying out some things. I con-tracted with them to do a small study in Wisconsin, teaching a unit in statistics forhigh school students. Gail Burrill, who later became president of NCTM, was thechair of the math department at the time and agreed to participate in the that study, we saw that the kind of approach the Dutch were using was veryinteresting, and we tried to incorporate it into a proposal for developing a middle-school program. So the background of MATHEMATICS in Contextis really a combi-nation of three things: the NCTM Curriculum and Evaluation Standards, theresearch base on a problem-oriented approach to the teaching of MATHEMATICS ,and the Dutch realistic MATHEMATICS education approach.

8 We submitted a propos-al to develop a middle-school program combining those ideas, and that programbecame MATHEMATICS in should note that although a substantial part of the ideas behind the program arefrom the Dutch approach, the materials themselves are not a translation of Dutchcurriculum materials. The materials were developed here by staff at the Universityof Wisconsin Madison, with the assistance of the Dutch, and of course, also withTHOMAS A. ROMBERG AND MEG MEYER4 DEVELOPERSM athematics in CONTEXT (MiC)1 Best reflected in the Journal of Research in MATHEMATICS Educationmonograph Learning to Add and Subtract. 2 Best reflected in the books Toward Effective Schooling: The IGE Experience; Reforming MATHEMATICS in America sCities; MATHEMATICS Assessment and Evaluation.

9 And Reform in School MATHEMATICS and Authentic reflected in the handbook chapters, Research on Teaching and Learning MATHEMATICS : Two Disciplines ofScientific Inquiry and Problematic Features of the School MATHEMATICS Curriculum, and in the recent bookMathematics Classrooms That Promote in CONTEXT (MiC) 2001, Education Development Center, assistance of a number of middle-school teachers who pilot tested and fieldtested the materials and provided a lot of feedback on the appropriateness of thematerials for American MATHEMATICS of MiCMathematics in Contextis organized around four mathematical strands: number,algebra, geometry , and statistics and probability. The number strand is built on theassumption that whole-number arithmetic would have been covered fairly well inany program up through grade 4; we are building on that.

10 There is a fair amountof work in the curriculum on number, particularly on rational numbers fractions,decimals, and percents. We re especially strong, we think, in work on ratios. The second strand is algebra: 13 of the 40 units are algebraic, dealing with what werefer to as the transition from informal to pre-formal to formal algebra over the 5th,6th, 7th and 8th grades. That s a very strong part of the program. Our whole approachis not to talk about algebra just as it always was in the typical 9th-grade Algebra Icourse. We talk about algebra as a set of tools used to solve certain kinds of prob-lems. In order to be able to solve those problems, students have to learn, for exam-ple, to write formulas, study the properties of formulas and equations, and be able tograph and talk about graphical solutions.