ONE POINT OF VIEW: Reclaiming School Mathematics

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ONE POINT OF VIEW: Reclaiming School MathematicsAuthor(s): Portia ElliottSource: The Arithmetic Teacher, Vol. 37, No. 8 (APRIL 1990), pp. 4-5Published by: National Council of Teachers of MathematicsStable URL: .Accessed: 12/06/2014 16:00Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . .JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact .National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher. This content downloaded from on Thu, 12 Jun 2014 16:00:36 PMAll use subject to JSTOR Terms and Conditions POINT OF VIEW Reclaiming School Mathematics Portia Elliott framers of the Curriculum and Evaluation Standards for School Mathe- matics (NCTM 1989) call for a radical "design change" in all aspects of mathematics education. They believe that "evaluation is a tool for implementing the Standards and effecting change systematically" (p. 189). They warn, however, that "without changes in how mathemat- ics is assessed, the vision of the math- ematics curriculum described in the standards will not be implemented in classrooms, regardless of how texts or local curricula change" (p. 252). Explicit in their warning is the per- ceived power that test constructors wield over curriculum designers and textbook publishers. Implicit in the warning is the sentiment that the tested curriculum is what will be taught regardless of the larger goals and objectives of classroom teachers and mathematics programs. How did test constructors get so powerful as to make curriculum designers, textbook publishers, and teachers cringe at the posting of mean scores, stanine Portia Elliott serves on the Editorial Panel of the Arithmetic Teacher and will serve as coed- itor with Mike ne s of the February 1991 fo- cus issue on evaluation. Readers are encour- aged to respond to this editorial by writing to the authors with copies to the Arithmetic Teacher for consideration for publication in "Readers' Dialogue." Please double-space all letters that are to be considered for publication. Editorials from readers are welcomed. scores, and standard-deviation re- sults? With our fixation on quantitative data, we must take full responsibility for failure to speak out against ex- cesses. By acclaiming one school dis- trict's superiority over another on the basis of national achievement tests; by proclaiming one student more priv- ileged than another because of these findings; and by claiming one teacher meritorious and another mediocre based on students' performances on entrance examinations from kinder- garten to graduate school, we have helped make "high-stakes testing" omnipresent and test constructors omnipotent. Because the stakes are so high and pressures from administrators and parents are great, teachers feel en- joined to teach to the test. We dis- avow any knowledge of how we fell victim to "measure-driven instruc- tion." We express feelings of power- lessness, as if testing took over by "right of eminent domain." But when we professional educators and the public repeated the unsubstantiated claims that tests could determine the relative worth of our students, we shared in the culpability for narrowing the focus of educational objectives to those that can be easily quantified. Through participation in, and accep- tance of, the competitive model im- plicit in the uses made of standardized tests, we handed "norm referenced" claim jumpers a "quitclaim" deed to the entire school curriculum. Armed with the Standards, it is time to stake a counterclaim on the school mathematics curriculum. Our claim should make students, not scores, the mathematically powerful. It should make teachers, not testers, the determiners of instructional objec- tives. It should make learning, not li- censing, the focal point of schooling. The reclamation process begins with the recognition that we have available indicators of success in mathematics that are more revealing than the re- sults on standardized tests. As seduc- tive as test scores have been, their perceived power must be resisted if schools are to reclaim their roles as coordinators of curriculum reforms; if teachers are to reclaim their rightful places on curriculum-evaluation teams; and if students ar to reclaim their mathematical power and become self-regulating, self-monitoring, and self-controlling individuals. In short, the reclamation of both curriculum and assessment is necessary to return accountability to school districts, ad- ministrators, teachers, parents, and students. The position expressed in this edi- torial has the endorsement of the Ed- itorial Panel of the Arithmetic Teach- er: Mathematics Education through the Middle Grades. It expresses our beliefs that evaluation must be tied to larger curricular goals and objectives; that evaluation data must come from various sources (e.g., observations, interviews, journal writings, portfo- lios, extended projects, norm- and cri- teria-referenced tests); and that eval- uations must be conducted by evaluation teams consisting of teach- ers, supervisors, administrators, par- ents, students, and test constructors serving as "tenants in common" to determine the best questions to ask and actions to take next to make mathematics accessible by all. 4 ARITHMETIC TEACHER This content downloaded from on Thu, 12 Jun 2014 16:00:36 PMAll use subject to JSTOR Terms and Conditions the right please see the "Call for Manuscripts" for the February 1992 focus issue on evaluation. We invite authors to join in the evaluation dis- cussion; to share evaluation strate- gies; and to offer examples for how school districts, teachers, and stu- dents can reclaim their mathematics curriculum and judge for themselves the quality of their own work. Reference National Council of Teachers of Mathematics, Commission on Standards for School Mathe- matics. Curriculum and Evaluation Stan- dards for School Mathematics. Reston, Va.: The Council, 1989. W THE CENTER FOR EXCELLENCE IN TEACHNG presents MORTENSEN, more than MATH Summer workshop focuses on practical and proven ideas for teaching elementary students to love mathematics using manipulatives. Hosted by the Princeton Montessori School, Princeton, NJ. For more information call 609-921-7377. Call for Manuscripts: Focus Issue on Evaluation The February 1992 issue of the Arithmetic Teacher: Mathematics Education through the Middle Grades is planned as another in the series of focus issues. The theme of the issue, evaluation, indicates the growing awareness that new instruc- tional techniques will require innovative evaluation strategies and that large-scale standardized testing (accountability testing) must change because of curricular and instructional changes, as well as advances in technology. These changes are having an impact at the classroom, school, school district, state and national levels. Manuscripts are being sought that describe evaluation techniques and promising current practices that support the National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics (1989) and its Pro- fessional Standards for Teaching Mathematics: Working Draft (1989). Seven cop- ies of a completed manuscript should be sent for review to the Arithmetic Teacher, 1906 Association Drive, Reston, VA 22091, by 1 November 1990. No author iden- tification should appear in the text of the manuscript. Authors should identify one category from those listed below that represents the major thrust of their manu- script. An article might, however, incorporate components of more than one cat- egory. Interdisciplinary coauthorship is encouraged. Evaluation What is the purpose of evaluation at the classroom, school, district, state, and na- tional levels? What purpose can accounta- bility testing serve in program evaluation or student assessment? How should evaluation be related to program goals, instructional objectives, and classroom practices? How can evaluation and assessment results be used to increase teachers' effectiveness and students' learning? Since the "tested curric- ulum" strongly determines what gets taught, how will tests have to be revamped to reflect the NCTM's curriculum stan- dards? Evaluation alternatives What evaluation techniques will yield data to give a multifaceted view of students1 un- derstandings, skills, and dispositions? What roles can observations, interviews, journals, portfolios, extended projects, holistic scor- ing, standardized tests, performance tests, surveys, checklists, self-reporting tech- niques, norm-referenced tests, and criteri- on-referenced tests play in the assessment of mathematics understandings and disposi- tions? How can students' learning styles be accommodated in evaluation practices? How can manipulatives be used effectively in testing situations? Why is a balance of means of evaluation necessary and appro- priate? How can real-life experiences be used in the evaluation process? Testing: Bias and equal-access Issues What special attention should be given to the role of testing with regard to "at risk" students and other special groups? What techniques can be used to evaluate and ac- commodate exceptionalities in learners? How can we evaluate the extent to which the curriculum standards' goal of "reaching all students" is being achieved? Mathematical understandings How can both conceptual and procedural understanding be evaluated? How should evaluation feedback on cognitive capabili- ties affect instructional decision making and classroom practices? What are some inno- vative ways of evaluating students' acquisi- tion of mathematics skills? How can stu- dents monitor their own progress? What are some approaches to evaluating metacogni- tive thought processes? How can learning be evaluated when students work in coop- erative groups? Mathematical dispositions What techniques are effective in evaluating mathematical attitudes and dispositions? How can we determine whether students value the role of mathematics in our culture? How can volitional competencies (e.g., will- ingness to persevere, ability to plan, inven- tiveness) be evaluated? How can we evalu- ate the perceptions and beliefs that underlie students' mathematical dispositions? How should evaluation feedback on dispositions affect classroom practices? Parents and community How can parents and the local community be involved in evaluation efforts? How can parents, community groups, and legislators be alerted to issues in assessment (potential misuse of test data, value of alternative ap- proaches for evaluation, appropriate use of technology, etc.)? How can perceptions about the need for "measurement-driven in- struction" be changed? Program evaluation What methods can be used to evaluate pro- gram effectiveness and consistency with the evaluation standards? What roles should students, teachers, administrators, and par- ents play in the evaluation of mathematics programs? Uses of technology What is the role of technology in evaluation? How can calculators be used effectively in testing situations? What role can computers and video recordings play in evaluating cog- nitive, affective, and volitional competen- cies? Should standardized tests be offered on computers? What is the role of adaptive testing in mathematics? Professional development How can preservile and in-service pro- grams include the investigation of alterna- tive evaluation approaches? What can be done to help educators become effective in self-evaluation, student assessment, and program evaluation? APRIL 1990 * This content downloaded from on Thu, 12 Jun 2014 16:00:36 PMAll use subject to JSTOR Terms and Conditions Contentsp. 4p. 5Issue Table of ContentsThe Arithmetic Teacher, Vol. 37, No. 8 (APRIL 1990), pp. 1-60Front MatterREADERS' DIALOGUE [pp. 2, 46]Correction: Imaginative Ideas for the Teacher of Mathematics, Grades K-12: Ranucci's Reservoir [pp. 46-46]Correction: TEACHING MATHEMATICS WITH TECHNOLOGY: Changing Variables Using Spreadsheet Templates [pp. 46-46]Correction: Hands-On Math: Volume 1. Apple IIe, IIc, or IIgs, 64K; RAM, single or dual disk, color monitor recommended, DOS 3.3 Applesoft BASIC and assembler, DOS 3.3 format storage disk; backup disk; multiple disks for multiple computer use by schools [pp. 46-46]ONE POINT OF VIEW: Reclaiming SchoolMathematics [pp. 4-5]STATION BREAK: A MATHEMATICS GAME USING COOPERATIVE LEARNINGAND ROLE PLAYING [pp. 8-12]GET IN TOUCH WITH SHAPE [pp. 14-16]DISCOVERING PI TWO APPROACHES [pp. 18-22]IMPLEMENTING THE "STANDARDS": Implications of NCTM's"Standards" for Teaching Fractions and Decimals [pp. 23-26]IDEAS [pp. 27-32]RESEARCH INTO PRACTICETeaching Mathematics and Thinking [pp. 34-37]USING PATTERNS TO PRACTICE BASIC FACTS [pp. 38-41]USING A POLAR COORDINATE SYSTEM IN THECLASSROOM [pp. 42-45]TEACHING MONEY WITH GRIDS [pp. 47-49]TEACHING MATHEMATICS WITH TECHNOLOGY: Data Base andSpreadsheet Templates with Public Domain Software [pp. 52-55]REVIEWING AND VIEWINGNew BooksFrom NCTMReview: untitled [pp. 56-56]Review: untitled [pp. 56-56]From Other PublishersFor PupilsReview: untitled [pp. 56-56]Review: untitled [pp. 56-57]Review: untitled [pp. 57-57]Review: untitled [pp. 57-57]Review: untitled [pp. 57-57]Review: untitled [pp. 57-57]For TeachersReview: untitled [pp. 57-58]Review: untitled [pp. 58-58]Review: untitled [pp. 58-58]Review: untitled [pp. 58-59]Review: untitled [pp. 59-59]Review: untitled [pp. 59-60]Review: untitled [pp. 60-60]Back Matter