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Investigated Was the Feasibility of Presnting Proof Materials to College-Capable Sixth-Grade Students

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Investigated Was the Feasibility of Presnting Proof Materials to College-Capable Sixth-Grade Students DOCUMENT RESUME ED 040 876 24 SE 008 988 AUTHOR King, Irvin L. TITLE A Formative Development of a Unit on Proof for Use in the Elementary School (Parts 1,2 and 3). INSTITUTION Wisconsin Univ., Madison. Research and Development Center for Cognitive Learning. SPONS AGENCY Office of Education (DHEW), Washington, D.C. Bureau of Research. REPORT NO TR-111 BUREAU NO BR-5-0216 PUB DATE Jan 70 CONTRACT OEC-5-10-154 NOTE 401p. EDRS PRICE EDRS Price ME -$1.50 HC-$20.15 DESCRIPTORS *Concept Formation, Doctoral Theses, *Elementary School Mathematics, Grade 6, *Instruction, *Mathematical Concepts, *Mathematics Education ABSTRACT Investigated was the feasibility of presnting proof materials to college-capable sixth-grade students. A unit on mathematical proof was developed using an iterative procedure. Formative evaluation procedures were used to improve various components of the unit, Included in the unit are terminal student behaviors, cartoon stories, and several classroom activities which use a desk computer. Results indicated that the iterative developmental procedures employed were highly successful. (Author/FL) A FORMATIVE DEVELOPMENT OF A UNITON PROOF FOR USE IN THE ELEMENTARY SCHOOL PART I Report from the Projecton Analysis of Mathematics Instruction U.S. DiPARIMENT OF HEALTH. EDUCATIONaWELFARE OFFICE OF EDUCATION , THIS DOCUMENT HAS BEEN REPRODUCED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGINATING IT.POINTS OF VIEW OR OPINION STATED DO NO NECESSARILY REPRESENT OFFICIAL OFFICE OF EDUCATION POSITION OR IICY. bo os O 0 1#) U.S.Office of Education Center No. C-03 Contract OE 5-10-154 N- OD 0 Technical Report No. 111 4e; A FORMATIVE DEVELOPMENT OF A UNITON PROOF FOR USE IN THE ELEMENTARYSCHOOL PART I Report from the Projecton Analysis of Mathematics Instruction By Irvin L. King Thomas A. Romberg, AssistantProfessor of Curriculum andInstruction and of Mathematics Chairman of the Examining Committee,andPrincipal Investigator Wisconsin Research and Development Center for Cognitive Learning The University of Wisconsin Janyary 1970 This Technical Report isa doctoral disse.ation reporting research supportedby the-Wisconsin Research and Development Center,for Cognitive Learning. Sinceit has been approved bya Uni- versity Examining Committee, it hasnot been reviewed by the Center.Itis published by the Center as a record ofsome of the Center's activities andas a service to the student. The bound original is in The University ofWisconsin Memorial Library. Published by the Wisconsin Researchand Development Center forCognitive Learning, supported in part as a research and developmentcenter by funds from the United StatesOffice of Education, Department of Health, Education, andWelfare. The opinions expressedherein do not necessarily reflect the positionor policy of the Office of Education andno official endorsement by the Office of Education should be inferred. Center No. C-03 / Contract OE 5-10-154 NATIONAL EVALUATION COMMITTEE Samuel Brownell Henry Chauncey Elizabeth Koontz Patrick Suppes Notessor of Utban Education Plesident Plesident (Andante School Educational testing S(tviro Professor Yale University National Eilhattion Association Department of Mathematics Stanton' University Launor F. Carter Martin Deutsch Roderick McPhee Serum Vice Plesident on *Benton J. Underwood ()hector. Institute LI Puniile-nt Professor fechnolog. and Development Developmental Studies System Development Corpotation Punahou School, Honolulu Vow tomtit of Psychology New Yolk Medical College f Jot thwesto in Univotilly Francis S. Chase Jack Edling G. Wesley Sowards Professor Director, Teaching Research Director, Elementary Education Department of Education Division Florida State University University of Chicago Oregon State System of Higher Education UNIVERSITY POLICY REVIEW BOARD Leonard Berkowitz John Guy Fowlkes Herbert J. Klausmeier M. Crawford Young Chairman Director Director, R & D Center Department of Psychology Associate Dean Wisconsin Improvement Program Professor of Educational The Graduate School Psychology Archie A. Buchmiller Robert E. Grinder Donald J. McCarty Deputy State Superintendent Chairman Dean Department of Public Instruction Department of Educational School of Education Psychology *James W. Cleary H. Clifton Hutchins ha Sharkansky Vice Chancellor for Academic Chairman Associate Professor of Political Affairs Department of Curriculum and Science Instruction Leon D. Epstein Clauston Jenkins Henry C. Weinlick Dean Assistant Director Executive Secretary College of letters and Science Coordinating Committee for Wisconsin Education Association Higher Education EXECUTIVE COMMITTEE Edgar F. Borgatta Russell J. Hosier Wayne Otto Richard L. Venezky Brittingham Professor of Professor of Curriculum and Professor of Curriculum and Assistant Professor of English Sociology Instruction and of Business Instruction (Reading) and of Computer Sciences Max R. Goodson *Herbert J. Klausmeier Robert G. Petzold Professor of Educational Policy Director, R & D Center Associate Dean of the School Studies Professor of Educational of Education Psychology Professor of Curriculum and Instruction and of Music FACULTY OF PRINCIPAL INVESTIGATORS Ronald R. Allen Gary A. Davis Max R. Goodson Richard G. Morrow Associate Professor of Speech Associate Professor of Professor of Educational Policy Assistant Professor of and of Curriculum and Educational Psychology Studies Instruction Educational Administration Vernon L. Allen M. Vere DeVault Warren 0. Hagstrom Wayne Otto Associate Professor of Psychology Professor of Curriculum and Professor of Sociology Professor cf Curriculum and (On leave 1968-69) Instruction (Mathematics) Instruction (Reading) Nathan S. Blount Frank H. Farley John G. Harvey Milton 0. Pella Associate Professor of English Assistant Professor of Associate Professor of Professor of Curriculum and and of Curriculum and Educational Psychology Mathematics and Curriculum Instruction (Science) Instruction and Instruction Robert C. Calfee John Guy Fowlkes (Advisor) Herbert J. Klausmeier Thomas A. Romberg Associate Professor of Psychology Professor of Educational Director, R & 0 Center Assistant Professor of Administration Professor of Educational Mathematics and of Dire-tor of the Wisconsin Psychology Curriculum and Instruction Improvement Program Robert E. Davidson Lester S. Golub Burton W. Kreitlow Richard L. Venezky Assistant Professor of Lecturer in Curriculum and Professor of Educational Policy Assistant Professor of English Educational Psychology Instruction and in English Studies and of Agricultural and of Computer Sciences and Extension Education MANAGEMENT COUNCIL *Herbert J. Klausmeier Thomas A. Romberg James E. Walter Dan G. Woolpert Director, R & D Center Director Director Director Acting Director, Program I Programs 2 and 3 Dissemination Section Operations and Business Mary R. Quilling Director Technical Section * COMMITTEE CHAIRMAN STATEMENT OF FOCUS The Wisconsin Research and DevelopmentCenter for Cognitive Learning focuses on contributing toa better understanding of cognitive learning by children and youth andto the improvement of relatededucational prac- tices. The strategy for research anddevelopment is comprehensive. It includes basic research togenerate new knowledge about the conditions and processes of learning and aboutthe processes of instruction, and the subsequent development ofresearch-based instructional materials, many of which are designed for use by teachersand others foruse by students. These materials are tested and refinedin school settings. Throughout these operations behavioralscientists, curriculum experts, academic scholars, and school peopleinteract, insuring that the results of Center activitiesare based soundly on knowledge of subjectmatter and cognitive learning and that theyare applied to the improvement of educational practice. This Technical Report is from Phase 2of the Project on Prototypic Instructional Systems in Elementary Mathematicsin Program 2. General objectives of the Programare to establish rationale and strategy for developing instructional systems,to identify sequences of concepts and cognitive skills, to developassessment procedures for those concepts and skills, to identifyor develop instructional materials associated with the concepts and cognitive skills,and to generate new knowledge about instructional procedures. Contributing to the Program objectives, the Mathematics Project, Phase 1, isdeveloping and testinga televised course in arithmetic for Grades 1-6 which providesnot only a complete program of instruction for the pupils but alsoinservice training for teachers. Phase 2 has a long-term goal of providingan individually guided instructionalprogram in elementary mathematics. Preliminary activities include identifying instructionalobjectives, student activities, teacher activities materials,and assessment procedures for integration intoa total mathematics curriculum. The third phase focuses on the developmentof a computer system for managing individually guided instruction inmathematics and on a laterex- tension of the system's applicability. iii ACKNOWLEDGEMENTS I wish to expressmy sincere thanks and gratitude to Professor Thomas A. Romberg for his help,encouragement, and patience during my years of graduate study. I also wish to thank ProfessorJohn G. '4. Harvey for his penetratinganalysis of many of the problemsencoun- tered during thecourse of this study. In addition, my sincere appreciationgoes to Professors Gary A. Davis, J. Marshall Osborn,and J. Fred Weaver for servingon my committee.
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