Ma DATE 72 NOTE 528P
Total Page:16
File Type:pdf, Size:1020Kb
DOCUMENT RESUME --ED 071 870 SE 015 453 . , . AUTHOR Lowry, William C., Ed. TITLE, The Slow Learner in Mathematics. NCTM Yearbook 35. INSTITUTION National Council of Teachers of Mathematics, Inz;., Washington, D.C. ma DATE 72 NOTE 528p.. AVAILABLE fROMNational Council of Teachers of Mathematics, 1201 Sixteenth Street N. W.., Washington, D. C, 20036 (8.50, $7.50 for NCTM members) . EDRS PRICE ?F -$0.65 HC Not Available from EDRS. ,DESCRIPTORS *Activity Learning; *Curriculum; *Insti tion; Instructional Materials; Laboratory Procedures; *Mathematics Education; Objectives; *Slow Learners; Teacher Education; Teaching Methods ABSTRACT The first part of this yearbook treats the characteristics and needs of the slow learner, the research .literature, behavioral objectives, and the creation ofa favorable learning environment. The second part, meant to providemore specific help for the classroom teacher, deals with teaching techniques, iudtisensory aids and activities, mathematics laboratories, and diagnostic-prescriptive procedures. The third part covers classroom management and school administration, curiciculum for slow learners, and program descriptions for in- service, teacher education. Two appendices present activities, games, applications, and sample lessons that have been found to be effective with slowlearners. (Author/DT) -,17,1 yrm -3. -14.404t4,14.1t.011',1"wl" YEARBOOKS published by the National Council of Teachers of Mathematics First. Yea 'book : A General Survey of Progress in the Last Twenty -fireYears Second Yearbook: Curriculum Problems in Teaching Mathematics Third Yearbook: Selected Topics in the Teaching of Mathematics Fourth Yearbook: Significant Changes and. Trends in the Teaching of Mathematics throughout the World since 1910 Fifth Yearbook: The Teaching of Geometry Sixth Yearbook: Mathematics in Modern Life Seventh Yearbook: The Teaching of Algebra Eighth Yearbook: The Teaching of Mathematics in the SecondarySchool Ninth Yearbook: Relational and Functional Thinking in Mathematics Tenth Yearbook: The Teaching of Arithmetic Eleventh Yearbook: The Place of Mathematic, in Modern Education Twelfth Yearbook: Approximate Computation Thirteenth Yearbook: The Nature of Proof Fourteenth Yearbook: The Training of Mathematics Teachers Fifteenth Yearbook: The Place of Mathematics in SecondaryEducation Sixteenth Yearbook: Arithmetic in General Education Seventeenth Yearbook: A Source Rook of Mathematical Applications Eighteenth Yearbook: Multi-Sensory Aids in the Teaching ofMathematics Nineteenth Yearbook: Surveying Instruments: Their Historyand Classroom Use Twentieth Yearbook: The Metric System of Weights and Measure, Twenty -first. Yearbook: The Learning of Mathematics: Its Theory and Practice Twenty-second Yearbook: Emerging Practice, in Alathematic, Education Twenty-third Yearbook: Insights rout Modern Mathematics Twenty-fourth Yearbook: The Growth of Mathematical Ideas, Grades K-12 Twenty-fifth YearbookInstruction in Arithmetic Twenty-sixth Yearbook: Evaluation in Mathematics Twenty-seventh Yearbook: Enrichment Mathematics for the Grade, Twenty-eighth Yearbook: Enrichment Mathematics for High School Twenty-ninth Yearbook: Topics in Mathematic, for Elementary SchoolTeachers Thirtieth Yearbook: More Topics in Mathematic, for Elementary School Teacher., Thirty-first Yearbook: Historical Topics for the MathematicsClassroom Thirty-second Yearbook: A History of Mathematics Education inthe United States and Canada Thirty-third Yearbook : The Teaching of Secondary SchoolMathematics Thirty-fourth Yearbook: Instructional Aids in Mathematics Thirty-fifth Yearbook: The Slow Learner in 3/athematic& The Slow Learner in Mathematics Thirty-fifth Yearbook National Council of Teachers of Mathematics 1972 PERMISSION TO REPRODUCE THIS COPY RIGHTED MATERIAL BY MICROFICHE ONLY .IAS BEEN GRANTED BY N.C.T.M. TO ERIC AND ORGANIZATIONS OPERATING UNDER AGREEMENTS WITH THE US OFFICE OF EDUCATION FURTHER REPVIDUCTION OUTS,E THE ERIC SYSTEM RECUIRES PER MISSION OF THE COPYRIGHT OWNER Copyright © 1972 by THE NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS.INC. 1201 Sixteenth Street, NW, Washington, D.C. 20036 All rights reserved Library of Congress Cataloging in Publication Data: National Council of Teachers of Mathematics. The slow learner in mathematics. (Its Yearbook 35) Includes bibliographies. 1. MathematicsStudy and teachingAddresses. essays, lectures.2. Slow learning children Addresses, essays, lectures.I. Title.II. Series. QA1.N3 35th[QA11] 512%1'07 72-8350 Printed in the United States of America Contents Preface vii Acknowledgments xii I. Characteristics and Needs of the Slow Learner 1 Richard TV. Schulz, Cedar Rapids Community Schools, Cedar Rapids, Iowa 2. The Research Literature 26 Len Pikaart, University of Georgia, Athens, Georgia James TV. Wilson. University of Georgia, Athens, Georgia 3. Behavioral Objectives 52 Henry II. Wolbesser, University of Maryland, College Park, Maryland Heather L. Carter. University of Texas, Austin, Texas 4. A Favorable Learning Environment 104 James R. Pearson, Dade County Public Schools, Miami, Florida 5. Adjustment of Instruction (Elementary School) 129 Charlotte W. Junge, Wayne State University, Detroit , Michigan 6. Teaching Styles (Secondary School) 163 Elizabeth A. Collins, Dade County Public Schools, Miami, Florida 7. Aids and Activities 182 Evan M. Maletsky. Montclair State College, Upper Montclair, New Jersey Vi CONTENTS 8.The Laboratory Approach 221 Patricia S. Davidson. Boston State College, Boston, Mas,a- chusetts Marton I. Walter, Graduate School of Education,Harvard University, Cambridge, Massaclmsetts 9. Diagnostic-Prescriptive Teaching 282 Vincent J. Glenn" The University of Connecticut,Storrs, Connecticut John W. Wilson, University of Maryland, CollegePark, Maryland 10. Classroom and School Administration 319 Paid V. Rog ler, Wilmington Public Schools, Wilmington,Dela- ware 11. Promising Programs and Practices 345 12. The Training of Teachers 402 Dora Helen Skypek, Emory University, Atlanta,Georgia Appendix A: Activities, Games, and Applications 444 Thomas E. Rowan, Maryland State Departmentof Education, Baltimore, Maryland William G. McKenzie, Prince Georges CountyPublic Schools, Upper Marlboro, Maryland Appendix B: Sample Lessons 487 Index . 521 Preface In the revolution that has reshaped school mathematics over the past twenty years, the major efforts at first were in behalf of the capable student. Experienced teachers, however, have long been aware that mathematically capable students comprise only a part of the student population. A group often as large as the capable group, and in some schools larger, is made up of students who have considerable difficulty learning mathematics and whose achievement is noticeably below de- sired levels. Dedicated mathematics teachers have addressed them- selves to the problems of these students for many years. By the sixth decade of the twentieth century, however, the need for greater math- ematical competency on the part of all members of society was becoming increasingly clear. National, state, and local interest started to focus more than previously on the large number of studentsin our schools who have trouble learning generally; and among these, of course, are those who have trouble learning mathematics. The Yearbook Planning Committee of the NCTM, at its April 1966 meeting, agreed to recommend to the Board of Directors a year- book on the slow learner in mathematics,, subject to the following limitations: 1. No attempt was to be made to identify such students beyond the general definition of "students who are not achieving at the desired level." 2. The yearbook was to deal with the subject matter objectivesfor slow learners and the methods for attaining these objectives at various levels. The Board approved the recommendation, and a planning com- mittee for the yearbook was formed. The planning committeehad as vii Viii PREFACE its immediate work the developmentof a proposal for a conference on the slow learner in mathematics. Itwas hoped the conference would generate ideas that wouldculminate in the yearbook. The planning committee completed itswork in April 1967, whereuponan editor and an editorial panel for theyearbook were appointed. Four of the original planning committeemembers remained on the editorial panel. Vincent Brant replaced .JackE. Forbes, who became chairman of the NCTNI Yearbook PlanningCommittee at that time. The conference approach to generatingideas for the yearbook did not prove feasible because of thecost of such an undertaking, and that approach was abandoned.During the early part of 1968 the editorial panel met twice. At thosemeetings we agreed on basic themes for the yearbook, selectedtentative titles for the chapters, sketched chrpter outlines, and selectedprospective authors. In August 1968 a schedule and a budget for theyearbook were proposed to the Board of Directors. The Boardapproved the proposal later that year. By early 1969 the writing team for the yearbookwas complete. The editorial panel agreed with thefirst limitation set by the Year- book Planning Committee and didnot attempt to identify slow learners other than by noting that theseare students who are net achieving at the desired level. \Vewere well aware that there are a number of reasons why students do not achieve. \Vewere also aware of the number of differentlabelsunderachiever, low achiever, low- ability student, disadvantaged student,and so forthappliea to various groups of these students. Wechose to use the term slow learner because the studentswe