TABLE OF CONTENTS
CHAPTER l Plenary Session Addresses	l
	Mathematics Improves the Mind	l
	George Polya

Major Problems of Mathematics Education
	Hans Freudenthal
	1.3	Young Children’s Acquisition of Language and Understanding of Mathematics	7
		    Hermina Sinclair
	Reactions to Hermina Sinclair’s Plenary Lecture	3
	Bill Higginson
	l	Some Experiences in Popularizing Mathematical Methods	l 6
		    Hua Loo-keng
	Reactions to Hua Loo-keng’s Plenary Lecture	23
	Dorothy Bernstein
	J.S. Gyakye Jackson
CHAPTER 2 - Universal Basic Education	27
	2. l	Mathematics in General Primary Education	27
		    Romanus O. Ohuche
	2.2	Back-to-Basics: Past, Present, Future	29
		    Max Sobel
	2.3	Suggested Mathematics Curricula for Students Who Leave School at Early Ages	32
		    Shirley Frye
		    Alonso B. Viteri Garrido
CHAPTER - Elementary Education	36
	Roots of Failure in Primary School Arithmetic	36
	Frederique Papy
	3.2	Do We Still Need Fractions in the ELementary Curriculum?	37
		    Peter Hilton
		    Mary Laycock
CHAPTER	Past-Secondary Education

Decline in Post-Secondary Students Continuing the Study of Mathematics 44
	James T. Fey
	R.R. McLone
Bienvenide F. Nebres
	4.2	Is Calculus Essential?	50
	Margaret E. Rayner
	Fred Roberts
	4.3	Mathematics and the Physical Science and Engineering	54
		    Gerhard Becker
		    Daniela Gori-Giorgi
		    Jean-Pierre Provost

Why	We Must and How We Can Improve the Teaching of Post-Secondary Mathematics 62 Henry L. Alder
	Detlef Laugwitz
	4.5	Alternate Approaches to Beginning’the Teaching of Calculus and the Effectiveness of These Methods	66
		    George Papy
		    Daniel Reisz
In What Ways Have the Mathematical Preparation of Students for Post-Secondary Mathematics Courses Changed? 70
	Kathleen Cross
	S.M. Sharfuddin
	4.7	Curriculum for A Mathematical Sciences Major	73
		    Alan Tucker
	4.8	University Programs with an Industrial Problem Focus	77
		    Jerome Spani er
		    Germund Dahlquist
		    A.Clayton Aucoin
		    Willian E. Boyce
		    J.L. Agnew
CHAPTER - The Profession of Teaching	89

Current Status and Trends in Teacher Education 89
	David Alexander
	Jeffrey Baxter
Sr. Iluminada C. Coronel, f.m.m.
	Hilary Shuard
	5.2	Integration of Content and Pedagogy in Pre-Service Teacher Education	96
		    Zbigniew Semadeni
		    Julian Weissglass

Preparation in Mathematics of a Prospective Elementary Teacher Today, in View of the Current Trends in Mathematics, in Schools, and in Society 00
	James E. Schultz
	5.4	Evaluation of Teachers and Their Teaching	102
		    Thomas J. Cooney
		    Edward C. Jacobsen
	5.5	Hand-held Calculators and Teacher Education	07
		    Willy Vanhamme

Computers in Mathematics Teacher Education 109
	Rosemary Fraser

The Mathematical Preparation of Secondary Teachers - Content and Method ill
	Trevor Fletcher
	5.8	Special Assistance for the Beginning Teacher	l 3
		    Edith Biggs
		    Mervyn Dunkley

The Making of a Professional Mathematics Teacher 8
	Gerald Rising
	Geoffry Howson

5.10	The Dilemma of Teachers Between Teaching What They Like and Teaching What the Pupils Need to Know:
How	Much Freedom Should Teachers Have to Add Materials, How Much Material, Which Teachers? l 24 Andrew C. Porter

5. l l Integration of Mathematical and Pedagogical Content In-Service Teacher Education: Successful and
	Unsuccessful Attempts	l 26
	David A. Sturgess
	E. Glenadine Gibb
	l 2	In-Service Education for Secondary Teachers	l 31
	Martin Barner
	Michel Darche
	Richard Pallascio
	5.13	Support Services for Teachers of Mathematics	l 40
		    Michael Silbert
		    Max Stephens
	5.14	What is a Professional Teacher of Mathematics?	44
		    John C. Egsgard
		    Jacques Nimier
		    Leopoldo Varela

CHAPTER - Geometry

Geometry in the Secondary School l 53
	Eric Gower
G.	Holland
Jean Pederson
Julio Castineira Merino

Geometric Activities in the Elementary School
Koichi Abe
John Del Grande

The Death of Geometry at the Post-Secondary Level l 65
	Branko Grunbaum
	Robert Osserman
	6.4	The Development of Children’s Spatial Ideas	7 l
		    Michael C. Mitchelmore
		    Dieter Lunkenbein
		    Kiyoshi Yokochi
		    Alan J. Bishop

CHAPTER - Stochastics l 79

Statistics:	Probability: Computer Science: Mathematics. Many Phases of One Program? l 79 Leo Klingen
	Richard S. Pieters
	7.2	Vigor, Variety and Vision - - the Vitality of Statistics and Probability	l 86
		    I.J. Good
	7.3	The Place of Probability in the Curriculum	l 90
		    Ruma Folk
		    Tibor Nemetz

The Nature of Statistics to be Taught in Schools l 98
	Jim Swift
	A.P. Shulte
	Peter Holmes
	7.5	Statistics and Probability in Teacher Education	202
		    Peter Holmes
		    Luis A. Santalo
CHAPTER 8 - Applications	207

Mathematics and the Biological Sciences - Implications for Teaching 207
	Sam O. Ale
	Diego Bricio Hernandez
	Lilia del Riego
	8.2	The Relationship of Mathematics and the Teaching of Mathematics with the Social Sciences	214
		    John Ling
		    Ivo W. Molenaar
		    Samuel Goldberg
	8.3	Applications, Modeling and Teacher Education	226
		    Aristedes C. Barreto
		    Hugh Burkhardt
	8.4	The Use of Modules to Introduce Applied Mathematics into the Curriculum	230
		    John Gaff ney
	8.5	Teaching Applications of Mathematics	233
		    F. van der Blij
		    Douglas A. Quadling
		    Paul C. Rosenbloom

The Interface between Mathematics and Imployment 236
	Connie Knox
	David R. Mathews
Rudolf Straesser
	Robert Lindsay
	P.C. Price
	Werner Blum
	8.7	How Effective are Integrated Courses in Mathematics and Science f or the Teaching of Mathematics?	247
		    Mogens Niss
		    Helmut Siemon
	8.8	Materials Available Worldwide for Teaching Applications of Mathematics at the School Level	252
		    Max S. Bell
	8.9	Mutualism in Pure and Applied Mathematics	267
		    Maynard Thompson
		    Donald Bushaw
		    Candido Sitia
CHAPTER	Problem Solving 276
		Teaching for Effective Problem Solving: A Challenging Problem	276
	Shmuel Avital
Jose R. Pascual Ibarra
	Ian Isaacs
	9.2	Real Problem Solving	283
Diana Burkhardt
	9.3	Mathematization, Its Nature and Its Use in Education	285
		    Eric Love
		    Marion Walter
		    David Wheeler
	9.4	The Mathematization of Situations Outside Mathematics from an Educational Point of View	291
		    RoIf Biehler
		    Tatsuro Miwa
		    Christopher Ormell
		    Vern Treilibs
CHAPTER	Special Mathematical Topics 299
	Algebraic CodingTheory	299
	J.H. van Lint
	Combinatorics	303
	Nicolas Balacheff
David Singmaster

The Impact of Algorithms on Mathematics Teaching 31 2
	Arthur Engel
		Operations Research	330
	William F. Lucas

Maxima and Minima Without Calculus 336
A.J. Lohwater
	Ivan Niven

Exploratory Data Analysis 344
Ram Gnanadesikan
Paul Tukey
Andrew F. Siegel
Jon R. Kettenring
xi

CHAPTER - Mathematics Curriculum

Successes and Failures of Mathematics Curricula in the Past Two Decades
H.	Brian Griffiths
Ubiratan D’Ambrosio
Stephen S. Willoughby

Curriculum Recommendations for the 1980’s by Several National Committees 366
Mohammed El Tom
W.H. Cockcroft
David F. Robitaille

Curriculum Changes During the 1980’s 371
Shigeo Katagiri
Alan Osborne
Hans-Christian Reichel

The Changing Curriculum - An International Perspective 382
E.E. Oldham

Models of Curriculum Development 384
Tashio Miyamoto and Ko Gimbayasgu
James M. Moser

Mathematics for Secondary School Students 388
Harold C. Trimble

What	Should be Dropped from the Secondary School Mathematics Curriculum to Make Room for New Topics? Ping-tung Chang
Zalman Usiskin
	Alternative Approaches to the Teaching of Algebra in the Secondary School	394
	    Harry S.J. Instone
	How Can You Use History of Mathematics in Teaching Mathematics in Primary and Secondary Schools?		396
Casey Hum phreys
Bruce Meserve
Leo Rogers
Maassouma M. Kazim

CHAPTER l 2 - The Begle Memorial Series on Research in Mathematics Education 405

Critical Variables in Mathematics Education 405
Richard E. Snow
Herbert J. Walberg

Some Critical Variables Revisited 41 2
Christine Keitel-Kreidt
Donald J. Dessart
L.	Ray Carry
Jens H. Lorenz
Nicholas A. Branca

Some New Directions for Research in Mathematics Education 424
Richard E. Mayer
Edward A. Silver
Robert B. Davis
Gunnar Gjone
John P. Keeves
Thomas Cooney

CHAPTER 13 - Research in Mathematics Education 444

The Relevance of Philosophy and History of Science and Mathematics for Mathematical Education 444
Niels Jahnke
Rolando Chauqui
Giles Lachaud
David Pimm
Research in Mathematical Problem Solving 452 Gerald A. Goldin
Alan H. Schoenfeld

Researchable Questions Asked by Teachers 456
Elaine Bologna
Sadaaki Fujimori
Douglas E. Scott
Richard J. Shumway

Alternative Methodologies for Research in Mathematics Education 461
George Booker
Jack Easley
Francois Pluvi nage
R.W. Scholz
Leslie P. Steffe
Joan Yates

Error Analyses of Childrens’ Arithmetic Performance 474
Annie Bessot
Leroy C. Callahan
Roy Hollands
Fredricka Reisman

Comparative Study of the Development of Mathematical Education as a Professional Discipline in Different Countries 482
Gert Schubring
Mahdi Abdeljaouad
Phillip S. Jones
Janine Rogalski
Gert Shubring
Derek Woodrow
Vaclaw Zawadowski

The Development of Mathematical Abilities in Children 489
Jeremy Kilpatrick
Horacio Rimoldi
Raymond Sumner
Ruth Rees

The Child’s Concept of Number 499
Karen Fuson
Shuntaro Sato
Claude Comiti
Tom Kieren
Gerhard Steiner

l 3.9	Relation Between Research on Mathematics Education and Research on Science Education. Problems of Common Interest and Future Cooperation 511
Charles Taylor
Anthony P. French
Robert Karplus
Gerard Vergnaud

13.10	Central Research Institutes for Mathematical Education. What Can They Contribute to the Development of the Discipline and the Interrelation between Theory and Practice? 520
Edward Esty
Georges Gloeser
Heini Halberstam
Yashihiko Hashimoto
	Thomas Romberg
	Christine Keitel
	B. Winkelman
13.11	The Functioning of Intelligence and the Understanding of Mathematics	530
	    Richard Lesh
	    Richard Skemp
	    Laurie Buxton
	    Nicholas Herscovics
	13.12	The Young Adolescent’s Understanding of Mathematics	541
		    Stanley Bezuska
		    Kath Hart
CHAPTER	- Assessment 546

Assessing Pupils’ Performance in Mathematics 546
	Norbert Knoche
Robert Lindsay
Ann McAloon

Issues, Methods and Results of National Mathematics Assessments 553
Bob Roberts
CHAPTER	- Competitions	557

Mathematical Competitions, Contests, Olympiads 557
Jan van de Croats
Neville Gale
Jose Ipina
Lucien Kieffer
Murray Klamkin
Peter J. O’Halloran
Peter R. Sanders
Janos Suranyi

Mathematics Competitions: Philosophy, Organization and Content 566
Albert Kalfus

CHAPTER 16 - Language and Mathematics 568

Language and the Teaching of Mathematics 568
A.	Geoffrey Howson

The Relationship Between the Development of Language in Children and the Development of Mathematical Concepts in Children
F.D. Lowenthal
Michele Pellerey
Colette Laborde
Tsutornu Hosoi

Teaching Mathematics in a Second Language 582
Maurizio Gnere
Althea Young

CHAPTER 17 - Objectives
	Teaching for Combined Process and Content Objectives	587
Alan W. Bell
A.J. Dawson
P.G. Human
	The Complementary Role of Intuitive and Analytical	Reasoning	595
Erich Wittmann
Efraim Fischbein
Leon A. Henkin

CHAPTER 18 - Technology 605

The Effect of the Use of Calculators on the Initial Development and Acquisition of Mathematical Concepts and
Skills	605
Hartwig Meissner

A Mini-Course on Symbolic and Algebraic Computer Programming Systems 606
Richard J. Fateman
The Use of Programmable Calculators in the Teaching of Mathematics 612
Klaus-D. Graf
Guy Noel
K.A. Keil
H.	Lothe

Perspectives and Experiences with Computer-Assisted Instruction in Mathematics 623 D. Alderman
R.	Gunzehauser

Computer Literacy Awareness in Schools; What, How and for Whom? 627
David C. Johnson
Claudette Vieules
Andrew Mol nor

The Technological Revolution and Its Impact on Mathematics Education 632
Andrea DiSessa

Calculators in the Pre-Secondary School 637
Marilyn Suydam
A.	Wynands
CHAPTER	Forms and Modes of Instruction 641

Distance Education for School-age Children 641
David Roseveare

Teaching Mathematics in Mixed-Ability Groups 643
Denis C. Kennedy
David Lingard

Approaching Mathematics through the Arts 648
Emma Castelnuovo
Paul Delannoy
James R.C. Leitzel

The Use and Effectiveness of Mathematics Instructional Games 652
Margariete Montague Wheeler

Strategies for Improving Remediation Efforts 654
Ronald Davis
Deborah Hughes Hallett
Gerald KuIm
Joan R. Leitzel

Individualized Instruction and Programmed Instruction 661
F.	Alvarado

CHAPTER 20 - Women and Mathematics 665

A Community Action Model to Increase the Participation of Girls and Young Women in Mathematics 665
Elizabeth Stage
	Kay Gilliland
	Nancy Kreinberg
	Elizabeth Fennema
	20.2	Contributions by Women to Mathematics Education
		    Kristina Leeb-Lundberg
	20.3	The Status of Women and Girls in Mathematics: Progress and Problems	674
		    Marjorie C. Carss
		    Eileen L. Poiani
		    Nancy Shelley
		    Dora Helen Skypek
	20.4	Special Problems of Women in Mathematics	682
		    Erika Schildkamp-Kundiger

CHAPTER - Special Groups of Students 688

Curriculum Organizations and Teaching Modes That Successfully Provide for the Gifted Learner 688
A.L. Blakers
Isabelle P. Rucker
Burt A. Kaufman
Gerald Rising
Dorothy S. Strong
Arnold E. Ross
Graham T.Q. Hoare

Distance Education for Adults 702
Michael Crampin

Adult Numeracy - Programmes for Adults Not in School 705
Anna Jackson
Peter Kaner

Problems of Defining the Mathematics Curriculum in Rural Communities 708
Desmond Broomes
P.K. Kuperus

Participation of the Handicapped in Mathematics 711
Robert Di eschbourg
Carole Greenes
Esther Pillar Grossi