Proceedings of the Fourth International Congress on Mathematical Education

1 — Plenary Session Addresses.- 1.1 Mathematics Improves the Mind.- 1.2 Major Problems of Mathematics Education.- 1.3 Young Children’s Acquisition of Language and Understanding of Mathematics.- Reactions to Hermina Sinclair’s Plenary Lecture.- 1.4 Some Experiences in Popularizing Mathematical Methods.- Reactions to Hua Loo-keng’s Plenary Lecture.- 2 — Universal Basic Education.- 2.1 Mathematics in General Primary Education.- 2.2 Back-to-Basics: Past, Present, Future.- 2.3 Suggested Mathematics Curricula for Students Who Leave School at Early Ages.- 3 — Elementary Education.- 3.1 Roots of Failure in Primary School Arithmetic.- 3.2 Do We Still Need Fractions in the ELementary Curriculum?.- 4 — Post-Secondary Education.- 4.1 Decline in Post-Secondary Students Continuing the Study of Mathematics.- 4.2 Is Calculus Essential?.- 4.3 Mathematics and the Physical Science and Engineering.- 4.4 Why We Must and How We Can Improve the Teaching of Post-Secondary Mathematics.- 4.5 Alternate Approaches to Beginning the Teaching of Calculus and the Effectiveness of These Methods.- 4.6 In What Ways Have the Mathematical Preparation of Students for Post-Secondary Mathematics Courses Changed?.- 4.7 Curriculum for A Mathematical Sciences Major.- 4.8 University Programs with an Industrial Problem Focus.- 5 — The Profession of Teaching.- 5.1 Current Status and Trends in Teacher Education.- 5.2 Integration of Content and Pedagogy in Pre-Service Teacher Education.- 5.3 Preparation in Mathematics of a Prospective Elementary Teacher Today, in View of the Current Trends in Mathematics, in Schools, and in Society.- 5.4 Evaluation of Teachers and Their Teaching.- 5.5 Hand-held Calculators and Teacher Education.- 5.6 Computers in Mathematics Teacher Education.- 5.7 The Mathematical Preparation of Secondary Teachers — Content and Method.- 5.8 Special Assistance for the Beginning Teacher.- 5.9 The Making of a Professional Mathematics Teacher.- 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?.- 5.11 Integration of Mathematical and Pedagogical Content In-Service Teacher Education: Successful and Unsuccessful Attempts.- 5.12 In-Service Education for Secondary Teachers.- 5.13 Support Services for Teachers of Mathematics.- 5.14 What is a Professional Teacher of Mathematics?.- 6 — Geometry.- 6.1 Geometry in the Secondary School.- 6.2 Geometric Activities in the Elementary School.- 6.3 The Death of Geometry at the Post-Secondary Level.- 6.4 The Development of Children’s Spatial Ideas.- 7 — Stochastics.- 7.1 Statistics: Probability: Computer Science: Mathematics. Many Phases of One Program?.- 7.2 Vigor, Variety and Vision -- the Vitality of Statistics and Probability.- 7.3 The Place of Probability in the Curriculum.- 7.4 The Nature of Statistics to be Taught in Schools.- 7.5 Statistics and Probability in Teacher Education.- 8 — Applications.- 8.1 Mathematics and the Biological Sciences — Implications for Teaching.- 8.2 The Relationship of Mathematics and the Teaching of Mathematics with the Social Sciences.- 8.3 Applications, Modeling and Teacher Education.- 8.4 The Use of Modules to Introduce Applied Mathematics into the Curriculum.- 8.5 Teaching Applications of Mathematics.- 8.6 The Interface between Mathematics and Imployment.- 8.7 How Effective are Integrated Courses in Mathematics and Science for the Teaching of Mathematics?.- 8.8 Materials Available Worldwide for Teaching Applications of Mathematics at the School Level.- 8.9 Mutualism in Pure and Applied Mathematics.- 9 — Problem Solving.- 9.1 Teaching for Effective Problem Solving: A Challenging Problem.- 9.2 Real Problem Solving.- 9.3 Mathematization, Its Nature and Its Use in Education.- 9.4 The Mathematization of Situations Outside Mathematics from an Educational Point of View.- 10 — Special Mathematical Topics.- 10.1 Algebraic Coding Theory.- 10.2 Combinatorics.- 10.3 The Impact of Algorithms on Mathematics Teaching.- 10.4 Operations Research.- 10.5 Maxima and Minima Without Calculus.- 10.6 Exploratory Data Analysis.- 11 — Mathematics Curriculum.- 11.1 Successes and Failures of Mathematics Curricula in the Past Two Decades.- 11.2 Curriculum Recommendations for the 1980’s by Several National Committees.- 11.3 Curriculum Changes During the 1980’s.- 11.4 The Changing Curriculum — An International Perspective.- 11.5 Models of Curriculum Development.- 11.6 Mathematics for Secondary School Students.- 11.7 What Should be Dropped from the Secondary School Mathematics Curriculum to Make Room for New Topics?.- 11.8 Alternative Approaches to the Teaching of Algebra in the Secondary School.- 11.9 How Can You Use History of Mathematics in Teaching Mathematics in Primary and Secondary Schools?.- 12 — The Begle Memorial Series on Research in Mathematics Education.- 12.1 Critical Variables in Mathematics Education.- 12.2 Some Critical Variables Revisited.- 12.3 Some New Directions for Research in Mathematics Education.- 13 — Research in Mathematics Education.- 13.1 The Relevance of Philosophy and History of Science and Mathematics for Mathematical Education.- 13.2 Research in Mathematical Problem Solving.- 13.3 Researchable Questions Asked by Teachers.- 13.4 Alternative Methodologies for Research in Mathematics Education.- 13.5 Error Analyses of Childrens’ Arithmetic Performance.- 13.6 Comparative Study of the Development of Mathematical Education as a Professional Discipline in Different Countries.- 13.7 The Development of Mathematical Abilities in Children.- 13.8 The Child’s Concept of Number.- 13.9 Relation Between Research on Mathematics Education and Research on Science Education. Problems of Common Interest and Future Cooperation.- 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?.- 13.11 The Functioning of Intelligence and the Understanding of Mathematics.- 13.12 The Young Adolescent’s Understanding of Mathematics.- 14 — Assessment.- 14.1 Assessing Pupils’ Performance in Mathematics.- 14.2 Issues, Methods and Results of National Mathematics Assessments.- 15 — Competitions.- 15.1 Mathematical Competitions, Contests, Olympiads.- 15.2 Mathematics Competitions: Philosophy, Organization and Content.- 16 — Language and Mathematics.- 16.1 Language and the Teaching of Mathematics.- 16.2 The Relationship Between the Development of Language in Children and the Development of Mathematical Concepts in Children.- 16.3 Teaching Mathematics in a Second Language.- 17 — Objectives.- 17.1 Teaching for Combined Process and Content Objectives.- 17.2 The Complementary Role of Intuitive and Analytical Reasoning.- 18 — Technology.- 18.1 The Effect of the Use of Calculators on the Initial Development and Acquisition of Mathematical Concepts and Skills.- 18.2 A Mini-Course on Symbolic and Algebraic Computer Programming Systems.- 18.3 The Use of Programmable Calculators in the Teaching of Mathematics.- 18.4 Perspectives and Experiences with Computer-Assisted Instruction in Mathematics.- 18.5 Computer Literacy / Awareness in Schools; What, How and for Whom?.- 18.6 The Technological Revolution and Its Impact on Mathematics Education.- 18.7 Calculators in the Pre-Secondary School.- 19 — Forms and Modes of Instruction.- 19.1 Distance Education for School-age Children.- 19.2 Teaching Mathematics in Mixed-Ability Groups.- 19.3 Approaching Mathematics through the Arts.- 19.4 The Use and Effectiveness of Mathematics instructional Games.- 19.5 Strategies for Improving Remediation Efforts.- 19.6 Individualized Instruction and Programmed Instruction.- 20 — Women and Mathematics.- 20.1 A Community Action Model to Increase the Participation of Girls and Young Women in Mathematics.- 20.2 Contributions by Women to Mathematics Education.- 20.3 The Status of Women and Girls in Mathematics: Progress and Problems.- 20.4 Special Problems of Women in Mathematics.- 21 — Special Groups of Students.- 21.1 Curriculum Organizations and Teaching Modes That Successfully Provide for the Gifted Learner.- 21.2 Distance Education for Adults.- 21.3 Adult Numeracy — Programmes for Adults Not in School.- 21.4 Problems of Defining the Mathematics Curriculum in Rural Communities.- 21.5 Participation of the Handicapped in Mathematics.