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[Mathematics Education 5] Alexander Karp, Bruce R. Vogeli (editors) - Russian Mathematics Education Programs and Practices (Mathematics Education) (2011, World Scientific Publishing Company)
Document Outline Contents Introduction Chapter 1. On the Mathematics Lesson Alexander Karp and Leonid Zvavich 1 Introduction 2 Who Participates in the Class and Where Classes Are Conducted: Background 2.1 Teachers and Students 2.2 The Mathematics Classroom and Its Layout 3 Certain Issues in Class Instruction Methodology 3.1 On the History of the Development of Class Instruction Methodology in Russia 3.2 Types of Lessons and Lesson Planning 4 Problem Solving in Mathematics Classes 5 Epilogue: Bad Lessons, and What One Would Like to Hope for References Chapter 2. The History and the Present State of Elementary Mathematical Education in Russia Olga Ivashova 1 Introduction 2 The History of Arithmetical Education in Russia During the 10th–18th Centuries 3 Elementary Mathematical Education in Russia in the 19th and Early 20th Centuries (through 1917) 3.1 The Method of Learning Operations 3.2 The Monographical Method of Learning the Numbers 3.3 On Some Pre-Revolution Handbooks for the Elementary School 4 Elementary Education in the Complex Programs of Soviet Russia, 1918–1932 5 The Study of Arithmetic in the Soviet Elementary School, 1932–1969 6 The Elementary Course in Mathematics in the Soviet School, 1969–1990s 7 Elementary Mathematical Education in Russia, 1990s 7.1 Fundamental Program Requirements and Characteristics of Contemporary Textbooks 7.2 The Content of the Elementary Course in Mathematics 7.2.1 Numbers and arithmetical operations 7.2.2 Arithmetical problems 7.2.3 Magnitudes 7.2.4 Geometrical content 7.2.5 Elements of algebra 7.2.6 Elements of combinatorics 7.2.7 Elements of logic, set theory, modeling 7.2.8 Working with data 8 Conclusion References Chapter 3. On the Teaching of Geometry in Russia Alexander Karp and Alexey Werner 1 Introduction 2 The Contents of the Course in Geometry in Russian Schools 3 The Aims and Characteristics of the Course in Geometry in Russia 4 On the Conditions Under Which Geometry Is Taught 5 Toward a History of the Course in Geometry in Russia (USSR) 5.1 From Kiselev to Kolmogorov 5.2 Kolmogorov’s Textbooks for Basic Schools 5.3 Geometry Textbooks for Basic Schools from the Late 1970s to the 1980s 5.3.1 A. V. Pogorelov’s geometry textbook 5.3.2 The geometry textbooks of L. S. Atanasyan and his coauthors 5.3.3 The textbooks of A. D. Alexandrov and his coauthors 5.4 Textbooks That Appeared After the Collapse of the USSR 5.4.1 I. F. Sharygin’s textbooks 5.4.2 The textbooks of I. M. Smirnova and V. A. Smirnov 5.4.3 The textbooks of A. L. Werner and his coauthors 6 Concerning Some Problems with the Course in Geometry in Russia in Recent Decades 6.1 The Problem of the Rigor of the Course in Geometry 6.2 Visual and Informal Geometry in the Study of Three-dimensional Geometry in Basic Schools 6.3 The New and the Old in the Teaching of Geometry References Chapter 4. On Algebra Education in Russian Schools Liudmila Kuznetsova, Elena Sedova, Svetlana Suvorova and Saule Troitskaya 1 Algebra as a School Subject 2 The Algebraic Component in the System of School Mathematics Education 3 The Content of Algebra Education in Russian Schools 4 Methodological Issues in Teaching Algebra 4.1 Basic School (grades 5–9; students aged 10–15) 4.1.1 An Overview 4.1.2 Algebra for students of ages 10–12 (grades 5–6) 4.1.3 Algebra for students of ages 12–15 (grades 7–9) 4.1.4 Examples of test problems 4.2 High School (grades 10–11; students aged 16–17) 4.2.1 An overview 4.2.2 The study of algebraic expressions in grades 10–11 4.2.3 Equations and inequalities in the basic and advanced courses in mathematics in grades 10–11 4.2.4 The final attestation in algebra for 11th graders References Chapter 5. Elements of Analysis in Russian Schools Mikhael Jackubson 1 Introduction 2 Elements of Analysis in Normative Documents 3 The History of Higher Mathematics Education in Russian (Soviet) Schools 3.1 The Second Third of the 18th Century to 1845 3.2 1846–1906 3.3 1907–1917 3.4 1918–1933 3.5 1934–1964 3.6 1965–1976 3.7 1977 to the End of the 1980s 3.8 Early 1990s to the Present 4 Introduction to Analysis: Functions in Basic School 5 Algebra and Elementary Calculus: Functions in Grades 10–11 6 Elements of Differential and Integral Calculus 6.1 Andrey Kolmogorov’s Textbook 6.2 The Textbooks of Alimov et al. and Kolyagin et al. 6.3 M. I. Bashmakov’s Textbook 6.4 New Generation Textbooks 6.4.1 The textbook of A. G. Mordkovich and I. M. Smirnova 6.4.2 The textbook of G. K. Muravin and O. V. Muravina 7 Conclusion References Chapter 6. Combinatorics, Probability, and Statistics in the Russian School Curriculum Evgeny Bunimovich 1 Finite Mathematics in the School Curriculum Prior to the Revolution of 1917 2 Finite Mathematics in the Secondary School Curriculum in the Soviet Period 3 Finite Mathematics in the Post-Soviet Period 4 Features of Contemporary Approaches to the Study of Finite Mathematics in Russian Schools 5 First Results of Teaching the Experimental Curriculum 6 Conclusion References Chapter 7. Schools with an Advanced Course in Mathematics and Schools with an Advanced Course in the Humanities Alexander Karp 1 Introduction 2 The Appearance of Schools and Classes with an Advanced Course in Mathematics 3 Mathematics Schools During the Period of Stagnation and Later 4 The Everyday Life of Mathematics Schools 5 Curricula, Textbooks, Approaches 5.1 On Curricula 5.2 On the Specifics of Teaching the Course in Mathematics 5.3 On the Content of Certain Topics in the Course 5.4 On Textbooks for Schools with an Advanced Course of Study in Mathematics 6 Schools with a Humanities Orientation 7 Curricula and Textbooks for Humanities-Oriented Schools 8 Conclusion References Chapter 8. Assessment in Mathematics in Russian Schools Alexander Karp and Leonid Zvavich 1 Introduction 2 General Assessment Issues 2.1 What Is Assessed and Why? 2.2 Assessment in the Past 2.3 Some Facts About the Organization of the Teaching Process and of Assessment 3 On the Nature of the Assignments Used for Assessment 4 Oral Questioning in Class 4.1 The “From the Seat” Response 4.2 The “At the Board” Response 4.2.1 Going over homework assignments 4.2.2 Questioning students about theoretical material 4.2.3 Solving problems on the blackboard 5 Written Work 5.1 Tests 5.2 Quizzes 5.3 Mathematical Dictations 5.4 Individual Written Questioning of the Student in Class 6 Long-Term Assignments 7 Exams and Oral Survey Tests 7.1 Oral Survey Tests 7.2 Exams 8 Conclusion References Chapter 9. Extracurricular Work in Mathematics Albina Marushina and Maksim Pratusevich 1 Introduction 2 Mass Forms of Extracurricular School Work 2.1 Mathematical Wall Newspapers 2.2 Mathematical Theatrical Evenings and Oral Mathematics Journals 2.3 Mathematical Tournaments 2.4 Written Problem-Solving Contests 3 School Mathematics Circles and Electives 3.1 Mathematics Circles in Grades 5–6 3.2 Mathematics Circles and Electives in Grades 7–9 3.3 Mathematics Circles and Electives in Grades 10–11 4 On Various Forms of Distance Learning 5 Selective Forms of Working with Students 5.1 On Mathematics Circles 5.2 Mathematics Summer Camps 5.3 Conferences 6 Conclusion References Chapter 10. On Mathematics Education Research in Russia Alexander Karp and Roza Leikin 1 Introduction 2 On Certain Features of the Organization of Scienti.c Research in the Area of Mathematics Education and on Our Sources 3 Issues in the Philosophy and Worldview of Mathematics Education 4 The Psychology of Mathematics Education 5 Problem Solving 6 The History of Mathematics Education 7 Issues of Differentiation in Education 8 The Organization of the Educational Process 9 Studying the Process of Teaching Mathematics: Connections Within Subjects, Continuity and Succession in Education 10 Teaching Aids 11 Teaching in Elementary Schools 12 On Teaching Speci.c Mathematical Subjects in Schools 13 Teaching in Nonpedagogical Institutions of Higher Education 14 Mathematics Teacher Education 14.1 General Questions of Mathematics Teacher Education 14.2 Special Aspects of the Methodological Preparation of Future Teachers 14.3 On Teaching Mathematics to Future Teachers 14.4 Technology in Mathematics Teacher Education 15 On Candidate’s Dissertations 16 Conclusion References Notes on Contributors Name Index Subject Index Do'stlaringiz bilan baham:
