Russian Mathematics Education

The following sections are included:

• Contents

• Introduction

The following sections are included:

• Introduction

• Who Participates in the Class and Where Classes Are Conducted: Background
  • Teachers and Students
  • The Mathematics Classroom and Its Layout

• Certain Issues in Class Instruction Methodology
  • On the History of the Development of Class Instruction Methodology in Russia
  • Types of Lessons and Lesson Planning

• Problem Solving in Mathematics Classes

• Epilogue: Bad Lessons, and What One Would Like to Hope for

• References

The following sections are included:

• Introduction

• The History of Arithmetical Education in Russia During the 10th–18th Centuries

• Elementary Mathematical Education in Russia in the 19th and Early 20th Centuries (through 1917)
  • The Method of Learning Operations
  • The Monographical Method of Learning the Numbers
  • On Some Pre-Revolution Handbooks for the Elementary School

• Elementary Education in the Complex Programs of Soviet Russia, 1918–1932

• The Study of Arithmetic in the Soviet Elementary School, 1932–1969

• The Elementary Course in Mathematics in the Soviet School, 1969–1990s

• Elementary Mathematical Education in Russia, 1990s
  • Fundamental Program Requirements and Characteristics of Contemporary Textbooks
  • The Content of the Elementary Course in Mathematics
    • Numbers and arithmetical operations
    • Arithmetical problems
    • Magnitudes
    • Geometrical content
    • Elements of algebra
    • Elements of combinatorics
    • Elements of logic, set theory, modeling
    • Working with data

• Conclusion

• References

The following sections are included:

• Introduction

• The Contents of the Course in Geometry in Russian Schools

• The Aims and Characteristics of the Course in Geometry in Russia

• On the Conditions Under Which Geometry Is Taught

• Toward a History of the Course in Geometry in Russia (USSR)
  • From Kiselev to Kolmogorov
  • Kolmogorov's Textbooks for Basic Schools
  • Geometry Textbooks for Basic Schools from the Late 1970s to the 1980s
    • A. V. Pogorelov's geometry textbook
    • The geometry textbooks of L. S. Atanasyan and his coauthors
    • The textbooks of A. D. Alexandrov and his coauthors
  • Textbooks That Appeared After the Collapse of the USSR
    • I. F. Sharygin's textbooks
    • The textbooks of I. M. Smirnova and V. A. Smirnov
    • The textbooks of A. L. Werner and his coauthors

• Concerning Some Problems with the Course in Geometry in Russia in Recent Decades
  • The Problem of the Rigor of the Course in Geometry
  • Visual and Informal Geometry in the Study of Three-dimensional Geometry in Basic Schools
  • The New and the Old in the Teaching of Geometry

• References

The following sections are included:

• Algebra as a School Subject

• The Algebraic Component in the System of School Mathematics Education

• The Content of Algebra Education in Russian Schools

• Methodological Issues in Teaching Algebra
  • Basic School (grades 5–9; students aged 10–15)
    • An Overview
    • Algebra for students of ages 10–12 (grades 5–6)
    • Algebra for students of ages 12–15 (grades 7–9)
    • Examples of test problems
  • High School (grades 10–11; students aged 16–17)
    • An overview
    • The study of algebraic expressions in grades 10–11
    • Equations and inequalities in the basic and advanced courses in mathematics in grades 10–11
    • The final attestation in algebra for 11th graders

• References

The following sections are included:

• Introduction

• Elements of Analysis in Normative Documents

• The History of Higher Mathematics Education in Russian (Soviet) Schools
  • The Second Third of the 18th Century to 1845
  • 1846–1906
  • 1907–1917
  • 1918–1933
  • 1934–1964
  • 1965–1976
  • 1977 to the End of the 1980s
  • Early 1990s to the Present

• Introduction to Analysis: Functions in Basic School

• Algebra and Elementary Calculus: Functions in Grades 10–11

• Elements of Differential and Integral Calculus
  • Andrey Kolmogorov's Textbook
  • The Textbooks of Alimov et al. and Kolyagin et al.
  • M. I. Bashmakov's Textbook

• New Generation Textbooks
  • The textbook of A. G. Mordkovich and I. M. Smirnova
  • The textbook of G. K. Muravin and O. V. Muravina

• Conclusion

• References

The following sections are included:

• Finite Mathematics in the School Curriculum Prior to the Revolution of 1917

• Finite Mathematics in the Secondary School Curriculum in the Soviet Period

• Finite Mathematics in the Post-Soviet Period

• Features of Contemporary Approaches to the Study of Finite Mathematics in Russian Schools

• First Results of Teaching the Experimental Curriculum

• Conclusion

• References

The following sections are included:

• Introduction

• The Appearance of Schools and Classes with an Advanced Course in Mathematics

• Mathematics Schools During the Period of Stagnation and Later

• The Everyday Life of Mathematics Schools

• Curricula, Textbooks, Approaches
  • On Curricula
  • On the Specifics of Teaching the Course in Mathematics
  • On the Content of Certain Topics in the Course
  • On Textbooks for Schools with an Advanced Course of Study in Mathematics

• Schools with a Humanities Orientation

• Curricula and Textbooks for Humanities-Oriented Schools

• Conclusion

• References

The following sections are included:

• Introduction

• General Assessment Issues
  • What Is Assessed and Why?
  • Assessment in the Past
  • Some Facts About the Organization of the Teaching Process and of Assessment

• On the Nature of the Assignments Used for Assessment

• Oral Questioning in Class
  • The “From the Seat” Response
  • The “At the Board” Response
    • Going over homework assignments
    • Questioning students about theoretical material
    • Solving problems on the blackboard

• Written Work
  • Tests
  • Quizzes
  • Mathematical Dictations
  • Individual Written Questioning of the Student in Class

• Long-Term Assignments

• Exams and Oral Survey Tests
  • Oral Survey Tests
  • Exams

• Conclusion

• References

The following sections are included:

• Introduction

• Mass Forms of Extracurricular School Work
  • Mathematical Wall Newspapers
  • Mathematical Theatrical Evenings and Oral Mathematics Journals
  • Mathematical Tournaments
  • Written Problem-Solving Contests

• School Mathematics Circles and Electives
  • Mathematics Circles in Grades 5–6
  • Mathematics Circles and Electives in Grades 7–9
  • Mathematics Circles and Electives in Grades 10–11

• On Various Forms of Distance Learning

• Selective Forms of Working with Students
  • On Mathematics Circles
  • Mathematics Summer Camps
  • Conferences

• Conclusion

• References

The following sections are included:

• Introduction

• On Certain Features of the Organization of Scientific Research in the Area of Mathematics Education and on Our Sources

• Issues in the Philosophy and Worldview of Mathematics Education

• The Psychology of Mathematics Education

• Problem Solving

• The History of Mathematics Education

• Issues of Differentiation in Education

• The Organization of the Educational Process

• Studying the Process of Teaching Mathematics: Connections Within Subjects, Continuity and Succession in Education

• Teaching Aids

• Teaching in Elementary Schools

• On Teaching Specific Mathematical Subjects in Schools

• Teaching in Nonpedagogical Institutions of Higher Education

• Mathematics Teacher Education
  • General Questions of Mathematics Teacher Education
  • Special Aspects of the Methodological Preparation of Future Teachers
  • On Teaching Mathematics to Future Teachers
  • Technology in Mathematics Teacher Education

• On Candidate's Dissertations

• Conclusion

• References

The following sections are included:

• Notes on Contributors

• Name Index

• Subject Index