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E-raamat: Number Concepts and Operations in the Middle Grades

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  • Formaat: EPUB+DRM
  • Sari: Routledge Revivals
  • Ilmumisaeg: 16-Jan-2026
  • Kirjastus: Routledge
  • Keel: eng
  • ISBN-13: 9781040818169
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  • Formaat: EPUB+DRM
  • Sari: Routledge Revivals
  • Ilmumisaeg: 16-Jan-2026
  • Kirjastus: Routledge
  • Keel: eng
  • ISBN-13: 9781040818169

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For many students, learning mathematics in the middle grades represents a watershed activity. If they fall behind or fail at this point, they are unlikely to recover and to pursue a career in the sciences or other mathematics-dependent occupations. Originally published in 1988, the authors reveal at least two of the reasons for this watershed experience. First, the content itself is much more complex than that at the primary grades, a complexity that was only then being fully appreciated. Second, conventional instruction often is based on faulty assumptions about the way in which the content is learned. The chapters present the latest understanding of the nature of the mathematics content in the middle grades and the processes by which it is learned.



For many students, learning maths in the middle grades represents a watershed activity. If they fall behind or fail at this point, they are unlikely to recover and to pursue a career in the sciences or other maths-dependent occupations. First published in 1988, the authors reveal at least two of the reasons for this watershed experience.

Preface. Series Forward J. T. Sowder. Introduction: Capturing the Major
Themes J. Hiebert & M. Behr. Part I: Analyses of Subject Matter
1.
Multiplicative School Word Problems: Theoretical Approaches and Empirical
Findings P. Nesher
2. Intensive Quantity and Referent Transforming Arithmetic
Operations J.L. Schwartz
3. Mathematical Meaning and Applicational Meaning in
the Semantics of Fractions and Related Concepts S. Ohlsson
4. Proportional
Reasoning R. Lesh, T. Post & M. Behr. Part II: Theoretical Analyses of
Emerging Competence
5. Children's Construction of Number Sequences and
Multiplying Schemes L. P. Steffe
6. Multiplicative Structures G. Vergnaud
7.
Personal Knowledge of Rational Numbers: Its Intuitive and Formal Development
T. E. Kieren. Part III: Effects of Conventional and Experimental Instruction
8. Mental Computation and Number Comparison: Their Roles in the Development
of Number Sense and Computational Estimation J. T. Sowder
9. Ratio and
Proportion K. Hart
10. Constructing and Using Meaning for Mathematical
Symbols: The Case of Decimal Fractions D. Wearne & J. Hiebert
11. A
Developmental Approach to the Identification and Teaching of Central
Conceptual Structures in Mathematics and Science in the Middle Grades R. Case
& R. Sandieson
12. Summary Comments: Meaning in Middle Grade Number Concepts
K. Fuson
13. Summary Comments: Developing a Research Agenda for Mathematics
in the Middle Grades R. Case. Participants.
Edited by James Hiebert and Merlyn Behr