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Cited by 329Mathematics Education and Teaching TechniquesMathematics Education and PedagogyCognitive and developmental aspects of mathematical skills

The DOI matches its Crossref record; 22 of the 23 references it cites were found in a registry or an index.

Knowing, Doing, and Teaching Multiplication

Lampert, Magdalene·1986·Cognition and Instruction
DOI 10.1207/s1532690xci0304_1
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Abstract

This investigation analyzes the structure and process of multidigit multiplication. It includes a review of recent theories of mathematical knowledge and a description of several fourth-grade math lessons conducted in a regular classroom setting. Four types of mathematical knowledge are identified: intuitive, concrete, computational, and principled knowledge. The author considers each type in terms of its relation to instructional issues and suggests that instruction should focus on strengthening the connections among the four types. Illustrations from instructional sessions show children generating and testing hypotheses when salient connections are made between concrete materials and principled, computational practices. Implications for teaching are discussed along with suggestions for future research.

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Citations

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Show all 23 references

Research works printed but not linked: 8

  1. Davis, R. B. (1983). Diagnosis and evaluation in mathematics instruction: Making contact with students" mental representations.In C. Smith (Ed.), Essential knowledge for beginning educators (pp. 101-1 11). Washington, DC: American Association of Colleges of Teacher Education.
  2. Hatano G., 1980, Dokkyo University Bulletin of Liberal Arts, 15, 84
  3. Hawkins D., 1985, For the Learning of Mathematics, 5, 2
  4. Kaput, J. (1985). Multiplicative wordproblems and intensive quantities: An integrated software response (Tech. Rep.).Cambridge, MA: Educational Technology Center, Harvard Graduate School of Education.
  5. Kitcher, P. (1984). Thenatureof mathematicalknowledge.New York: Oxford University Press.
  6. Resnick, L. B. (1983). Adevelopmental theory of number understanding.In H. Ginsburg (Ed.), The development of mathematical thinking (pp.110- 152). New York: Academic.
  7. Saxe, G. B. & Posner, J. (1983). The development of numerical cognition: Cross cultural perspectives.In H. Ginsburg (Ed.), Thedevelopment of mathematical thinking (pp. 292-3 18). New York: Academic.
  8. Schwartz, J. (1981). The role of semantic understanding in solving multiplication and division word problems (Final report to the NIE, Grant NIE-G-80-0144).Cambridge, MA: Massachusetts Institute of Technology.

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Metadata

Authors
Lampert, M.
Corresponding author
Lampert, Magdalene
Venue
Cognition and Instruction
Publisher
Informa UK Limited
Published
1986-12
Volume
3
Issue
4
Pages
305-342
ISSN
  • 0737-0008 (ISSN-L)
  • 1532-690X
DOI
10.1207/s1532690xci0304_1
OpenAlex
W1979890010
Cited by
329
References
23
Citations by year
2026: 1 · 2025: 3 · 2024: 4 · 2023: 2 · 2022: 6 · 2021: 7 · 2020: 10 · 2019: 9 · 2018: 5 · 2017: 9 · 2016: 7 · 2015: 9 · 2014: 4 · 2013: 14 · 2012: 7
FWCI
41.28
Type
journal article
Language
en
Open access
closed
Locations
Cognition and Instruction (publishedVersion)
Topics
  • Social Sciences › Education › Mathematics Education and Teaching Techniques
  • Social Sciences › Education › Mathematics Education and Pedagogy
  • Social Sciences › Psychology › Developmental and Educational Psychology › Cognitive and developmental aspects of mathematical skills
Keywords
mathematical knowledge, intuitive knowledge, fourth grade mathematics, mathematics education, hypothesis generation, children's mathematical thinking

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