CoChat
Sign Up
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
Open this paper in CoChat — free account

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.

Overview

Integrity signals

Registry

Crossref · 10.1207/s1532690xci0304_1

Cites

22 of 22 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Citations

Cites

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.

Cited by

Sorted by citations

Items 301–327 of 327

Related

See all

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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review