The effects of physical materials on kindergartners' learning of number concepts

Cognition and Instruction

Volumn 18, Issue 3, 2000, Pages 285-316

  Chao, Shaw Jing ^a   Stigler, James W ^a   Woodward, J Arthur ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005665743     PISSN: 07370008     EISSN: None     Source Type: Journal    
DOI: 10.1207/S1532690XCI1803_1     Document Type: Article

References (48)

1. Baratta-Lorton, M. (1972). Workjobs. Menlo Park, CA: Addison-Wesley.
2. Baratta-Lorton, M. (1976). Mathematics their way. Menlo Park, CA: Addison-Wesley.
3. Baroody, A. J. (1989). A guide to teaching mathematics in the primary grades. Boston: Allyn & Bacon.
4. Beishuizen, M. (1993). Mental strategies and materials or models for addition and subtraction up to 100 in Dutch second grades. Journal for Research in Mathematics Education, 24, 294-323.
5. Chase, W. G., & Simon, H. A. (1973). The mind's eye in chess. In W. G. Chase (Ed.), Visual information processing (pp. 215-281). New York: Academic.
6. Cheng, P. W., Holyoak, K. J., Nisbett, R. E., & Oliver, L. M. (1986). Pragmatic versus syntactic approaches to training deductive reasoning. Cognitive Psychology, 18, 293-328.
7. Chi, M. (1978). Knowledge structures and memory development. In R. Siegler (Ed.), Children's thinking, what develops? (pp. 73-96). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
8. Dienes, Z. P. (1964). Building up mathematics (2nd ed.). London: Hutchinson Educational.
9. Doi, S. (1974). A study on the formation of number concepts. Shinshu University Bulletin of Education, 31, 49-64.
10. Flexer, R. J. (1986). The power of five: The step before the power of ten. Arithmetic Teacher, 34(3), 5-9.
11. Fuson, K. C. (1988). Children's counting and concepts of number. New York: Springer-Verlag.
12. Fuson, K. C., & Hall, J. W. (1983). The acquisition of early number word meanings: A conceptual analysis and review. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 49-107). New York: Academic.
13. Fuson, K. C., Richards, J., & Briars, D. J. (1982). The acquisition and elaboration of the number word sequence. In C. J. Brainerd (Ed.), Children's logical and mathematical cognition (pp. 32-92). New York: Springer-Verlag.
14. Gelman, F., & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
15. Ginbayashi, K. (1984). Principles of mathematics education - Achievements of AMI. Tokyo: Association of Mathematical Instruction.
16. Ginsburg, H. P., & Baroody, A. J. (1990). Test of early mathematics ability (2nd ed.). Austin, TX: PRO-ED.
17. Gravemeijer, K. (1994). Educational development and developmental research in mathematics education. Journal for Research in Mathematics Education, 25, 443-471.
18. Griffin, S. A., Case, R., & Siegler, R. S. (1994). Rightstart: Providing the central conceptual prerequisites for first formal learning of arithmetic to students at risk for school failure. In K. McGilly (Ed.), Classroom lessons: Integrating cognitive theory and classroom practice (pp. 25-49). Cambridge, MA: MIT Press.
19. Hatano, G. (1980, April). Mental regrouping strategy for addition: An alternative model to counting-on. Paper presented at the National Council of Teachers of Mathematics Research Presession, Seattle, WA.
20. Hatano, G. (1982). Learning to add and subtract: A Japanese perspective. In T. P. Carpenter, J. M. Moster, & T. A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 211-223). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
21. Henik, A., & Tzelgov, J. (1982). Is three greater than five: The relation between physical and semantic size in comparison tasks. Memory and Cognition, 10(4), 389-395.
22. Hiebert, J., Wearne, D., & Grant, G. J. (1994). Benefits of using physical materials for learning mathematics: The development of mental tools. Unpublished manuscript, University of Delaware.
23. Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36(6), 6-11.
24. Jordan, N. C., Huttenlocher, J., & Levine, S. C. (1992). Differential calculation abilities in young children from middle- and low-income families. Developmental Psychology, 28, 644-653.
25. Klein, A. S., Beishuizen, M., & Treffers, A. (1998). The empty number line in Dutch second grades: Realistic versus gradual program design. Journal for Research in Mathematics Education, 29, 443-464.
26. Levine, S. C., Jordan, N. C., & Huttenlocher, J. (1992). Development of calculation abilities in young children. Journal of Experimental Child Psychology, 53, 72-103.
27. Marsh, L. G., & Cooke, N. L. (1996). The effects of using manipulatives in teaching math problem solving to students with learning disabilities. Learning Disabilities Research & Practice, 11, 58-65.
28. Marzola, E. S. (1987). Using manipulatives in math instruction. Journal of Reading, Writing, & Learning Disabilities International, 3, 9-20.
29. Miller, K. F., & Stigler, J. (1987). Counting in Chinese: Cultural variation in a basic cognitive skill. Cognitive Development, 2, 279-305.
30. Miura, I. T., Kim, C. C., Chang, C., & Okamoto, Y. (1988). Effects of language characteristics on children's cognitive representation of number: Cross-national comparisons. Child Development, 59, 1445-1450.
31. Nesher, P. (1989). Microworlds in mathematical education: A pedagogical realism. In L. B. Resnick (Ed.), Knowing, learning, and instruction: Essays in honor of Robert Glaser (pp. 187-215). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
32. Raphael, D., & Wahlstrom, M. (1989). The influence of instructional aids on mathematics achievement. Journal for Research in Mathematics Education, 20, 173-190.
33. Ross, S. H. (1986, April). The development of children's place-value numeration concepts ingrades two through five. Paper presented at the annual meetings of the American Educational Research Association, San Francisco.
34. Siegler, R. S., & Robinson, M. (1982). The development of numerical understandings. In H. Reese & L. P. Lipsitt (Ed.), Advances in child development and behavior (pp. 241-312). New York: Academic.
35. Siegler, R. S., & Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), Origins of cognitive skills (pp. 229-293). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
36. Sowell, E. J.(1989). Effects of manipulative materials in mathematics instruction. Journal for Research in Mathematics Education, 20, 498-505.
37. Stern, C. (1949). Children discover arithmetic. New York: Harper.
38. Stigler, J. W. (1984). "Mental abacus": The effect of abacus training on Chinese children's mental calculation. Cognitive Psychology, 16, 145-176.
39. Suydam, M. N., & Higgins, J. L. (1977). Review and synthesis of studies of activity-based approaches to mathematics teaching. Columbus, OH: ERIC/SMEAC.
40. Tang, S. S., & Stigler, J. W. (1987). Easy as 1,2,3? Charting the developmental course of automatic number recognition. Unpublished manuscript, University of Chicago.
41. Tang, S., & Stigler, J. W. (1991, November). Structure versus variety in concrete representations of number. Paper presented at the 32nd Annual Meeting of the Psychonomics Society, San Francisco.
42. Thompson, C. S.,& Van de Walle, J. (1984). Let's do it: The power of 10.Arithmetic Teacher, 32(7), 6-11.
43. Treffers, A., & De Moor, E. (1990). Proeve van een nationaal programma van het reken-wiskunde-onderwijs opde basisschool. Deel2: Basisvaardigheden en cijferen [Specimen of a national program for primary mathematics teaching: Part 2. Basic mental strategies and written computation]. Tilburg, The Netherlands: Zwijsen.
44. U.S. Department of Education. (1986). What works: Research about teaching and learning. Washington, DC: Author.
45. Van de Walle, J. A. (1988). The early development of number relations. Arithmetic Teacher, 35(6), 15-32.
46. Wirtz, R. (1978, April). An elementary mathematics curriculum for all children. Paper presented at the National Council of Supervisors of Mathematics meeting, San Diego, CA.
47. Wirtz, R. (1980). New beginnings. Monterey, CA: Curriculum Development Associates.
48. Woodward, J. A., Bonett, D. G., & Brecht, M. (1990). Introduction to linear models and experimental design. San Diego, CA: Harcourt Brace Jovanovich.