Relations among Dimensions of Statistical Knowledge

Abstract

Ways of knowing statistical concepts are reviewed. A general three-category structure for knowing is proposed: (a) calculations, (b) propositions, and (c) conceptual understandings. Test items were developed that correspond to the first category and to a partitioning of the two latter categories into words and symbols. Thirty-one items covering the five types were administered to 57 graduate students. Correlation of student scores on the 10-item calculations subtest and the 10-item propositions subtest was .61, whereas the other two intercategory correlations were .40 (Calculations vs. Conceptual Understandings) and .37 (Propositions vs. Conceptual Understandings). The results suggest that students should be tested in more than one domain, and that instructors should expect students to develop conceptual understanding in addition to skills in computation.

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References

Anderson, J. R. (1983). The architecture of cognition. Cambridge, MA: MIT Press.

Baroody, A. J. and Ginsburg, H. P. (1986). The relationships between initial meaningful and mechanical knowledge of arithmetic. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 75-112). Hillsdale, NJ: Erlbaum.

Chi, M. T. H. and Bassok, M. (1989). Learning from examples via self-explanations. In L. B. Resnick (Ed.), Knowing, learning, and instruction: Essays in honor of Robert Glaser (pp. 251-282). Hillsdale, NJ: Erlbaum.

Ehrenberg, A. S. C. (1976). Symbols or concepts? The Statistician, 25, 191-193.

Ghiselli, E. E. , Campbell, J. P. , and Zedeck, S. (1981). Measure- ment theory for the behavioral sciences. San Francisco: Free- man.

Hiebert, J. and Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, NJ: Erlbaum.

Khamis, H. J. (1989, August). Manual computations-A tool for reinforcing concepts and techniques. Paper presented at the annual meeting of the American Statistical Association, Washington, DC.

Lampert, M. (1986). Knowing, doing, and teaching multiplication. Cognition and Instruction, 3, 305-342.

Lord, F. M. and Novick, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.

10.

Marks, R. G. (1989, August). Emphasizing concepts instead of computations in teaching biostatistics. Paper presented at the annual meeting of the American Statistical Association, Washington, DC.

11.

Nesher, P. (1986). Learning mathematics: A cognitive perspective. American Psychologist, 41, 1114-1122.

12.

Resnick, L. B. and Omanson, S. F. (1987). Learning to understand arithmetic. In R. Glaser (Ed.), Advances in instructional psychology (Vol. 3, pp. 41-94). Hillsdale, NJ: Erlbaum.

13.

Skemp, R. R. (1978). Relational understanding and instrumental understanding. Arithmetic Teacher, 26, 9-15.