Assessing schematic knowledge of introductory probability theory
Received: 18 May 2004 Accepted: 05 March 2005 DOI:
Cite this article as: Birney, D.P., Fogarty, G.J. & Plank, A. Instr Sci (2005) 33: 341. doi:10.1007/s11251-005-3198-7 Abstract
The ability to identify schematic knowledge is an important goal for both assessment and instruction. In the current paper, schematic knowledge of statistical probability theory is explored from the declarative-procedural framework using multiple methods of assessment. A sample of 90 undergraduate introductory statistics students was required to
classify 10 pairs of probability problems as similar or different; to identify whether 15 problems contained sufficient, irrelevant, or missing information (text-edit); and to solve 10 additional problems. The complexity of the schema on which the problems were based was also manipulated. Detailed analyses compared text-editing and solution accuracy as a function of text-editing category and schema complexity. Results showed that text-editing tends to be easier than solution and differentially sensitive to schema complexity. While text-editing and classification were correlated with solution, only text-editing problems with missing information uniquely predicted success. In light of previous research these results suggest that text-editing is suitable for supplementing the assessment of schematic knowledge in development. Keywords: assessing schematic knowledge statistical probability theory text-editing References Anderson, J.R. 1982 Acquisition of cognitive skill Psychological Review 89 369 406 CrossRef Google Scholar Anderson, J.R. 1990The Adaptive Character of Thought (Vol.1) Erlbaum NJ: Hillsdale Google Scholar Anderson, J.R., Milson, R. 1989 Human memory: An adaptive perspective Psychological Review 96 703 719 CrossRef Google Scholar Anderson, J.R., Neves, D.M. 1981 Knowledge compilation: Mechanisms for the automatization of cognitive skills Anderson, J.R. eds. Cognitive Skills and their Acquisition Lawrence Erlbaum Associates Hillsdale, NJ 57 84 Google Scholar Anderson, J.R., Schunn, C.D. 2000 Implications of the ACT-R learning theory: No magic bullets Glaser, R. eds. Advances in Instructional Psychology (Vol. 5) Erlbaum Mahwah, NJ 1 33 Google Scholar Benaroch, M. 2001 Declarative representation of strategic control knowledge International Journal of Human–Computer Studies 55 881 917 CrossRef Google Scholar Birney, D.P., Halford, G.S. 2002 Cognitive complexity of suppositional reasoning: An application of the relational complexity metric to the knight-knave task Thinking and Reasoning 8 109 134 CrossRef Google Scholar Braine, M.D.S. 1990 The “Natural Logic” approach to reasoning Overton, W.F. eds. Reasoning, Necessity, and Logic: Developmental Perspectives Lawrence Erlbaum Hillsdale, NJ 133 157 Google Scholar Byrne, R.M.J., Handley, S.J. 1997 Reasoning strategies for suppositional deductions Cognition 62 1 49 CrossRef PubMed Google Scholar Carraher, T.N., Carraher, D., Schliemann, A.D. 1985 Mathematics in the streets and in schools British Journal of Developmental Psychology 3 21 29 Google Scholar Chandler, P., Sweller, J. 1991 Cognitive load theory and the format of instruction Cognition and Instruction 8 293 332 Google Scholar Chen, Z. 1999 Schema induction in children’s analogical problem solving Journal of Educational Psychology 91 703 715 CrossRef Google Scholar Cheng, P.W., Holyoak, K.J 1985 Pragmatic reasoning schemas Cognitive Psychology 17 391 416 CrossRef PubMed Google Scholar Chi, M.T., Fletovich, P.J.H., Glaser, R. 1981 Categorization and representation of physics problems by experts and novices Cognitive Sciences 5 121 152 Google Scholar Chi, M.T., Glaser, R., Rees, E. 1982 Expertise in problem solving Sternberg, R.J. eds. Advances in the Psychology of Human Intelligence (Vol. 1) Lawrence Erlbaum Associates Hillsdale, New Jersey 7 75 Google Scholar Cohen, N.J., Poldrack, R.A., Eichenbaum, H. 1997 Memory for items and memory for relations in the procedural/declarative memory framework Memory 5 131 178 PubMed Google Scholar Cook, M 2001 Mathematics: The thinking arena for problem solving Costa, A.L. eds. Minds. A Resource Book for Teaching Thinking ASCD VA Google Scholar Cooper, G., Sweller, J. 1987 Effects of schema acquisition and rule automation on mathematical problem-solving transfer Journal of Educational Psychology 79 347 362 CrossRef Google Scholar Jong, T., Ferguson-Hessler, M. 1986 Cognitive structures of good and poor novice problem solvers in physics Journal of Educational Psychology 78 279 288 CrossRef Google Scholar Jong, T., Ferguson-Hessler, M. 1996 Types and qualities of knowledge Educational Psychologist 31 105 113 Google Scholar
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