Strategic competence: issues of task-specific strategies in arithmetic
DOI:
https://doi.org/10.7146/nomad.v5i3.146501Abstract
This article focuses on the term strategy and on strategy use in elementary arithmetic. The central theoretical viewpoint in the article includes strategy variability as a fundamental characteristic of mathematical cognition. The theoretical and research base for the acqusition and development of strategic competence is reviewed, and the characteristics of children are discussed from a developmental perspective. Across all areas, the primary focus of this review is to provide a framework for studying the differences, if any, between mathematically normal and mathematically disabled children with regard to the pattern of development that unfolds as the children move up through primary school.
References
Anderson, J.R. (1983). The architecture of cognition. Cambridge MA: Harvard University Press.
Anderson, J.R. (1989). A theory of origin of human knowledge. Artificial Intelligence, 40,313-351. https://doi.org/10.1016/0004-3702(89)90052-0
Ashcraft, M.H. (1982). The development of mental arithmetic: A chronometric approach. Developmental Review, 2, 213-236. https://doi.org/10.1016/0273-2297(82)90012-0
Ashcraft, M.H. (1990). Strategic processing in children's mental arithmetic: A review and proposal. In D.F. Bjorklund (Ed.), Children's strategies: Contemporary view of cognitive development (pp. 185-211). Hillsdale, NJ: Erlbaum.
Ashcraft, M.H. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44, 75-106. https://doi.org/10.1016/0010-0277(92)90051-I
Ashcraft, M.H., & Battaglia, J. (1978). Cognitive arithmetic: Evidence for retrieval and decision processes in mental addition. Journal of Experimental Psychology: Human Learning and Memory, 4, 527-538. https://doi.org/10.1037//0278-7393.4.5.527
Ashcraft, M.H., & Kellas, G. (1974). Organization in normal and retarded children: Temporal aspects of storage and retrieval. Journal of Experimental Psychology, 103, 502-508. https://doi.org/10.1037/h0037285
Bisanz, J., & LeFevre, J.A. (1990). Strategic and nonstrategic processing in the development of mathematical cognition. In D.F. Bjorklund (Ed.), Children 's strategies. Contemporary views of cognitive development (pp. 213-244). Hillsdale, NJ: Erlbaum.
Bjorklund, D. F. & Harnishfeger, K.K. (1990). Children's strategies: Their definition and origins. In D.F. Bjorklund (Ed.), Children's strategies. Contemporary views of cognitive development (pp. 309-323). Hillsdale, NJ: Erlbaum.
Bjorklund, D. F., Muir-Broaddus, J.E., & Schneider, W. (1990). The role of knowledge in development of strategies. In D.F. Bjorklund (Ed.), Children's strategies. Contemporary views of cognitive development (pp. 93-128). Hillsdale, NJ: Erlbaum.
Borkowski, J. G., Schneider, W., & Pressley, M. (1987). "Spontaneous" strategy use: Perspectives from metacognitive theory. Intelligence, 11,61-75. https://doi.org/10.1016/0160-2896(87)90027-4
Borkowski, J. G., & Turner, L.A. (1990). Transsituational characteristics of metacognition. In W. Schneider & F.E. Weinert (Eds.), Interactions among aptitudes, strategies, and knowledge in cognitive performance (159-176). New York: Springer-Verlag. https://doi.org/10.1007/978-1-4612-3268-1_13
Bruner, J. S., Goodnow, J. J., & Austin, G. A. (1956). A study of thinking. New York: Wiley. https://doi.org/10.2307/1292061
Bråten, I. ( 1993). Cognitive strategies: a multi-componential conception of strategy use and strategy instruction. Scandinavian Journal of Educational Research, 37, 217-242. https://doi.org/10.1080/0031383930370304
Burton, L. (1992). Do young children think mathematically? Early Childhood Care and Development Journal Special issue on young children and mathematics , 82, 55-63. https://doi.org/10.1080/0300443920820106
Campbell, J.I.D., & Clark, J.M. (1989). Time course of error priming in number-fact retrieval: Evidence for excitatory and inhibitory mechanisms. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 920-929. https://doi.org/10.1037//0278-7393.15.5.920
Carpenter, T.P., & Moser, J.M. (1982). The development of addition and subtraction problem solving skills. In T.P. Carpenter, J.M.Moser, & T.A. Romberg (Eds.), Addition and subtraction: A cognitive perspective (pp. 9-24). Hillsdale, NJ: Erlbaum. https://doi.org/10.1201/9781003046585-2
Chi, M.T.H. (1978). Knowledge structures and memory development. In Siegler, R.S. (Ed.), Children's Thinking: What Develops? (pp. 73-96). Hillsdale, NJ: Erlbaum.
English, L.D. (1991). Young children's combinatoric strategies. Educational Studies in Mathematics, 22, 451-474. https://doi.org/10.1007/BF00367908
Flavell, J.H. (1971). Stage-related properties of cognitive development. Cognitive Psychology, 2, 421-453. https://doi.org/10.1016/0010-0285(71)90025-9
Fuson, K.C. (1982). An analysis of the counting-on solution procedure in addition. In T.P. Carpenter, J.M. Moser, and T.A. Romberg, (Eds.), Addition and subtraction: A cognitive perspective (pp. 67-82). Hillsdale, NJ: Erlbaum. https://doi.org/10.4324/9781003046585-6
Geary, D.C. (1990). A componential analysis of early learning deficit in mathematics. Journal of Experimental Psychology, 49, 363-383. https://doi.org/10.1016/0022-0965(90)90065-G
Geary, D.C, & Burlingham-Dubree, M. (1989). External validation of the strategy choice model for addition. Journal of Experimental Child Psychology, 47, 175-192. https://doi.org/10.1016/0022-0965(89)90028-3
Geary, D,C, Widaman, K.F., Little, T.D., & Cormier, P. (1987). Cognitive addition: Comparison of learning disabled and academically normal elementary school children. Cognitive Development, 2, 249-269. https://doi.org/10.1016/S0885-2014(87)90075-X
Gelman, R., & Gallistel, C.R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
Gelman, R., & Meck, E. (1983). Preschoolers' counting: Principles before skill. Cognition, 13, 343-359. https://doi.org/10.1016/0010-0277(83)90014-8
Goldman, S.R. (1989). Strategy instruction in mathematics. Learning Disabilitv Quarterly, 12, 43-55. https://doi.org/10.2307/1510251
Goldman, S.R., Pellegrino, J.W., & Mertz, D.L. (1988). Extended practice of basic addition facts: Strategy changes in learning-disabled students. Cognition and Instruction, 5, 223-265. https://doi.org/10.1207/s1532690xci0503_2
Greeno, J.G., & Johnson, W. (1984). Competence for solving and understanding problems. Paper presented at the International Congress of Psychology, Acapulco.
Greeno, J.G., Riley, M.S., & Gelman, R. (1984). Conceptual competence and children's counting. Cognitive Psychology, 16, 94-143. https://doi.org/10.1016/0010-0285(84)90005-7
Groen, G.J., & Parkman, J.M. (1972). A chronometric analysis of simple addition. Psychological Review, 97, 329-343. https://doi.org/10.1037/h0032950
Halford, G.S. (1993). Children's understanding. The development of mental models. Hillsdale, NJ: Erlbaum.
Harnishfeger, K.K., & Bjorklund, D.F. (1990). Children's strategies: A brief history.In D.F. Bjorklund (Ed.), Children 's strategies. Contemporary views of cognitive development (pp. 1-22). Hillsdale, NJ: Erlbaum.
Kolligan, J., & Sternberg, R.J. (1987). Intelligence, information processing, and specific learning disabilities: A triarchic synthesis. Journal of Learning Disabilities, 20, 8-17. https://doi.org/10.1177/002221948702000103
Ostad, S.A. (1991). Telling på alvor The seriousness of counting . Tangenten. Tidsskrift for matematikk i grunnskolen, 4, 25-27.
Ostad, S.A. (1992). Bærekraftige matematikkunnskaper, en funksjon av ferdighet eller forståelse? Good mathematics knowledge, a function of skills or understanding? Norsk Pedagogisk Tidsskrift, 6, 320-326.
Ostad, S.A. (1997). Developmental differences in addition strategies: a comparison of mathematically disabled and mathematically normal children. British Journal of Educational Psychology, 67, 345-357. https://doi.org/10.1111/j.2044-8279.1997.tb01249.x
Pellegrino, J.W., & Goldman, S.R. (1987). Information processing and elementary mathematics. Journal of Learning Disabilities, 20, 23-57. https://doi.org/10.1177/002221948702000105
Pressley, M., Forrest-Pressley, D.L., Elliot-Faust, D., & Miller, G. (1985). Children's use of cognitive strategies, how to teach strategies, and what to do if they can't be taught. In M. Pressley & C.J. Brainerd (Eds.), Cognitive learning and memory in children (pp. 1-47). New York: Springer-Verlag. https://doi.org/10.1007/978-1-4613-9544-7_1
Pressley, M., Borkowski, J.G., & Schneider, W. (1987). Cognitive strategies: Good strategy users coordinate metacognition and knowledge. In R. Vasta & G. Whitehurst (Eds.), Annals of child development (pp. 89-129). New York: JAI Press.
Pressley, M., Borkowski, J.G., & Schneider. (1990). Good information processing: What it is and how education can promote it. Internationaljournal of Educational Research, 13,857-867. https://doi.org/10.1016/0883-0355(89)90069-4
Schneider, W. (1993). Domain-specific knowledge and memory performance in children. Educational Psychology Review, 5, 257-273. https://doi.org/10.1007/BF01323047
Schneider, W., & Weinert, F.E. (1990). The role of knowledge, strategies, and aptitudes in cognitive performance: concluding comments. In W. Schneider & F.E. Weinert (Eds.). Interactions among aptitudes, strategies, and knowledge in cognitive performance (pp. 286-302). New York: Springer-Verlag. https://doi.org/10.1007/978-1-4612-3268-1
Siegler, R.S. (1987a). The perils of averaging data over strategies: An example from children's addition. Journal of Experimental Psychology: General, 166, 250-264. https://doi.org/10.1037//0096-3445.116.3.250
Siegler, R.S. (1987b). Strategy choices in subtraction. In J. Sloboda & D. Rogers (Eds.), Cognitive processes in mathematics (pp. 81-106). Oxford: Clarendon Press.
Siegler, R.S. (1988). Individual differences in strategy choices: Good students, not-so-good students, and perfectionists. Child Development, 59, 833-851. https://doi.org/10.2307/1130252
Siegler, R.S. (1989). Hazards of mental chronometry: An example from children's subtraction. Journal of Educational Psychology, 81, 497-506. https://doi.org/10.1037/0022-0663.81.4.497
Siegler, R.S. (1990). How content knowledge, strategies, and individual differences interact to produce strategy choices. In W. Schneider, & F. Weinert (Eds.), Interactions among aptitudes, strategies, and knowledge in cognitive performance (pp. 73-89). New York: Springer-Verlag. https://doi.org/10.1007/978-1-4612-3268-1_7
Siegler, R.S. (1991). In young children's counting, procedures precede principles. Educational Psychology Review, 3, 127-135. https://doi.org/10.1007/BF01417924
Siegler, R.S., & Campbell, J. (1989). Individual differences in children's strategy choices. In P.L. Ackerman, R.J. Sternberg & R. Glaser (Eds.),Learning and individual differences (219-254). New York: Freeman.
Siegler, R.S., & Jenkins, E. (1989). How children discover new strategies. Hillsdale, NJ: Erlbaum.
Siegler, R.S., & Robinson, M. (1982). The development of numerical understandings. In H. Reese & L.P. Lipsitt, (Eds.), Advances in child development and behavior (pp. 241- 312). New York: Academic Press. https://doi.org/10.1016/S0065-2407(08)60072-5
Siegler, R.S., & Shrager, J. (1984). Strategy choice in addition and subtraction: How do children know what to do? In C. Sophian (Ed.), Origin of cognitive skills (pp. 229- 293). Hillsdale, NJ: Erlbaum.
Tulving, E. (1983). Elements of episodic memory. New York: Oxford University Press.
VanLehn, K., & Brown, J.S. (1980). Planning nets: A representation for formalizing analogies and semantic models of procedural skills. In R.E. Snow, P.A.Federico, & W.E.Montague (Eds.), Aptitude, learning, and instruction: Vol. 2. Cognitive prosess analyses and problem solving (pp. 95-137). Hillsdale, NJ: Erlbaum. https://doi.org/10.4324/9781003163145-18
Willatts, P. (1990). Development of problem-solving strategies in infancy. In D.F. Bjorklund (Ed.), Children's strategies. Contemporary views of cognitive development (pp. 23-66). Hillsdale, NJ: Erlbaum.
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