Perceptual learning and the technology of expertise: Studies in fractioin learning and algebra

Pragmatics and Cognition

Volumn 16, Issue 2, 2008, Pages 356-405

  Kellman, Philip J ^a   Massey, Christine ^b   Roth, Zipora ^b   Burke, Timothy ^a   Zucker, Joel ^a   Saw, Amanda ^a,d   Aguero, Katherine E ^b,e   Wise, Joseph A ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c New Roads School   (United States)

^d Academy II ^*  (United States)

^e Harelem Children's Zone Promise   (United States)

Author keywords

Algebra; Fluency; Fractions; Instruction; Learning technology; Mathematics; Mathematics learning; Pattern recognition; Perception; Perceptual learning; Perceptual learning module (PLM)

Indexed keywords

EID: 49549083007     PISSN: 09290907     EISSN: 15699943     Source Type: Journal    
DOI: 10.1075/pc.16.2.07kel     Document Type: Article

References (54)

1. Ahissar, M. and Hochstein, S. 1997. "Task difficulty and learning specificity". Nature 387: 401-406.
2. Anderson, J.R., Corbett, A.T., Fincham, J.M., Hoffman, D., and Pelletier, R. 1992. "General principles for an intelligent tutoring architecture". In J. Regian and V. Shute (eds), Cognitive Approaches to Automated Instruction. Hillsdale, NJ: Lawrence Erlbaum, 81-106.
3. Anderson, J.R., Corbett, A.T., Koedinger, K.R., and Pelletier, R. 1995. "Cognitive tutors: Lessons learned". The Journal of the Learning Sciences 4(2): 167-207.
4. Barsalou, L. W. 1999. "Perceptual symbol systems". Behavioral and Brain Sciences 22: 577-660.
5. Behr, M.J., Harel, G., Post, T., and Lesh, R. 1992. "Rational number, ratio, and proportion". In D. Grouws (ed), Handbook of Research on Mathematics Teaching and Learning. New York-Macmillan, 296-333.
6. Bryan, W.L. and Harter, N. 1899. "Studies on the telegraphic language. The acquisition of a hierarchy of habits". Psychological Review 6(4): 345-375.
7. Chandler, P. and Sweller, J. 1991. "Cognitive load theory and the format of instruction. Cognition and Instruction 8: 293-332.
8. Chase, W.G. and Simon, H.A. 1973. "Perception in chess". Cognitive Psychology 4 (1): 55-81.
9. Fable, M. and Poggio, T. (eds). 2002. Perceptual Learning. Cambridge, MA: The MIT Press.
10. Foster, D. 2007. "Making meaning in algebra: Examining students' understandings and misconceptions". Assessing Mathematical Proficiency 53:163-176.
11. Garrigan, P. and Kellman, P.J. 2008. "Perceptual learning depends on perceptual constancy". Proceedings of the National Academy of Sciences, USA. 105(6): 2248-2253.
12. Gibson, E.J. 1969. Principles of Perceptual Learning and Development. New York: Appleton-Century-Crofts.
13. Gibson, J.J. 1966. The Senses Considered as Perceptual Systems. Boston: Houghton Mifflin.
14. Gibson, J.J. 1979. The Ecological Approach to Vision Perception. Boston: Houghton Mifflin.
15. Gibson, J.J. and Gibson, E.J. 1955. "Perceptual learning: Differentiation or enrichment?" Psychological Review 62: 32-41.
16. Goldstone, R.L. 1998. "Perceptual learning". Annual Review of Psychology 49: 585-612.
17. Goldstone, R.L. 2000. "Unitization during category learning". Journal of Experimental Psychology: Human Perception & Performance 26 (1): 86-112.
18. Hackenberg, A.J. 2007. "Units coordination and the construction of improper fractions: A revision of the splitting hypothesis". Journal of Mathematical Behavior 26: 27-47.
19. James, W. 1890. The Principles of Psychology (1983 ed.). Cambridge, MA: Harvard University Press.
20. Karpicke, J. and Roediger III, H.L. 2007. "Expanding retrieval practice promotes short-term retention, but equally spaced retrieval enhances long-term retention". Journal of Experimental Psychology: Learning, Memory, and Cognition 33(4): 704-719.
21. Kellman, P.J. 2002. "Perceptual learning". In R. Gallistel (ed), Stevens' Handbook of Experimental Psychology, Vol. 3. Learning, Motivation, and Emotion, Third Edition. New York: Wiley, 259-299.
22. Kellman, P.J. and Arterberry, M.E. 1998. The Cradle of Knowledge: Development of Perception in Infancy. Cambridge, MA: The MIT Press.
23. Kellman, P.J. and Kaiser, M.K. 1994. "Perceptual learning modules in flight training". Proceedings of the 38th Annual Meeting of the Human Factors and Ergonomics Society, 1183-1187.
24. Kellman, P.J. and Massey, C. 2005. "Background and validation research on perceptual learning and adaptive sequencing technologies". Unpublished Technical Report, Insight Learning Technology, Inc.
25. Knuth, E.J., Alibali, M.W, McNeil, N.M., Weinberg, A., and Stephens, A.C. 2005. "Middle school students' understanding of core algebraic concepts: Equivalence & variable". Zentralblatt für Didaktik der Mathematik 37(1): 68-76.
26. Knuth, E.J., Stephens, A.C., McNeil, N.M., and Alibali, M.W. 2006. "Does understanding the equal sign matter? Evidence from solving equations". Journal for Research in Mathematics Education 37(4): 297-312.
27. Lamon, S. 2001. "Presenting and representing: From fractions to rational numbers". In A. Cuoco and F. Curcio (eds), The Roles of Representation in School Mathematics. 2001 Yearbook. Reston, VA: National Council of Teachers of Mathematics, 146-165.
28. Landauer, T.K. and Bjork, R.A. 1978. "Optimum rehearsal patterns and name learning". In M.M. Gruneberg, P.E. Morris, and R.N. Sykes (eds), Practical Aspects of Memory. London: Academic Press, 625-632.
29. Landy, D. and Goldstone, R.L. In press. "How abstract is symbolic thought?" Journal of Experimental Psychology: Learning, Memory, and Cognition.
30. Mayer, R.E. and Moreno, R. 1998. "A split attention effect in multimedia learning: Evidence for dual processing systems in working memory". Journal of Educational Psychology 90: 312-320.
31. Merzenich, M.M., Jenkins, W.M., Johnston, P., Schreiner, C., Miller, S., and Tallal, P. 1996. "Temporal processing deficits of language-learning impaired children ameliorated by training". Science 271(5245): 77-81.
32. Mettler, E. and Kellman, P.J. 2006. "Unconscious discovery in concrete and abstract perceptual learning". Paper presented at the Annual Meeting of the Psychonomics Society, Houston, Texas.
33. Michotte, A. 1962. The Perception of Causality. Andover, MA: Methuen.
34. Michotte, A., Thines, G., and Crabbe, G. 1964. Les Compléments Amodaux des Structures Perceptives [The Amodal Complements of Perceptual Structures]. Louvain: Publications de l'Université de Louvain.
35. Olive, J. 1999. "From fractions to rational numbers of arithmetic: A reorganization hypothesis". Mathematical Thinking and Learning 1(4):279-314.
36. Olive, J. 2001. "Connecting partitioning and iterating: A path to improper fractions". In M. van den Heuvel-Panhuizen (ed), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education (PME-25, Vol. 4). Utrecht: Freudenthal Institute, 1-8.
37. Olive, J. and Steffe, L.P. 2002. "The construction of an iterative fractional scheme: The case of Joe". Journal of Mathematical Behavior 20: 413-437.
38. Olive, J. and Vomvoridi, E. 2006. "Making sense of instruction on fractions when a student lacks necessary fractional schemes: The case of Tim". Journal of Mathematical Behavior 25: 18-45.
39. Paas, G. W. C. and van Merrienboer, J. J. G. 1994. "Variability of worked examples and transfer of geometrical problem solving skills: A cognitive load approach". Journal of Educational Psychology 1: 122-133.
40. Petrov, A.A., Dosher, B.A., and Lu, Z. 2005. "The dynamics of perceptual learning: An incremental reweighting moder". Psychological Review 112(4): 715-743.
41. Post, T.R., Behr, M.J., and Lesh, R. 1986. "Research-based observations about children's learning of rational number concepts". Focus on Learning Problems in Mathematics 8(1): 39-48.
42. Recanzone, G.H., Schreiner, C.E., and Merzenich, M.M. 1993. "Plasticity in the frequency representation of primary auditory cortex following discrimination training in adult owl monkeys". Journal of Neuroscience 13(1): 87-103.
43. Schmidt, R.A. and Bjork R.A 1992. "New conceptualizations of practice: Common principles in three paradigms suggest new concepts for training". Psychological Science 3(4): 207-217.
44. Schneider, W. and Shiffrin, R.M. 1977. "Controlled and automatic human information process- ing: I. Detection, search, and attention". Psychological Review 84 (1): 1-66.
45. Shiffrin, R.M. and Schneider, W. 1977. "Controlled and automatic information processing: II. Perceptual learning, automatic attending and a general theory". Psychological Review 84(2): 127-190.
46. Shipley, T.F. and Zacks, J.M. (eds). 2008. Understanding Events: From Perception to Action. NY: Oxford University Press.
47. Silva, A. and Kellman, P.J. 1999. "Perceptual learning in mathematics: The algebra-geometry connection". In M. Hahn and S.C. Stoness (eds), Proceedings of the Twenty-first Annual Conference of the Cognitive Science Society. Mahwah, NJ: Lawrence Erlbaum, 683-689.
48. Steffe, L.P. 2002. "A new hypothesis concerning children's fractional knowledge". Journal of Mathematical Behavior 20: 267-307.
49. Sweller, J., Chandler, C., Tierney, P., and Cooper, M. 1990. "Cognitive load as a factor in the structuring of technical material". Journal of Experimental Psychology: General, 119(2): 176-192.
50. Tallal, P., Merzenich, M., Miller, S., and Jenkins, W. 1998. "Language learning impairment: Integrating research and remediation". Scandinavian Journal of Psychology 39(3): 197-199.
51. Thompson, P, 1995. "Notations, convention, and quantity in elementary mathematics". In J. Sowder and B. Schapelle (eds), Providing a Foundation for Teaching Middle School Mathematics. Albany, NY: SUNY Press, 199-221.
52. Thompson, P. and Saldanha, L. 2001. "Fractions and multiplicative reasoning". In J. Kilpatrick, G. Marti, and D. Schifter (eds), Research Companion to the Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 95-114.
53. Tzur, R. 1999. "An integrated study of children's construction of improper fractions and the teacher's role in promoting the learning". Journal for Research in Mathematics Education 30 (4): 390-416.
54. Wise, J.A., Kubose, T., Chang, N., Russell, A., and Kellman, P.J. 2000. "Perceptual learning modules in mathematics and science instruction". In D. Lemke (ed), Proceedings of the TechEd 2000 Conference. Amsterdam: IOS Press, 169-176.