A Complexity Theory Model in Science Education Problem Solving: Random Walks for Working Memory and Mental Capacity
Tóm tắt
The present study examines the role of limited human channel capacity from a science education perspective. A model of science problem solving has been previously validated by applying concepts and tools of complexity theory (the working memory, random walk method). The method correlated the subjects' rank-order achievement scores in organic-synthesis chemistry problems with the subjects' working memory capacity. In this work, we apply the same nonlinear approach to a different data set, taken from chemical-equilibrium problem solving. In contrast to the organic-synthesis problems, these problems are algorithmic, require numerical calculations, and have a complex logical structure. As a result, these problems cause deviations from the model, and affect the pattern observed with the nonlinear method. In addition to Baddeley's working memory capacity, the Pascual-Leone's mental (M-) capacity is examined by the same random-walk method. As the complexity of the problem increases, the fractal dimension of the working memory random walk demonstrates a sudden drop, while the fractal dimension of the M-capacity random walk decreases in a linear fashion. A review of the basic features of the two capacities and their relation is included. The method and findings have consequences for problem solving not only in chemistry and science education, but also in other disciplines.
Tài liệu tham khảo
Addison, P.S. (1997). Fractals and chaos. Bristol and Philadelphia: Institute of Physics Publishing.
Arecchi, F. T. (2001). Complexity versus complex systems: A new approach to scientific discovery. Nonlinear Dynamics, Psychology, and Life Sciences, 5, 21–35.
Atkins, P. W. (1978). Physical Chemistry, Oxford: Oxford University Press.
Atkinson, R. C. & Shiffrin, R. M. (1968). Human memory: a proposed system and its control processes, in K. W. Spence (Ed.), The Psychology of learning and motivation: Advances in research and theory, Vol. 2 (pp. 89–195). New York: Academic Press.
Baddeley, A. D. (1986). Working memory. Oxford, UK: Oxford University Press.
Baddeley, A. D. (1990). Human memory: Theory and practice. London: Erlbaum.
Baddeley, A. D. (1992a). Is working memory working? The fifteenth Bartlett Lecture. Quarterly Journal of Experimental Psychology, 44, 1–31.
Baddeley, A. D. (1992b). Working memory. Science, 255, 556–559.
Baddeley, A. (1994). The magical number seven: Still magic after all these years? Psychological Review, 101, 353–356.
Baddeley, A. (1996). Exploring the central executive. Quarterly Journal of Experimental Psychology, 49A, 5–28.
Baddeley, A. D. & Logie, R. H. (1992). Auditory imagery and working memory. I D. Reisberg (Ed.), Auditory imagery, (pp. 521–539). Hillsdale, NJ: Erlbaum.
Braver, T. S. & Cohen, J. D. (2001). Working memory, cognitive control, and the prefrontal cortex: Computational and empirical studies. Cognitive Processing, 2, 25–55.
Bunde, A. & Havlin, S. (1994). Fractals in science. Springer-Verlag.
Cabeza, R. & Nyberg, L. (2000). Imaging cognition II: An empirical review of 275 PET and fMRI studies. Journal of Cognitive Neuroscience, 12, 1–47.
Cambel, A. B. (1993). Applied chaos theory. NY: Academic Press.
Case, R. (1978). Piaget and beyond: Toward a developmentally based theory and technology of instruction. In R. Glaser (Ed.), Advances in instructional psychology (pp. 167–228). Hillsdale, NJ: Lawrence Erlbaum.
Case, R. (1991). Advantages and limitations of neo-Piagetian position. In R. Case (Ed.), The mind's staircase (pp 37–51). Hillsdale, NJ, Lawrence Erlbaum.
Chi, M. Y. H. (1978) Knowledge structures and memory development. In R. S. Siegler (Ed.), Children's thinking: What develops? (pp. 73–96). Hilldale, NJ: Erlbaum.
Della Sala, S. & Logie, R. H. (1993). When working memory does not work: The role of working memory in neuropsychology. In F. Boller & Spinnler (Eds.), Handbook of neuropsychology. Vol. 8 (pp. 1–63). Amsterdam: Elsevier.
Dempster, F. N. (1981). Memory span: Sources of individual and developmental difference. Psychological Bulletin, 89, 63–100.
Dooley, K. J., & Van de Ven, A. H. (1998). A primer on diagnosing dynamical organizational processes. Paper presented at 8th Annual Conference of the Society for Chaos Theory in Psychology & Life Science, Boston.
Feller, W. (1957). An introduction to probability theory and its applications. Vol. 1. New York: Wiley.
Furey, M. L., Pietrini, P., Haxby, J. V. (2000). Cholinergic enhancement and increased selectivity of perceptual processing during working memory, Science, 290, 2315–2319.
Halford, G. (1982). Development of thought. Hillsdale, NJ: Erlbraum.
Johnson, J. M. (1982). The Figural Intersection Test (FIT): A measure of mental (M) attentional energy. Unpublished manuscript. Ontario: York University.
Johnstone, A. H. (1984). New stars for the teacher to steer by? Journal of Chemical Education, 61, 847–849.
Johnstone, A. H., & Al-Naeme, F. F. (1991). Room for scientific thought? International Journal of Science Education, 13, 187–192.
Johnstone, A. H. & El-Banna, H. (1986). Capacities, demands and processes-A predictive model for science education. Education in Chemistry, 23, 80–84.
Johnstone, A. H. & El-Banna, H. (1989). Understanding learning difficulties-A predictive research model. Studies in Higher Education, 14, 159–168.
Johnstone, A. H., Hogg, W. R., & Ziane, M. (1993). A working memory model applied to physics problem solving. International Journal of Science Education, 15, 663–672.
Johnstone, A. H. & Kellet, N. C. (1980). Learning difficulties in school science-Towards a working hypothesis. European Journal of Science Education, 2, 175–181.
McGaugh, J. L. (2000). Memory—A century of consolidation. Science, 287, 248–251.
Miller, G. A. (1956). The magic number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63, 81–97.
Miller, G. A. (1994). The magical number seven, plus or minus two: some limitation on our capacity for processing information. Psychological Review, 101, 343–352.
Morra, S., Miozo, C. & Stopesi, A. (1988). Working memory (or the M operator) and the planning of children's drawings, Journal of Experimental Child Psychology, 46, 41–73.
Morra, S., & Stoffel, C. (1991). A comparison of two developmental models of verbal STM span. Paper presented at the International Conference on Memory, University of Lancaster, UK, July.
Niaz, M. (1987). Relation between M-space of students and M-demand of different items of general chemistry and its interpretation based upon the neo-Piagetian theory of Pascual-Leone. Journal of Chemical Education, 64, 502–505.
Niaz, M. (1988b). The information processing demand of chemistry problems and its relation to Pascual-Leone's functional M-capacity. International Journal of Science Education, 10, 231–238.
Niaz, M. (1988b). Manipulation of M-demand of chemistry problems and its effect on student performance: A neo-Piagetian study. Journal of Research in Science Teaching, 25, 643–657.
Niaz, M. (1989a). Relation between Pascual-Leone's structural and functional M-space and its effect on problem solving in chemistry. International Journal of Science Education, 11, 93–99.
Niaz, M. (1989b). Dimensional analysis: A neo-Piagetian evaluation of M-demand of chemistry problems. Research in Science and Technological Education, 7, 153–170.
Niaz, M. (1989c). The relationship between M-demand, algorithms, and problem solving. Journal of Chemical Education, 66, 422–424.
Niaz, M. (1991). Correlates of formal operational reasoning: A neo-Piagetian analysis. Journal of Research in Science Teaching, 28, 19–40.
Niaz, M. (1994). Pascual-Leone's theory of constructive operators as an explanatory construct in cognitive development and science achievement. Educational Psychology, 14, 23–43.
Niaz, M. (1996). Reasoning strategies of students in solving chemistry problems as a function of developmental level, functional M-capacity and disembedding ability. International Journal of Science Education, 18, 525–541.
Niaz, M., & Lawson, A. E. (1985). Balancing chemical equations: The role of developmental level and mental capacity. Journal of Research in Science Teaching, 22, 41–51.
Niaz, M., & Logie, R. H. (1993). Working memory, mental capacity and science education: Towards an understanding of the ‘working memory overload hypothesis’. Oxford Review of Education, 19, 511–525.
Niaz, M., & Robinson, W. R. (1992). Manipulation of logical structure of chemistry problems and its effect on student performance. Journal of Research in Science Teaching, 29, 211–226.
Nicolis, J. S., & Tsuda, I. (1985). Chaotic dynamics of information processing: The “magic number seven plus-minus two” revisited. Bulletin of Mathematical Biology, 47, 343–365.
Opdenacker, C., Fierens, H., Brabant, I.V., Spruyt, J., Slootmaekers, P. J., & Johnstone, A. H. (1990). Academic performance in solving chemistry problems related to student working memory capacity. International Journal of Science Education, 12, 177–185.
Peng, C.-K., Buldyrev, S. V. Goldberger, A. L., Halvin, S., Simons, M., Stanley, H. E. (1993). Finite-size effects on long-range correlation: Implication for analyzing DNA sequences. Physical Review E, 47, 3730.
Pascual-Leone, J. (1969). The encoding and decoding of symbols by children: A new experimental Paradigm and neo-Piagetian model. Journal of Experimental Child Psychology, 8, 328–355.
Pascual-Leone, J. (1970). A mathematical model for the transition rule in Piaget’s developmental stages. Acta Psychologica, 32, 301–345.
Pascual-Leone, J. (1987). Organismic processes for neo-Piagetian theories: A dialectal causal account of cognitive development. International Journal of Psychology, 22, 531–570.
Pascual-Leone, J., & Burtis, P. J. (1974). FIT: Figural Intersection Test, a group measure of M-space. Unpublished manuscript. Ontario: York University.
Pascual-Leone & Goodman, D. (1979). Intelligence and experience. Instructional Science, 8, 301–367.
Pascual-Leone, J., Goodman, D., Ammon, P. & Subelman, I. (1978). Piagetian theory and neo-Piagetian analysis as psychological guides in education. In: J. M. Gallagher & J. A. Easley (Eds.), Knowledge and development, Vol. 2 (pp. 234–289), New York: Plenum.
Peitgen, H. O., Saupe, D. (1988). The science of fractal images. Berlin: Springer.
Peitgen, H. O., Jurgens, H., & Saupe, D. (1992). Chaos and fractal. Berlin: Springer.
Peng, C.-K., Buldyrev, S. V. Goldberger, A. L., Halvin, S., Simons, M., Stanley, H. E. (1993). Finite-size effects on long-range correlation: Implication for analyzing DNA sequences. Physical Review E, 47, 3730.
Robbins, T. W., Mehta, M. A., Sahakian, B. J. (2000). Boosting working memory. Science, 290, 2275–2277.
Scandarmalia, M. (1977). Information processing capacity and the problem of horizontal decalage: A demonstration using combinatorial reasoning task. Child Psychology, 48, 301–345.
Shallice, T. (1988). From neuropsychology to mental structure. Cambridge: Cambridge University Press.
Simon, A. H. (1974). How big is a chunk? Science, 183, 482–488.
Shiffrin, R. M., and Nosofsky, R. M. (1994). Seven plus or minus two: A commentary on capacity limitations. Psychological Review, 101, 357–361.
Smith, E. & Jonides, J. (1997). Working Memory: A view from neuroimaging. Cognitive Psychology, 33, 5–42.
Sprott, J. C. & Rowlands, G. (1995). Chaos data analyzer. NY: Physics Academic Software.
Stamovlasis, D. & Tsaparlis, G. (2001). Application of complexity theory to an information-processing model in science education. Nonlinear Dynamics, Psychology and Life Sciences, 5, 267–286.
Tsaparlis, G. (1998). Dimensional analysis and predictive models in problem solving. International Journal of Science Education, 20, 335–350.
Tsaparlis, G. & Angelopoulos, V. (2000). A model of problem solving: Its operation, validity, and usefulness in the case of organic-synthesis problems. Science Education, 84, 131–153.
Tsaparlis, G., Kousathana, M., & Niaz, M. (1998). Molecular-equilibrium problems: Manipulation of logical structure and of M-demand, and their effect on student performance. Science Education, 82, 437–454.
Tschacher, W., Scheier, C., Grawe, K., (1998). Order and pattern formation in psychotherapy. Nonlinear Dynamics, Psychology and Life Sciences, 2, 195–215.
Voss, R. F., (1992). Evolution of long-range fractal correlations and 1/f noise in DNA sequence. Physical Review Letters, 68, 3805.
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., & Farmer, J. D. (1992). Testing for nonlinearity in time series: The method of surrogate data. Physica D, 58, 77–94.
Wechsler, D. (1955). Wechsler adult intelligence scale manual. New York: Psychological Corporation.
Witkin, H. A., Dyk, R. B., Faterson, H. F., Goodenough, D. R., & Karp, S. A. (1962). Psychological differentiation. New York: Wiley.