Application of Complexity Theory to an Information Processing Model in Science Education

Nonlinear Dynamics, Psychology, and Life Sciences - Tập 5 - Trang 267-287 - 2001
Dimitrios Stamovlasis1, Georgios Tsaparlis1
1Department of Chemistry, University of Ioannina, Ioannina, Greece

Tóm tắt

The current work examines the role of working-memory capacity in problem solving in science education. It treats an information-processing model with tools of complexity theory. Nonlinear methods are used to correlate the subjects' achievement scores with working-memory capacity. Data have been taken from the achievement scores in simple organic-synthesis chemical problems. The subjects (N = 319) were in grade twelve (age 17–18). Problems of various Z-demands (that is the number of steps needed to solve the problem) from two to eight were used. Rank-order sequences of the subjects, according to their scores, were generated, and each score was then replaced by the value of subject's working memory capacity measured by the digit backward span test. Then the sequences were mapped onto a one-dimensional random walk model and when treated as dynamic flows were found to possess fractal geometry with characteristics depending on the Z-demand of the problem. The findings were interpreted using concepts from complexity theory, such as correlation exponents, fractal dimensions and entropy. The null hypothesis was tested with surrogate data.

Tài liệu tham khảo

Addison, P. S. (1997). Fractals and chaos. Bristol and Philadelphia: Institute of Physics Publishing. Baddeley, A. D. (1986). Working memory. Oxford, UK: Oxford University Press. Baddeley, A. D. (1990). Human memory: Theory and practice. London: Erlbaum. Banerjee, S., Sibbald, P. R., & Maze, J. (1990). Quantifying the dynamics of order and organization in biological systems. Journal of Theoretical Biology, 143, 91–111. Bunde, A., & Havlin, S. (1994). Fractals in science. Springer-Verlag. Cambel, A. B. (1993). Applied chaos theory. NY: Academic Press. Dooley, K. J., & Van de Ven, A. H. (1998). A primer on diagnosing dynamical organizational processes. Paper presented in 8th Annual Conference of the Society for Chaos Theory in Psychology & Life Sciences, Boston. Grassberger, P., & Procaccia, I. (1983a). Measuring the strangeness of strange attractors. Physica D 9,189–208. Grassberger, P., & Procaccia, I. (1983b). Characterization of strange attractors. Physical Review Letters, 50(5), 346–349. Green, P. E., & Carroll, J. D. (1976). Mathematical tools for applied multivariate analysis. New York: Academic Press. Hao, Bai-Lin. (1989). Elementary symbolic dynamics. Singapore: World Scientific. Haken, H. (1988). Information and self organization (a macroscopic approach to complex systems). Berlin: Springer. Hurst, H. (1951). Long term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116, 770–799. 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). Aworking 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. Kantz, H., & Schreiber, T.N. (1999). Nonlinear time series analysis. Cambridge, UK: Cambridge University Press. Landsberg, P. T. (1984). Can entropy and order increase together? Physics Letters, 102A, No.4, 171–173. Niaz, M. (1989). Dimensional analysis: A neo-Piagetian evaluation of M-demand of chemistry problems. Research in Science and Technology Education, 7, 153–170. 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, G., & Prigogine, I. (1989). Exploring complexity. W. H. Freeman and Company, New York. 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. Peitgen, H. O., & Saupe, D. (1988). The science of fractal images. Berlin: Springer. Peitgen, H. O., Jurgens, H., & Saupe, D. (1992). Chaos and fractals. Berlin: Springer. Peng, C.-K., Buldyrev, S. V. Goldberger, A. L., Havlin, S., Simons, M., & Stanley, H. E. (1993). Finite-size effects on long-range correlation: Implication for analyzing DNA sequences. Physical Review E, 47, 3730. Scandarmalia, M. (1977). Information processing capacity and the problem of horizontal decalage: A demonstration using combinatorial reasoning task. Child Psychology, 48, 301–345. Shannon, C. E., & Weaver, W. (1949). The mathematical theory of communication. Urbana: University of Illinois Press. Sprott, J. C., & Rowlands, G. (1995). Chaos data analyzer. Physical Academy Software. 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. 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 Science, 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. Wechsler, D. (1955). Wechsler adult intelligence scale manual. New York: Psychological Corporation.