A Comparison of Programming Languages and Algebraic Notation as Expressive Languages for Physics

  • Bruce L. Sherin
Article

Abstract

The purpose of the present work is to consider some of the implications of replacing, for the purposes of physics instruction, algebraic notation with a programming language. Whatis novel is that, more than previous work, I take seriously the possibility that a programming language can function as the principle representational system for physics instruction. This means treating programming as potentially having a similar status and performing a similar function to algebraic notation in physics learning. In order to address the implications of replacing the usual notational system with programming, I begin with two informal conjectures: (1) Programming-based representations might be easier for students to understand than equation-based representations, and (2) programming-based representations might privilege a somewhat different ``intuitive vocabulary.'' If the second conjecture is correct, it means that the nature of the understanding associated with programming-physics might be fundamentally different than the understanding associated with algebra-physics.

In order to refine and address these conjectures, I introduce a framework based around two theoretical constructs, what I callinterpretive devices and symbolic forms. A conclusion of this work is that algebra-physics can be characterized as a physics of balance and equilibrium, and programming-physics as a physics of processes and causation. More generally, this work provides a theoretical and empirical basis for understanding how the use of particular symbol systems affects students' conceptualization.

algebra cognition physics programming representations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. Abelson, H. and di Sessa, A. (1980). Turtle Geometry. Cambridge, MA: MIT Press.Google Scholar
  2. Bork, A. M. (1967). Fortran for Physics. Reading, MA: Addison-Wesley.Google Scholar
  3. Bruner, J. S. (1966). On cognitive growth. In J. S. Bruner, R. R. Olver and P. M. Greenfield (Eds), Studies in Cognitive Growth II (pp. 30-67). New York: John Wiley and Sons.Google Scholar
  4. Carpenter, T. P. and Moser, J. M. (1983). The development of addition and subtraction problem-solving skills. In T. P. Carpenter, J. M. Moser and T. A. Romberg (Eds), Addition and Subtraction: A Cognitive Perspective (pp. 9-24). Hillsdale, NJ: Erlbaum.Google Scholar
  5. Chi, M. T. H., Feltovich, P. J. and Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science 5: 121-152.Google Scholar
  6. di Sessa, A. A. (1984). Phenomenology and the evolution of intuition. In D. Gentner and A. Stevens (Eds), Mental Models. Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
  7. di Sessa, A. A. (1986). From logo to boxer. Australian Educational Computing 1(1): 8-15.Google Scholar
  8. di Sessa, A. A. (1989). A child's science of motion: Overview and first results. In U. Leron and N. Krumholtz (Eds), Proceedings of the the Fourth International Conference for Logo and Mathematics (pp. 211-231). Haifa, Israel.Google Scholar
  9. di Sessa, A. A. (1993). Toward an epistemology of physics. Cognition and Instruction 10(2 and 3): 165-255.Google Scholar
  10. di Sessa, A. A. (2000). Changing Minds: Computers, Learning, and Literacy. Cambridge, MA: MIT Press.Google Scholar
  11. di Sessa, A. A. and Abelson, H. (1986). Boxer: A reconstructible computational medium. Communications of the ACM 29(9): 859-868.Google Scholar
  12. di Sessa, A. A., Abelson, H. and Ploger, D. (1991). An overview of Boxer. Journal of Mathematical Behavior 10(1): 3-15.Google Scholar
  13. Ehrlich, K. and Soloway, E. (1984). An empirical investigation of tacit plan knowledge in programming. In J. C. Thomas and M. L. Schneider (Eds), Human Factors in Computer Systems (pp. 113-133). Norwood, NJ: Ablex.Google Scholar
  14. Ehrlich, R. (1973). Physics and Computers: Problems, Simulations, and Data Analysis. Boston: Houghton Mifflin.Google Scholar
  15. Feynman, R. (1965). The Character of Physical Law. Cambridge, MA: MIT Press.Google Scholar
  16. Feynman, R. P., Leighton, R. P. and Sands, M. (1963). Lectures on Physics. Reading, MA: Addison-Wesley.Google Scholar
  17. Forbus, K. D. (1984). Qualitative process theory. Artificial Intelligence 24: 85-168.Google Scholar
  18. Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 243-275). New York: Macmillan Publishing Company.Google Scholar
  19. Goody, J. (1977). The Domestication of the Savage Mind. New York: Cambridge University Press.Google Scholar
  20. Goody, J. and Watt, I. (1968). The consequences of literacy. In J. Goody (Ed.), Literacy in Traditional Societies (pp. 304-345). Cambridge, England: Cambridge University Press.Google Scholar
  21. Gould, H. and Tobochnik, J. (1988). An Introduction to Computer Simulation Methods. Reading, MA: Addison-Wesley.Google Scholar
  22. Hayes, P. J. (1979). The naive physics manifesto. In D. Michie (Ed.), Expert Systems in the Micro-Electronic Age (pp. 242-270). Edinburgh, Scotland: Edinburgh University Press.Google Scholar
  23. Hayes, P. J. (1984). The second naive physics manifesto. In J. Hobbs (Ed.), Formal Theories of the Commonsense World (pp. 1-36). Hillsdale, NJ: Ablex.Google Scholar
  24. Herscovics, N. and Kieran, C. (1980). Constructing meaning for the concept of equation. Mathematics Teacher 73(8): 572-580.Google Scholar
  25. Horwich, P. (1987). Asymmetries in Time. Cambridge, MA: MIT Press.Google Scholar
  26. Johnson, M. (1987). The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason. Chicago: University of Chicago Press.Google Scholar
  27. Kieran, C. (1992). The learning and teaching of school algebra. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 390-419). New York: Macmillan.Google Scholar
  28. de Kleer, J. and Brown, J. S. (1984). A qualitative physics based on confluences. Artificial Intelligence 24: 7-83.Google Scholar
  29. Larkin, J. (1983). The role of problem representation in physics. In D. Gentner and A. Stevens (Eds), Mental Models (pp. 75-98). Hillsdale, NJ: Erlbaum.Google Scholar
  30. Larkin, J., McDermott, J., Simon, D. P. and Simon, H. A. (1980). Expert and novice performance in solving physics problems. Science 208: 1335-1342.Google Scholar
  31. Letovsky, S., Pinto, J., Lampert, R. and Soloway, E. (1987). A cognitive analysis of a code inspection. In G. M. Olson, S. Sheppard and E. Soloway (Eds), Empirical Studies of Programmers: Second Workshop (pp. 231-247). Norwood, NJ: Ablex.Google Scholar
  32. Linn, M. C., Sloane, K. D. and Clancy, M. J. (1987). Ideal and actual outcomes from precollege Pascal instruction. Journal of Research in Science Teaching 24(5): 467-490.Google Scholar
  33. MacDonald, W. M., Redish, E. F. and Wilson, J. M. (1988). The M.U.P.P.E.T. manifesto. Computers in Physics 2: 23-30.Google Scholar
  34. Mann, L. M. (1991). The implications of functional and structural knowledge representations for novice programmers. Unpublished dissertation manuscript. University of California, Berkeley.Google Scholar
  35. McClosky, M. (1984). Naive theories of motion. In D. Gentner and A. Stevens (Eds), Mental Models (pp. 289-324). Hillsdale, NJ: Erlbaum.Google Scholar
  36. Misner, C. W. and Cooney, P. J. (1991). Spreadsheet Physics. Reading: MA: Addison-Wesley.Google Scholar
  37. Noss, R. and Hoyles, C. (1996). Windows on Mathematical Meanings: Learning Cultures and Computers. Dordrecht: Kluwer Academic Publishers.Google Scholar
  38. Olson, D. R. (1994). The World on Paper. New York: Cambridge University Press.Google Scholar
  39. Papert, S. (1980). Mindstorms. New York: Basic Books.Google Scholar
  40. Redish, E. F. and Risley, J. S. (1988). The Conference on Computers in Physics Instruction: Proceedings. Redwood City, CA: Addison-Wesley.Google Scholar
  41. Redish, E. F. and Wilson, J. M. (1993). Student programming in the introductory physics course: M.U.P.P.E.T. Am. J. Phys. 61: 222-232.Google Scholar
  42. Reed, S. K. (1998). Word Problems: Research and Curriculum Reform. Mahwah, NJ: Erlbaum.Google Scholar
  43. Repenning, A. (1993). Agentsheets: A tool for building domain-oriented dynamic, visual environments. Unpublished dissertation manuscript. University of Colorado.Google Scholar
  44. Resnick, M. (1994). Turtles, Termites and Traffic Jams: Explorations in Massively Parallel Microworlds. Cambridge, MA: MIT Press.Google Scholar
  45. Riley, M. S., Greeno, J. G. and Heller, J. I. (1983). Development of children's problemsolving ability in arithmetic. In H. P. Ginsberg (Ed.), The Development of Mathematical Thinking (pp. 153-196), New York: Academic Press.Google Scholar
  46. Scribner, S. and Cole, M. (1981). The Psychology of Literacy. Cambridge, MA: Harvard University Press.Google Scholar
  47. Sfard, A. (1987). Two conceptions of mathematical notions: Operational and structural. In J. C. Bergeron, N. Herscovics and C. Kieran (Eds), Proceedings of the Eleventh International Conference for the Psychology of Mathematics Education (pp. 162-169). Montreal, Canada.Google Scholar
  48. Sfard, A. (1991). On the dual nature of mathematical conceptions. Educational Studies in Mathematics 22: 1-36.Google Scholar
  49. Sherin, B. (1996). The symbolic basis of physical intuition: A study of two symbol systems in physics instruction. Unpublished dissertation manuscript. UC Berkeley.Google Scholar
  50. Sherin, B. (in press). How students understand physics equations. Cognition and Instruction.Google Scholar
  51. Sherin, B., di Sessa, A. A. and Hammer, D. (1993). Dynaturtle revisited: Learning physics through the collaborative design of a computer model. Interactive Learning Environments 3(2): 91-118.Google Scholar
  52. Soloway, E. (1986). Learning to program = Learning to construct mechanisms and explanations. Communications of the ACM 29(9): 850-858.Google Scholar
  53. Vygotsky, L. (1986). Thought and Language. Cambridge, MA: MIT Press.Google Scholar
  54. Whorf, B. L. (1956). Language, Thought, and Reality: Selected Writings of Benjamin Lee Whorf. Cambridge, MA: MIT Press.Google Scholar
  55. Wilensky, U. (1993). Connected mathematics-building concrete relationships with mathematical knowledge. Unpublished dissertation manuscript. MIT.Google Scholar
  56. Wilensky, U. (1997). What is normal anyway? Therapy for epistemological anxiety. Educational Studies in Mathematics 33(2): 171-202.Google Scholar
  57. Wilensky, U. (1999). GasLab-an extensible modeling toolkit for exploring micro-and macro-views of gases. In N. Roberts, W. Feurzeig and B. Hunter (Eds), Computer Modeling and Simulation in Science Education. Berlin: Springer Verlag.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Bruce L. Sherin
    • 1
  1. 1.School of Education and Social PolicyNorthwestern UniversityEvanston

Personalised recommendations