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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Abelson, H. and di Sessa, A. (1980). Turtle Geometry. Cambridge, MA: MIT Press.
Bork, A. M. (1967). Fortran for Physics. Reading, MA: Addison-Wesley.
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.
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.
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.
di Sessa, A. A. (1984). Phenomenology and the evolution of intuition. In D. Gentner and A. Stevens (Eds), Mental Models. Hillsdale, NJ: Lawrence Erlbaum.
di Sessa, A. A. (1986). From logo to boxer. Australian Educational Computing 1(1): 8-15.
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.
di Sessa, A. A. (1993). Toward an epistemology of physics. Cognition and Instruction 10(2 and 3): 165-255.
di Sessa, A. A. (2000). Changing Minds: Computers, Learning, and Literacy. Cambridge, MA: MIT Press.
di Sessa, A. A. and Abelson, H. (1986). Boxer: A reconstructible computational medium. Communications of the ACM 29(9): 859-868.
di Sessa, A. A., Abelson, H. and Ploger, D. (1991). An overview of Boxer. Journal of Mathematical Behavior 10(1): 3-15.
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.
Ehrlich, R. (1973). Physics and Computers: Problems, Simulations, and Data Analysis. Boston: Houghton Mifflin.
Feynman, R. (1965). The Character of Physical Law. Cambridge, MA: MIT Press.
Feynman, R. P., Leighton, R. P. and Sands, M. (1963). Lectures on Physics. Reading, MA: Addison-Wesley.
Forbus, K. D. (1984). Qualitative process theory. Artificial Intelligence 24: 85-168.
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.
Goody, J. (1977). The Domestication of the Savage Mind. New York: Cambridge University Press.
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.
Gould, H. and Tobochnik, J. (1988). An Introduction to Computer Simulation Methods. Reading, MA: Addison-Wesley.
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.
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.
Herscovics, N. and Kieran, C. (1980). Constructing meaning for the concept of equation. Mathematics Teacher 73(8): 572-580.
Horwich, P. (1987). Asymmetries in Time. Cambridge, MA: MIT Press.
Johnson, M. (1987). The Body in the Mind: The Bodily Basis of Meaning, Imagination, and Reason. Chicago: University of Chicago Press.
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.
de Kleer, J. and Brown, J. S. (1984). A qualitative physics based on confluences. Artificial Intelligence 24: 7-83.
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.
Larkin, J., McDermott, J., Simon, D. P. and Simon, H. A. (1980). Expert and novice performance in solving physics problems. Science 208: 1335-1342.
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.
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.
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.
Mann, L. M. (1991). The implications of functional and structural knowledge representations for novice programmers. Unpublished dissertation manuscript. University of California, Berkeley.
McClosky, M. (1984). Naive theories of motion. In D. Gentner and A. Stevens (Eds), Mental Models (pp. 289-324). Hillsdale, NJ: Erlbaum.
Misner, C. W. and Cooney, P. J. (1991). Spreadsheet Physics. Reading: MA: Addison-Wesley.
Noss, R. and Hoyles, C. (1996). Windows on Mathematical Meanings: Learning Cultures and Computers. Dordrecht: Kluwer Academic Publishers.
Olson, D. R. (1994). The World on Paper. New York: Cambridge University Press.
Papert, S. (1980). Mindstorms. New York: Basic Books.
Redish, E. F. and Risley, J. S. (1988). The Conference on Computers in Physics Instruction: Proceedings. Redwood City, CA: Addison-Wesley.
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.
Reed, S. K. (1998). Word Problems: Research and Curriculum Reform. Mahwah, NJ: Erlbaum.
Repenning, A. (1993). Agentsheets: A tool for building domain-oriented dynamic, visual environments. Unpublished dissertation manuscript. University of Colorado.
Resnick, M. (1994). Turtles, Termites and Traffic Jams: Explorations in Massively Parallel Microworlds. Cambridge, MA: MIT Press.
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.
Scribner, S. and Cole, M. (1981). The Psychology of Literacy. Cambridge, MA: Harvard University Press.
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.
Sfard, A. (1991). On the dual nature of mathematical conceptions. Educational Studies in Mathematics 22: 1-36.
Sherin, B. (1996). The symbolic basis of physical intuition: A study of two symbol systems in physics instruction. Unpublished dissertation manuscript. UC Berkeley.
Sherin, B. (in press). How students understand physics equations. Cognition and Instruction.
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.
Soloway, E. (1986). Learning to program = Learning to construct mechanisms and explanations. Communications of the ACM 29(9): 850-858.
Vygotsky, L. (1986). Thought and Language. Cambridge, MA: MIT Press.
Whorf, B. L. (1956). Language, Thought, and Reality: Selected Writings of Benjamin Lee Whorf. Cambridge, MA: MIT Press.
Wilensky, U. (1993). Connected mathematics-building concrete relationships with mathematical knowledge. Unpublished dissertation manuscript. MIT.
Wilensky, U. (1997). What is normal anyway? Therapy for epistemological anxiety. Educational Studies in Mathematics 33(2): 171-202.
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.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sherin, B.L. A Comparison of Programming Languages and Algebraic Notation as Expressive Languages for Physics. International Journal of Computers for Mathematical Learning 6, 1–61 (2001). https://doi.org/10.1023/A:1011434026437
Issue Date:
DOI: https://doi.org/10.1023/A:1011434026437