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

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## 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 call*interpretive 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.

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## REFERENCES

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