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Interactive video: A bridge between motion and math

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Abstract

This paper examines the characteristics of interactive digitized video as a medium in which motion is presented to students learning graphical representations. We situate graphs of motion as early topics in learning calculus, the bugaboo of many math students. In comparing video to both everyday perceptions and mathematical representations, we construct a conceptual framework that compares these three contexts along several dimensions: object extent, scale, time, and space. We then examine one student's experience constructing graphs of her own design from a video image and describe her work in the context of the our conceptual framework. To further specify the unique characteristics of video, we compare it as a medium with that of computer simulations of motion, in particular as studied by diSessa et al. (1991).

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References

  • Ackerman, E. (1991). Personal communication.

  • Barnes, M. (1991). Investigating Change: An Introduction to Calculus for Australian Schools. Carlton South, Victoria, Australia: Curriculum Corporation.

    Google Scholar 

  • Bresnahan, S., Ducas, T. and Rubin, A. (1994). Cartwheeling in CamMotion. Hands On! (Vol. 17, No. 2).

  • CamMotion. (1995). Cambridge, MA: VIEW Project, TERC.

  • Confrey, J. (1994). How compatible are radical constructivism, social-cultural approaches and social constructivism? In L. Steffe (Ed.), Constructivism in Education. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • diSessa, A., Hammer, D., Sherin, B. and Kolpakowski, T. (1991). Inventing graphing: Meta-representational expertise in children. Journal of Mathematical Behavior 10: 117–160.

    Google Scholar 

  • Ducas, T. (1993). Active video: the promise of AVID learning. Journal for College Science Teaching. 23(3): (Dec. 1993/Jan 1994) 166–172.

    Google Scholar 

  • Duckworth, E. (1987). The Having of Wonderful Ideas. New York: Teachers College Press.

    Google Scholar 

  • Edgerton, H. (1987). Stopping Time: The Photographs of Harold Edgerton. New York: Harry N. Abrams Inc.

    Google Scholar 

  • Ferrini-Mundy, J. and Guether, K. (1991) An overview of the calculus curriculum reform effort: Issues for learning, teaching, and curriculum development. The American Mathematical Monthly 98(7): 627–635.

    Google Scholar 

  • GraphAction. (1995). Watertown, MA: Tom Snyder Productions, Inc.

  • Hall, R. and Rubin, A. (in press) ... there's five little notches in here: Dilemmas in Teaching and learning the conventional structure of rate. In J. Greeno and S.G. Goldman (Eds.), Thinking Practices. Hillsdale, NJ: Lawrence Erlbaum and Associates.

  • HIP Physics. (1994). Watertown, MA: Tom Snyder Productions, Inc.

  • Kaput, J. (1991). Democratizing Access to Calculus: New Routes to Old Roots. Dartmouth, MA: University of Massachusetts.

    Google Scholar 

  • Kaput, J. and Nemirovsky, R. (1995) Moving to the next level: A mathematics of change theme throughout the K-16 curriculum. UME Trends 6(6): 20–21.

    Google Scholar 

  • Lightman, Alan P. (1992). Einstein's Dreams. London: Bloomsbury.

    Google Scholar 

  • Measurement in Motion. (1994). Santa Cruz, CA: Learning in Motion.

  • Mokros, J.R. and Tinker, R.F. (1987). The impact of microcomputer-based labs on children's ability to interpret graphs. Journal of Research in Science Teaching 24: 369–383.

    Google Scholar 

  • Nemirovsky, R. (1993). Rethinking calculus education. Hands On 16(1).

  • Nemirovsky, R. (1994) On ways of symbolizing: The case of Laura and velocity sign. The Journal of Mathematical Behavior 13: 389–422.

    Google Scholar 

  • Nemirovsky, R. and Rubin, A. (1991), “It makes sense if you think about how the graphs work. But in reality ...” In F. Furinghetti (Ed.), Proceedings of the 15th Annual Meeting, North American Chapter of the International Group for the Psychology of Mathematics Education 3: 57–64.

  • Piaget, J. (1970). Genetic Epistemology. New York: Norton & Norton.

    Google Scholar 

  • Raymo, C. (1995). “The ways of a crow — That's calculus in motion”. The Boston Globe, February 20, 1995, 48.

  • Rubin, A. (1994) Annual Report on the VIEW Project. Unpublished document, Cambridge: TERC. 1994.

    Google Scholar 

  • Rubin, A. and Boyd, A. (1994). Perspectives on Learning the Mathematics of Motion: Videos and Discussion. Paper presented at the conference of the American Educational Research Association, New Orleans, LA.

  • Russell, S.J., Mokros, J., Tierney, C. and others (1994–1996). Investigations in Number, Data, and Space. A K-5 Mathematics Curriculum. Palo Alto: Dale Seymour Publications.

    Google Scholar 

  • Steffe, L. and Cobb, P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education 14(2): 83–94.

    Google Scholar 

  • Thompson, P. (1991). The Development of the concept of speed and its relationship to concepts of rate. G. Harel and J. Confrey (Eds), The Development of Multiplicative Reasoning in the Learning of Mathematics New York: SUNY Press.

    Google Scholar 

  • Thornton, R. and Sokolow, D. (1990). Learning motion concepts using real time microcomputer based tools. American Journal of Physics 58(9): 858–866.

    Google Scholar 

  • Tierney, C., Nemirovsky, C. and Noble, T. (1995a). Investigations in Number, Data and Space: Patterns of Change. Palo Alto, CA: Dale Seymour Publications.

    Google Scholar 

  • Tierney, C., Nemirovsky, C. and Weinberg, A. (1995b). Investigations in Number, Data and Space: Changes over Time. Palo Alto, CA: Dale Seymour Publications.

    Google Scholar 

  • Trowbridge, D.E. and McDermott, L.C. (1980). Investigation of student understanding of the concept of velocity in one dimension. American Journal of Physics 48(12): 1020.

    Google Scholar 

  • VideoGraph. (1994). Raleigh, NC: Robert Beichner, North Carolina State University.

  • von Glasersfeld, E. (1984). An introduction to radical constructivism. In P. Watzlawick (Ed.), The Invented Reality (pp. 17–40). New York: W. W. Norton.

    Google Scholar 

  • Zollman, D. (1994). Digital Video Interactive: A Case Study in Physics. Lawrence, KA: Kansas State University.

    Google Scholar 

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Boyd, A., Rubin, A. Interactive video: A bridge between motion and math. Int J Comput Math Learning 1, 57–93 (1996). https://doi.org/10.1007/BF00191472

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