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Math in motion: Using CBRs to enact functions
Article

## Despina Stylianou, Beverly Smith, City College, The City University of New York, United States ; James J. Kaput, University of Massachusetts, Dartmouth, United States

JCMST Volume 24, Number 3, ISSN 0731-9258 Publisher: Association for the Advancement of Computing in Education (AACE), Waynesville, NC USA

## Abstract

This paper reports on results of an exploratory study on undergraduate pre-service teachers' understanding of graphical representations of motion functions. The study described pre-service teachers' explorations using a CBR device. Pre-service teachers' growth was studied in two dimensions: (a) in their learning of the mathematics involved and (b) in their learning of the pedagogy related to the mathematics and the technology used. Through their interaction with the device, pre-service teachers were able to overcome common misconceptions with respect to the mathematics and also to develop pedagogical insights regarding the teaching of the concepts.

## Citation

Stylianou, D., Smith, B. & Kaput, J.J. (2005). Math in motion: Using CBRs to enact functions. Journal of Computers in Mathematics and Science Teaching, 24(3), 299-324. Norfolk, VA: Association for the Advancement of Computing in Education (AACE). Retrieved August 19, 2019 from https://www.learntechlib.org/primary/p/5905/.

© 2005 Association for the Advancement of Computing in Education (AACE)

### Keywords

## References

View References & Citations Map- Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93 (4), 373-397.
- Ball, D. L. & Cohen, D. K. (1999). Developing Practice, Developing Practitioners: Toward a Practice-Based Theory of Professional Education. In G.
- Beckman, C. E. & Rozanski, K. (1999). Graphs in real time. Mathematics Teaching in the Middle School, 5 (2), 92-99.
- Berg, C. A. & Smith, P. (1995). Assessing students’ abilities to construct and interpret line graphs: Disparities between multiple-choice and free-response instruments. Science Education, 78, 527-554.
- Bowers, J. & Doerr, H. M. (2001). An analysis of pre-service teachers’ dual roles in understanding the mathematics of change: Eliciting growth with technology. Journal of Mathematics Teacher Education, 4 (2), 115-137.
- Brown, C. & Borko, H. (1992). Becoming a mathematics teacher. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 209-239). New York: Macmillan .
- Doerr, H. M., Rieff, C., & Tabor, J. (1999). Putting math in motion with Calculator-Based Labs. Mathematics Teaching in the Middle School, 4 (6), 364367.
- Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students’ achievement and attitude levels in precollege mathematics courses. Journal for Research in Mathematics Education, 34 (5), 433-463.
- Graham, E. & Sharp, J. (1999). An investigation into able students’ understanding of motion graphs. Teaching Mathematics and its Applications, 18, 3, 128-135.
- Greeno, J. G. (1988). Situated activities of learning and knowing in mathematics. In M. Behr, C. Lacampagne, & M. Wheeler (Eds.), Proceedings of the 10th annual meetings of PME-NA (pp. 481-521). DeKalb, IL.
- Grouws, D. & Smith, M. S. (2000). NAEP Findings on the Preparation and Practices of Mathematics Teachers. In E. A. Silver & P. A. Kenney, P. A. (Eds.), Results from the Seventh National Assessment of Educational Progress (pp. 107-140). Reston, VA: NCTM.
- Janvier, C. (1978).Translation processes in mathematics education. In C. Janvier (Ed.), Problems of representation in mathematics learning and problem solving. (pp. 27-31). Hillsdale, NJ: LEA.
- Kaput, J. (1986). Information technology and mathematics: Opening new representational windows. Journal of Mathematical Behavior, 5, 187-207.
- Kaput, J. (1987). Representation and mathematics. In C. Janvier (Ed.), Problems of representation in mathematics learning and problem solving. Hillsdale, NJ: LEA.
- Kaput, J., & Roschelle, J. (1997). Deepening the impact of technology beyond assistance with traditional formalism in order to democratize access to ideas underlying calculus. In Proceedings of the 21st Conference of the Psycholst Conference of the Psychology
- Kaput, J., & Roschelle, J. (2000, October). Shifting representational infrastructures and reconstituting content to democratize access to the math of change and variation: Impacts on cognition, curriculum, learning and teaching. Paper presented at a workshop to “Integrate Computer-based Modeling and Scientiﬁ c Visualization into K–12 Teacher Education Programs.” Ballston, VA.
- Kieran, C. (2001). Looking at the role of technology in facilitating transition from arithmetic to algebraic thinking through the lens of a model of algebraic activity. In Proceedings of the 12th Study Conference of the International Commission on Mathematical Instruction (pp. 713–720). Australia, The University of Melbourne.
- Kilpatrick, J., & Swafford, J. (2001). Adding it up: helping children learn mathematics. Washington, DC.: National Research Council.
- Linn, M., Layman, J., & Nachmias, R. (1987). Cognitive consequences of microcomputer-based laboratories: graphing skills development. Contemporary Educational Psychology, 12, 244-253.
- Minick, N. (1996). The development of Vygotsky’s thought. In H. Daniels, (Ed.), An introduction to Vygotsky (pp. 28-52). London: Routledge.
- Mokros, J. R., & Tinker, R. F. (1987). The impact of microcomputer-based labs on children’s abilities to interpret graphs. Journal of Research in Science Teaching, 24, 369-383.
- Moreno, L., Rojano, T., Bonilla, E. & Rerrusquia, E. (1999) The incorporation of new technologies to school culture. In Proceedings of the 21st Annual st Annual
- Nachmias, R., & Linn, M. C. (1987). Evaluations of science laboratory data: The role of computer-presented information. Journal of Research in Science Teaching, 24, 491-506.
- National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.
- Nemirovsky R. (1993). Motion, ﬂ ow, and contours: The experience of continuous change. Unpublished Doctoral Dissertation. Harvard University, Cambridge, MA.
- Ochs, E., Jacoby, S., & Gonzales, P. (1994). Interpretive journeys: How physicists talk and travel through graphic space. Conﬁ gurations, 2 (1), 151-171. Parke, C., Lane, S., Silver, E., & Magone, M. (2003). Using assessment to improve middle grades mathematics teaching and learning: suggested activities using QUASAR tasks, scoring criteria, and students’ work ’ work ’
- Roth, W. M., & McGinn, M. K. (1997). Graphing: Cognitive ability or practice? Science Education, 81, 91-106.
- Schoenfeld, A., Smith, J., & Arcavi, A. (1994). Learning: The microgenetic analysis of one student’s evolving understanding of a complex subject matter
- Simon, M. A. & Schifter, D. (1991). Towards a constructivist perspective: An intervention study of mathematics teachers. Educational Studies in Mathematics, 22, 4, 309-331.
- Smith, B. S. (2000). Preservice elementary mathematics teachers’ developing beliefs and their reactions to alternative assessment practices (Doctoral dissertation, Teacher College - Columbia University, 2000). Dissertation Abstracts International, 61, 2227.
- Smith, M. S. (2001). Practice-based professional development for teacher of mathematics. Reston, VA: National Council of Teachers of Mathematics. Stylianou, D. A. (2002). Interaction of visualization and analysis – The negotiation of a visual representation in problem solving. Journal of Mathematical Behavior, 21, 3, 303-317.
- Stylianou, D. A. & Kaput, J. J. (2002). Linking phenomena to representations: A gateway to the understanding of complexity. Mediterranean Journal for Research in Mathematics Education, 1(2), 99-111.
- Stylianou, D. A. & Shapiro, L. (2002). Reforming college algebra: The effect of the use of a cognitive tutor in a college algebra developmental course. Journal of Educational Media, 27, 3, 147-171.
- Von Glaserfeld, E. (1995). A constructivist approach to teaching. In L. Steffe & J. Gale (Eds.), Constructivism in education (pp. 3-15). Hillsdale, NJ: Erlbaum.
- Vygotsky, L. (1962). Thought and language. (E. Hanfmann & G. Vakar, Trans.). Cambridge, MA: Massachusetts Institute of Technology. (Original work published in 1934.)
- Weiss, I. R. (1995). Mathematics Teachers’ Response to the Reform Agenda: Re- ’ Response to the Reform Agenda: Re- ’
- Sults of the 1993 National Survey of Science and Mathematics Education. Paper presented at the annual meeting of the American Education Research Association, San Francisco, Ca., April, 1995.

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