Abstract
Many learning environments, computer-based or not, have been developed for either students or teachers alone to engage them in mathematical inquiry. While some headway has been made in both directions, few efforts have concentrated on creating learning environments that bring both teachers and students together in their teaching and learning. In the following paper, we propose game design as such a learning environment for students and teachers to build on and challenge their existing understandings of mathematics, engage in relevant and meaningful learning contexts, and develop connections among their mathematical ideas and their real world contexts. To examine the potential of this approach, we conducted and analyzed two studies: Study I focused on a team of four elementary school students designing games to teach fractions to younger students, Study II focused on teams of pre-service teachers engaged in the same task. We analyzed the various games designed by the different teams to understand how teachers and students conceptualize the task of creating virtual game learning environment for others, in which ways they integrate their understanding of fractions and develop notions about students' thinking in fractions, and how conceptual design tools can provide a common platform to develop meaningful fraction contexts. In our analysis, we found that most teachers and students, when left to their own devices, create instructional games to teach fractions that incorporate little of their knowledge. We found that when we provided teachers and students with conceptual design tools such as game screens and design directives that facilitated an integration of content and game context, the games as well as teachers' and students' thinking increased in their sophistication. In the discussion, we elaborate on how the design activities helped to integrate rarely used informal knowledge of students and teachers, how the conceptual design tools improved the instructional design process, and how students and teachers benefit in their mathematical inquiry from each others' perspectives. In the outlook, we discuss features for computational design learning environments.
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REFERENCES
Baker, S. (1994). The development of children's fraction thinking in a first grade classroom. Unpublished doctoral dissertation, University of Wisconsin-Madison.
Ball, D. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. The Elementary School Journal 93(2): 373-397.
Baylor, A. (1997). The effects of designing instruction for text upon learning. Unpublished doctoral dissertation, University of South Carolina.
Behr, M., Harel, G., Post, T. and Lesh, R. (1993). Rational numbers: Toward a semantic analysis - emphasis on the operator construct. In T. P. Carpenter, E. Fennema and T. Romberg (Eds), Rational Numbers: An Integration of Research (pp. 13-48). Hillside, N.J.: Lawrence Erlbaum.
Block, J. H. and King, N. R. (Eds) (1987). School Play. New York: Garland.
Bride, J. W. and Lamb, C. E. (1991). Using commercial games to design teacher-made games for the mathematics classroom. Arithmetic Teacher 38: 14-22.
Bright, G. W., Harvey, J. G. and Wheeler, M. M. (1985). Learning and mathematics games. Journal for Research in Mathematics Education, Monograph, Vol. 1. Reston, Va.: NCTM.
Brophy, J. E. (1991). Conclusion to advances in research on teaching, Vol. II: Teachers' knowledge of subject matter as it relates to their teaching practice. In J. Brophy (Ed.), Advances in Research on Teaching: Teachers' Subject Matter Knowledge and Classroom Instruction, Vol. II.(pp. 349-364). Greenwich, Conn.: JAI Press.
Brown, A. L. and Campione, J. C. (1996). Psychological theory and the design of innovative learning environments: On procedures, principles and systems. In L. Schauble and R. Glaser (Eds), Innovations in Learning: New Environments for Education (pp. 289-325). Mahaw, N.J.: Lawrence Erlbaum Associates.
Bruner, J., Jolly, A. and Sylva, K. (Eds) (1976). Play: Its Role in Development and Evolution. New York: Basic Books.
Carpenter, T. P., Fennema, E. and Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instructions. Elementary School Journal 97(1): 1-20.
Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G., Trigatti, B. and Perlwitz, M. (1991). Assessment of a problem-centered second-grade mathematics project. Journal for Research in Mathematics Education 22: 3-29.
Cobb, P., Yackel, T. and Wood, T. (1992). Interaction and learning in mathematics classroom situations. Educational Studies in Mathematics 23: 99-122.
Confrey, J. (1996). Strengthening early algebra through a splitting approach in elementary education. Paper presented at the annual meeting of the American Educational research Association, New York, NY.
Dugdale, S. (1981). Green globs: A microcomputer application for graphing of equations. CERL Report E-21, University of Illinois, Urbana.
Edwards, L. (1991). Children's Learning in a Computer Microworld for Transformation Geometry. Journal for Research in Mathematics Education 22(2): 122-137.
Fennell, F., Houser, L. L., McPartland, D. and Parker, S. (1984, February). Ideas. Arithmetic Teacher 31: 27-33.
Fennema, E. and Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 147- 164). New York: Macmillan.
Fennema, E., Franke, M. L., Carpenter, T. P. and Carey, D. A. (1993). Using children's knowledge in instruction. American Educational Research Journal 30: 555-583.
Fennema, E., Carpenter, T., Franke, M., Levi, L., Jacobs, V. and Empson, S. (1996). A longitudinal study of learning to use children's thinking in mathematics instruction. Journal for Research in Mathematics Education 27(4): 403-434.
Fischer, G. and Lemke, A. C. (1987/88). Construction kits and design environments. Human-Computer Interaction 3: 179-222.
Franke, M. L., Kafai, Y. B. and Shih, J. (1997, April). Pre-service Teachers' Conceptions of Learning through Making Games. Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, Ill.
Franke, M. L., Carpenter, T. P., Fennema, E., Ansell, E. and Behrend, J. (in press). Understanding teachers' self-sustaining, generative change in the context of professional development. Teaching and Teacher Education.
Grouws, D. (Ed.) (1992). Handbook of Research on Mathematics Teaching and Learning. New York: Macmillan.
Harel, I. (1991). Children Designers. Norwood: Ablex.
Harel, G. and Confrey, J. (1994). The Development of Multiplicative Reasoning. Albany, NY: SUNY.
Hiebert, J., Carpenter, T. O., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A. and Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The case of mathematics. Educational Researcher 25(4): 12-21.
Hiebert, J. and Behr, M. (1988). Number Concepts and Operations in the Middle Grades. Hillsdale, N.J.: Lawrence Erlbaum.
Kafai, Y. B. (1995). Minds in Play: Computer Game Design as a Context for Learning. Hillsdale, N.J.: Lawrence Erlbaum Associates.
Kerslake, D. (1986). Children's Understanding of Mathematics: 11-16.Windsor, England: NFER-Nelson.
Kieren, T. (1976). On the mathematical cognitive and instructional foundations of rational numbers. In R. Lesh (Ed.), Number and Measurement. Columbus, OH: ERIC/SMEAC.
Kieren, T. (1988). Personal knowledge of rational numbers: Its intuitive and formal development. In J. Hiebert and M. Behr (Eds), Number Concepts and Operations in theMiddle Grades. Hillsdale, N.J.: Lawrence Erlbaum.
Kieren, T. (1993). Rational numbers and fractional numbers: From quotient fields to recursive understanding. In T. P. Carpenter, E. Fennema and T. Romberg (Eds), Rational Numbers: An Integration of Research (pp. 49-84). Hillsdale, N.J.: Lawrence Erlbaum.
Lampert, M. (1989).When the problem is not the question and the solution not the answer: Mathematical knowing and teaching. American Educational Research Journal 27(1): 2963.
Lave, J. (1988). Cognition in Practice: Mind, Mathematics, and Culture in Everyday Life. Cambridge: Cambridge University Press.
Lave, J. (1996). Teaching as learning in practice. Mind, Culture and Activity 3(3): 149-164.
Leinhardt, G. and Smith, D. A. (1985). Expertise in mathematics instruction: Subject matter knowledge. Journal of Educational Psychology 3: 247-2741.
Lehrer, R. and Franke, M. L. (1992). Applying personal construct psychology to the study of teachers' knowledge of fractions. Journal for Research in Mathematics Education 23(3): 223-241.
Loef, M. (1991). Understanding teachers; Knowledge about building instruction on children's mathematical thinking: Application of a personal construct approach. Unpublished doctoral dissertation, University of Wisconsin-Madison.
Mack, N. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education 21: 16-32.
Malone, T. W. and Lepper, M. R. (1987). Making learning fun: A taxonomy of intrinsic motivations for learning. In R. E. Snow and M. J. Farr (Eds), Aptitude, Learning and Instruction. Volume 3: Conative and Affective Process Analyses (pp. 223-253). Hillsdale, N.J.: Erlbaum.
Munby, H. (1982). The place of teachers; beliefs in research on teaching thinking and decision making, and an alternative methodology. Instructional Science 11: 201-225.
Piaget, J. (1951). Play, Dreams, and Imitation in Childhood. New York: W. Norton.
Pope, M. and Keen, T. (1981). Personal Construct Psychology in Education. London: Academic.
Post, T. R. (1981). Fractions: Results and implications from national assessment. Arithmetic Teacher 28(9): 26-31.
Priester, S. (1984, March). SUM 9.9: A game for decimals. Arithmetic Teacher 31: 46-47.
Provenzo, E. F. (1991). Video Kids: Making Sense of Nintendo. Cambridge,Mass.: Harvard University Press.
Resnick, L. (1987). Learning in school and out. Educational Researcher 16(12): 13-20.
Saxe, G. B. and Bermudez, T. (1996). Emergent mathematical environments in children's games. In P. Nesher, L. D. Steffe, P. Cobb, B. Goldin and B. Greer (Eds), Theories of Mathematical Learning (pp. 51-68). Hillsdale, N.J.: Lawrence Erlbaum Associates.
Schifter, D. and Fosnot, C. T. (1993). Reconstructing Mathematics Education: Stories of Teachers Meeting the Challenge of Reform.New York: Teachers College Press.
Solas, J. (1992). Investigating teacher and student thinking about the process of teaching and learning using autobiography and repertory grid. Review of Educational Research 62(2): 205-225.
Streefland, L. (1991). Fractions in Realistic Mathematics Education. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Streefland, L. (1993). Fractions: A realistic approach. In T. P. Carpenter, E. Fennema and T. A. Romberg (Eds), Rational Numbers: An Integration of Research. Hillsdale, N.J.: Lawrence Erlbaum Associates.
Sutton-Smith, B. (1986). Toys as Culture. New York: Gardener Press.
Wood, T., Cobb, P. and Yackel, E. (1991). Change in teaching mathematics: A case study. American Educational Research Journal 28(3): 587-616.
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Kafai, Y., Franke, M., Ching, C. et al. Game Design as an Interactive Learning Environment for Fostering Students' and Teachers' Mathematical Inquiry. International Journal of Computers for Mathematical Learning 3, 149–184 (1998). https://doi.org/10.1023/A:1009777905226
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DOI: https://doi.org/10.1023/A:1009777905226