Abstract
In this study, we seek to describe how the meaning of a tool was co-constructed by the students and their teacher and how the students used the tool to construct mathematical meaning out of particular tasks. We report the results of a qualitative, classroom-based study that examined (1) the role, knowledge and beliefs of a pre-calculus teacher, (2)how students used graphing calculators in support of their learning of mathematics, (3) the relationship and interactions between the teacher's role, knowledge and beliefs and the students' use of the graphing calculator in learning mathematics, and (4) some constraints of the graphing calculator technology that emerged within the classroom practice. We found five patterns and modes of graphing calculator tool use emerged in this practice: computational tool, transformational tool, data collection and analysis tool, visualizing tool, and checking tool. The results of this study suggest that nature of the mathematical tasks and the role, knowledge and beliefs of the teacher influenced the emergence of such rich usage of the graphing calculator. We also found that the use of the calculator as a personal device can inhibit communication in a small group setting, while its use as a shared device supported mathematical learning in the whole class setting.
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REFERENCES
Adams, T.: 1997, 'Addressing students' difficulties with the concept of function: Applying graphing calculators and a model of conceptual change', Focus on Learning Problems in Mathematics 19(2), 43-57.
Cobb, P. and Yackel, E.: 1996 'Constructivist, emergent, and sociocultural perspectives in the context of developmental research', Educational Psychologist 31(3/4), 175-190.
Confrey, J. and Doerr, H.M.: 1996, 'Changing the curriculum to improve student understandings of function', in D.F. Treagust, R. Duit and B.J. Fraser (eds.), Improving Teaching and Learning in Science and Mathematics, Teachers College Press, New York, pp. 162-171.
Doerr, H.M.: 1998, 'Student thinking about models of growth and decay', in A. Olivier and K. Newstead (eds.), Proceedings of the 22nd Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, University of Stellenbosch, Stellenbosch, Africa, pp. 256-263.
Doerr, H.M. and Tripp, J.: 1999, 'Understanding how students develop mathematical models', Mathematical Thinking and Learning 1(3), 231-254.
Drijvers, P. and Doorman, M.: 1996, 'The graphics calculator in mathematics education', Journal of Mathematical Behavior 15(4), 425-440.
Dunham, P. and Dick, T.: 1994, 'Research on graphing calculators', The Mathematics Teacher 87(6), 440-445.
Farrell, A.M.: 1996, 'Roles and behaviors in technology-integrated precalculus classrooms', Journal of Mathematical Behavior 15(1), 35-53.
Hiebert, J., Carpenter, T.P., Fennema, E., Fuson, K., Wearne, D., Murray, H., Olivier, A. and Human, P.: 1997, Making Sense: Teaching and Learning Mathematics with Understanding, Heinemann, Portsmouth, NH.
Hollar, J.C. and Norwood, K.: 1999, 'The effects of a graphing-approach intermediate algebra curriculum on students' understanding of function', Journal for Research in Mathematics Education 30(2), 220-226.
Lave, J. and Wenger, E.: 1991, Situated learning: Legitimate peripheral participation, Cambridge University Press, New York.
Leinhardt, G., Zaslavsky, O. and Stein, M.K.: 1990, 'Functions, graphs, and graphing: Tasks, learning and teaching', Review of Educational Research 60(1), 1-64.
Meira, L.: 1995, 'Mediation by tools in the mathematics classroom', in L. Meira and D. Carraher (eds.), Proceedings of the 19th Annual Conference of the International Groups for the Psychology of Mathematics Education, Vol. 1, ERIC Clearinghouse, Columbus, OH, pp. 102-111.
Meira, L.: 1998, 'Making sense of instructional devices: The emergence of transparency in mathematical activity', Journal for Research in Mathematics Education 29(2), 121-142.
Moschkovich, J., Schoenfeld, A. and Arcavi, A.: 1993, 'Aspects of understanding: On multiple perspectives and representations of linear relations and connections among them', in T.A. Romberg, T.P. Carpenter and E. Fennema (eds.), Integrating Research on the Graphical Representations of Functions, Lawrence Erlbaum Associates, Hillsdale, NJ, pp. 69-100.
National Council of Teachers of Mathematics.: 1989, Curriculum and Evaluation Standards for School Mathematics, Author, Reston, VA.
Penglase, M. and Arnold, S.: 1996, 'The graphics calculator in mathematics education: A critical review of recent research', Mathematics Education Research Journal 8(1), 58-90.
Porzio, D.T.: 1997, March, Examining Effects of Graphing Calculator Use on Students' Understanding of Numerical, Graphical and Symbolic Representations of Calculus Concepts, Paper presented at the Annual Meeting of the American Educational Research Association, Chicago, IL. (ERIC Document Reproduction Service No. ED 410 112.)
Quesada, A.R. and Maxwell, M.E.: 1994, 'The effects of using graphing calculators to enhance college students' performance in precalculus', Educational Studies in Mathematics 27(2), 205-215.
Roth, W.-M. and McGinn, M.K.: 1997, 'Graphing: Cognitive ability or practice?', Science Education 81(1), 91-106.
Ruthven, K.: 1990, 'The influence of graphing calculator use on translation from graphic to symbolic forms', Educational Studies in Mathematics 21(5), 431-450.
Shoaf-Grubbs, M.M.: 1994, 'The effect of the graphing calculator on female students' spatial visualization skills and level of understanding in elementary graphing and algebra concepts', in E. Dubinsky, A. Schoenfeld and J. Kaput (eds.), Research in Collegiate Mathematics Education, Vol. 1, American Mathematical Society in cooperation with the Mathematical Association of America, Providence, RI, pp. 169-194.
Simmt, E.: 1997, 'Graphing calculators in high school mathematics', Journal of Computers in Mathematics and Science Teaching 16(2/3), 269-289.
Tharp, M.L., Fitzsimmons, J.A. and Ayers, R.L.: 1997, 'Negotiating a technological shift: Teacher perception of the implementation of graphing calculators', Journal of Computers in Mathematics and Science Teaching 16(4), 551-75.
Williams, C.G.: 1993, 'Looking over their shoulders: Some difficulties students have with graphing calculators', Mathematics and Computer Education 27(3), 198-202.
Wilson, M.R. and Krapfl, C.M.: 1994, 'The impact of graphics calculators on students' understanding of function', Journal of Computers in Mathematics and Science Teaching 13(3), 252-264.
Yerushalmy,M.: 1991, 'Student perceptions of aspects of algebraic function using multiple representation software', Journal of Computer Assisted Learning 7(1), 42-57.
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Doerr, H.M., Zangor, R. Creating Meaning for and with the Graphing Calculator. Educational Studies in Mathematics 41, 143–163 (2000). https://doi.org/10.1023/A:1003905929557
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DOI: https://doi.org/10.1023/A:1003905929557