<p>Solving problems on functions: role of the graphing calculator</p>

Vilma Mesa

doi:10.30827/pna.v2i3.6198

Autores/as

Vilma Mesa University of Michigan, Estados Unidos

DOI:

https://doi.org/10.30827/pna.v2i3.6198

Palabras clave:

Calculadoras gráficas, Funciones, Resolución de problemas

Resumen

To study the roles that the graphing calculator plays in solving problems about functions, a small quasi-experimental study was conducted with four pairs of undergraduate students solving problems with and without the graphing calculator. The analysis of the protocols of the sessions did not reveal major differences that could be attributed to the presence or absence of the tool but indicated differences in strategies used with each problem that could be explained in terms of the nature of the knowledge at stake and to students’ availability of that knowledge. The study suggests a model for conducting research that looks for explaining the effects of technology in learning and instruction.

Resolución de problemas sobre funciones: papel de la calculadora gráfica

Con el fin de analizar el papel que la calculadora gráfica juega en la resolución de problemas sobre funciones, se hizo un pequeño estudio cuasi-experimental con cuatro pares de estudiantes de pre-grado variando la condición de la disponibilidad de la calculadora. El análisis de los protocolos de las sesiones revela que no hay mayores diferencias que se puedan atribuir a la presencia o ausencia de la calculadora gráfica; sin embargo, las diferencias observadas en el uso de estrategias que se usaron en cada problema pueden explicarse en términos de la naturaleza del conocimiento en juego y de la disponibilidad de tal conocimiento para los estudiantes. El estudio sugiere además un modelo para realizar investigaciones que busquen explicar los efectos de la tecnología en el aprendizaje y en la instrucción.

Handle: http://hdl.handle.net/10481/4389

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Citas

Alkhateeb, H. M., & Wampler, J. (2002). Graphing calculators and students' conception of the derivative. Perceptual and Motor Skills, 94, 165-170. DOI: https://doi.org/10.2466/pms.2002.94.1.165

Artzt, A. F., & Armour-Thomas, E. (1990). Protocol analysis of group problem solving in mathematics: A cognitive-metacognitive framework for assessment. Paper presented at the Annual Meeting of the American Educational Research Association, Boston.

Balacheff, N. (1993). Artificial intelligence and real teaching. In C. Keitel & K. Ruthven (Eds.), Learning from computers: Mathematics education and technology (pp. 131-158). Berlin: Springer Verlag. DOI: https://doi.org/10.1007/978-3-642-78542-9_6

Carulla, C., & Gómez, P. (1996). Graphic calculators and precalculus: Effects on curriculum design. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th PME Conference (Vol. 1, pp. 161). Valencia: Universidad de Valencia.

Demana, F., Schoen, H. L., & Waits, B. K. (1993). Graphing in the K-12 curriculum: The impact of the graphing calculator. In T. A. Romberg, T. Carpenter & E. Fennema (Eds.), Integrating research on the graphical representation of functions (pp. 28-37). Hillsdale: Erlbaum.

Dick, T. (2000). Much more than a toy: Graphing calculators in Secondary school calculus. In P. Gómez & B. K. Waits (Eds.), Roles of the graphing calculator in the classroom (pp. 31-48). Bogotá: una empresa docente.

Dion, G., Harvey, A., Jackson, C., Klag, P., Lui, J., & Wright, C. (2001). A survey of calculator usage in high schools. School, Science and Mathematics, 101, 427-438. DOI: https://doi.org/10.1111/j.1949-8594.2001.tb17878.x

Figg, C., & Burson, J. (2005). Across the curriculum with handheld computers. Computers in the schools, 22, 131-143. DOI: https://doi.org/10.1300/J025v22n03_11

Gómez, P., & Fernández, F. (1997). Graphing calculator use in precalculus and achievement in calculus. In E. Pehkonen (Ed.), Psychology of Mathematics Education (Vol. 3, pp. 1-8). Lahti: University of Helsinki.

Gómez, P., & Mesa, V. (Eds.). (1995). Situaciones problematicas en pre-cálculo [Problematic situations in pre-calculus]. México and Bogotá: Editorial Iberoamerica and una empresa docente.

Graham, A. T., & Thomas, M. O. J. (2000). Building a versatile understanding of algebraic variables with a graphic calculator. Educational Studies in Mathematics, 41(3), 265-282. DOI: https://doi.org/10.1023/A:1004094013054

Hennessy, S. (1997). Portable technologies and graphing investigations: Review of the literature. Milton Keynes: The Open University.

Hennessy, S., Fung, P., & Scanlon, E. (2001) The role of the graphic calculator in mediating graphing activity. International Journal of Mathematics for Education in Science and Technology, 32(2), 267-290. DOI: https://doi.org/10.1080/00207390010022176

Hiebert, J., & Carpenter, T. (1992). Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65-97). New York: National Council of Teachers of Mathematics.

Hollar, J. C., & Norwood, K. (1999). The effects of a graphing-approach intermediate algebra curriculum on students' understanding of functions. Journal for Research in Mathematics Education, 30(2), 220-226. DOI: https://doi.org/10.2307/749612

Kaput, J. (1992). Technology and mathematics education. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 515-556). New York: Macmillan.

Mesa, V. (1996). The role of the graphing calculator in solving problems on functions. Unpublished master's thesis, University of Georgia, Athens, GA.

Mesa, V., & Gómez, P. (1996). Graphing calculators and pre-calculus: An exploration of some aspects of students' understanding. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th Conference of the International Group of the Psychology of Mathematics Education (Vol. 3, pp. 391-398). Valencia: Universidad de Valencia.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston: Author.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: Author.

Noss, R., & Hoyles, C. (1996). Windows of mathematical meaning. Dordrecht: Kluwer. DOI: https://doi.org/10.1007/978-94-009-1696-8

Quesada, A. R., & 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. DOI: https://doi.org/10.1007/BF01278922

Resnick, L. B. (1987). Education and learning to think. Washington: National Academy Press.

Roschelle, J. M., Pea, R. D., Hoadley, C. M., Gordin, D. N., & Means, B. M. (2000). Changing how and what children learn in school with computer-based technologies. The Future of Children, 10(2), 76-101. DOI: https://doi.org/10.2307/1602690

Ruthven, K. (1990). The influence of graphic calculator use on translation from graphic to symbolic forms. Educational Studies in Mathematics, 21(5), 431-450. DOI: https://doi.org/10.1007/BF00398862

Schoenfeld, A. (1983). Episodes and executive decisions in mathematical problem-solving. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 345-395). New York: Academic Press.

Schoenfeld, A. (Ed.). (1987). Cognitive science and mathematics education. Hillsdale: Erlbaum.

Schoenfeld, A. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-370). New York: Macmillan.

Shumway, R. J. (1990). Supercalculators and the curriculum. For the Learning of Mathematics, 10(2), 2-9.

Simmt, E. (1997). Graphing calculators in high school mathematics. The Journal of Computers in Mathematics and Science, 16(2), 269-289.

Slavit, D. (1994). The effect of graphing calculators on students' conceptions of function. Paper presented at the Annual Meeting of the American Educational Research Association, New Orleans, LA.

Smith, J. P. (1998). Graphing calculators in the mathematics classrooms. Columbus: ERIC Clearinghouse for Science, Mathematics, and Environmental Education.

Smith, K. B., & Schotsberger, P. G. (1997). Assessing the use of graphing calculators in college algebra: Reflecting on dimensions of teaching and learning. School Science and Mathematics, 97(7), 368-376. DOI: https://doi.org/10.1111/j.1949-8594.1997.tb17378.x

Vahey, P., Tatar, D., & Roschelle, J. M. (2004). Leveraging handhelds to increase student learning: Engaging middle school students with the mathematics of change. Paper presented at the International Conference of the Learning Sciences: Embracing diversity in the learning sciences, University of California-Los Angeles, Santa Monica, CA.

Valero, P., & Gómez, C. (1996). Precalculus and graphic calculators: The influence on teacher's beliefs. In L. Puig & A. Gutiérrez (Eds.), Proceedings of the 20th PME Conference (Vol. 4, pp. 371-378). Valencia: Universidad de Valencia.

Williams, S. R. (1993). Some common themes and uncommon directions. In T. A. Romberg, T. Carpenter & E. Fennema (Eds.), Integrating research on the graphical representation of functions (pp. 313-337). Mahwah: Earlbaum.