La educación matemática, resolución de problemas, y el empleo de herramientas computacionales

Referencias

Arcavi, A. (2005). Developing and using symbol sense in mathematics. For the learning of mathematics, 25, 2, pp.42-47. Arcavi, Abraham., & Hadas, Nurit. (2000). Computer mediated learning: An example of an approach. International Journal of Computers for Mathematical Learning, 5, pp.25-45. Camacho-Machín, M., Depool-Rivero, R. & Santos-Trigo, M. Students’ use of derive software in comprehending and making sense of definite integral and area concepts. Research in Collegiate Mathematics Education (2010). American Mathematical Society, Vol. 16: 29-50. Camacho, M. & Santos, L.M. (2004a). El estudio de fenómenos de variación haciendo uso de herramientas tecnológicas. Revista UNO, Vol. 37, pp. 105-122, España. Camacho, M. & Santos, M. (2004). La relevancia de los problemas en el aprendizaje de las matemáticas a través de la resolución de problemas. NÚMEROS, vol. 58, pp. 45-60, España. Camacho, M., Depool. R., & Santos, M. (2004). Promoting students’ comprehension of definite integral and area concepts through the use of derive software. Proceedings of the XXVI Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, pp. 447-454. University of Toronto, Canada. Charles, R. & Silver, E. (1988) (Eds.). The teaching and assessing of mathematical problem solving. Reston VA: The National Council of Teachers of Mathematics. Curcio, F. (1987) (Ed.), Teaching and learning: A Problem-solving focus. Reston VA: The National Council of Teachers of Mathematics. Devlin, K. (1994). Mathematics. The science of patterns. NY:Scientific American Library. English, L. (Ed.) (2002). Handbook of international research in mathematics education. Mahwah, NJ: Lawrence Erlbaum. Goldenberg, P. & Cuoco, A. (1998). What is dynamic geometry? In R.Leher & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space, pp. 351- 367. Mahwah, NJ: Lawrence Erlbaum Associates. Kaput, J. (1992). Technology and mathematics education. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning, pp. 515-556. NY: Macmillan. PISA (Programme for International Student Assessment) (2006). Assessing Scientific, Reading and Mathematical Literacy. A Framework for PISA 2006. Paris: Organization for Economic Co operation and Development. Kelly, A., E. & Lesh, R. (Eds.), Handbook of research design in mathematics education. Mahwah, NJ: Lawrence Erlbaum. Lehrer, R. & Chazan, D. (Eds.) (1998). Designing learning environments for developing understanding of geometry and space. Mahwah, NJ: Lawrence Erlbaum. Lester, F. K. (2005). On the theoretical, conceptual, and philosophical foundation for research in mathematics education. ZDM 2005 Vol.37, 6, p.458. Moreno, L. & Santos, M. Democratic access and use of powerful mathematics in an emerging country. In L. English (Ed.). Handbook of International Research in Mathematics Education. NY: Routledge, Taylor & Francis Group. Segunda Edición, (2008), ISBN 13: 978-0-8058-5875-4: 319- 351. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston VA: The Council. National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Reston VA: The Council. Perkins, D. (1995). Outsmarting IQ. The emerging science of learnable intelligence. N.Y:The Free Press. PMENA, 2001, 2002, 2003, 2004. Proceedings of the 23, 24, 25. 26 annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Columbus OH: ERIC Clearinghouse for Science, Mathematics, and Environmental Education. Polya, G. 1945. How to Solve it. Princeton, NJ: Princeton University Press. Romberg, T.A., & Kaput, J. (1999). Mathematics worth teaching, mathematics worth understanding. En E. Fennema & T. A. Romberg (Eds.), Mathematics clasroom that promote understanding (pp. 3-17). Mahwah, NJ: Lawrence Erlbaum. Santos T. L.M (2007). Resolución de problemas matemáticos. Fundamentos cognitivos. Mexico, DF: Trillas. Santos-Trigo, M. & Barrera-Mora, F. (2007). Contrasting and looking into some mathematicseducation frameworks. The Mathematics Educator, 10(1), pp. 81-106. Santos-Trigo, M. & Camacho-Machín, M. Towards the construction of a framework to deal with routine problems to foster mathematical inquiry. PRIMUS, (2009), ISSN: 1051-1970, 19(3): 260-279. Santos-Trigo, M. & Espinosa-Pérez, H. High School Teachers’ use of dynamic software to generate serendipitous mathematical relations. The Montana Mathematics Enthusiast, 2010, ISSN 1551-3440, Vol. 7, no.1, pp.31-46. Montana Council of Teachers of Mathematics & Information Age Publishing. Santos, M (2004). Exploring the Triangle Inequality and Conic Sections Using Dynamic Software for Geometry. Mathematics Teacher, Vol 97, No 1, pp. 68-72. Santos, M. (2001). Potencial didáctico del softaware dinámico en el aprendizaje de las matemáticas. Avance y Perspectiva, 20, pp. 247-258. Este trabajo también lo publicó la revista Expresiones de la Dirección General de Educación Tecnológica Industria, pp. 5-17 Santos, M. (2002). Students’ use of mathematical representations in problem solving. Mathematics and Computer Education Journal, pp. 101-114, Spring Issue. Santos, M. (2002a). Students’ use of technological tools to construct conceptual systems in mathematical problem solving. En F. Hitt (Ed.), Representation and mathematics visualization, pp. 111-125. Working Group Representation and Visualization: PMENA. Santos, M. (2003). Procesos de Transformación de Artefactos Tecnológicos en Herramientas de Resolución de Problemas Matemáticos. Boletín de la Asociación Matemática Venezolana. Vol X, No2. pp. 195-212. Santos, M. (2004). The Role of Technology in Students’ Conceptual Constructions in a Sample Case of Problem Solving. Focus on Learning Problems in Mathematics. Spring Edition, vol 26, 2, pp. 1-17. Santos, M. (2004b). The role of dynamic software in the identification and construcction of mathematical relationships. Journal of Computers in Mathematics and Science Teaching, 23 (4), pp, 399-413. Santos, M. & Espinoza H. (2002). Searching and exploring properties of geometric configurations via the use of dynamic software. International Journal of Mathematical Education in Science and Technology, 33(1), pp. 37-50. Santos, M. & Vargas, C. (2003). Más allá del uso de exámenes estandarizados. Avance y Perspectiva, 22, pp. 9-22. Schoenfeld, A. H. (1985). Mathematical problem solving. New York: Academic Press. Schoenfeld, A., H. (1998). Reflections on a course in mathematical problem solving. Research in Collegiate Mathematics Education III., pp. 81-113. Silver, E. A. (1987). Foundations of cognitive theory and research for mathematics problemsolving instruction, In Alan H. Schoenfeld (Ed), Cognitive science and mathematics education, Hillsdale, NJ: Lawrence Erlbaum Associates, pp. 1-31. Whimbey, A. & Lochhead, J.(1976). Problem solving & comprehension. 6th edition, Mahwah, NJ: Lawrence Erlbaum. Zbiek, R. M., Heid, M.K., & Blume, G. W. (2007). Research on technology in mathematics education. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 1169-1207). NCTM, Charlotte, NC: Information Age Publishing.