Challenges, teachers and gifted learners in mathematics
Abstract
In this paper we reflect on the nature of the mathematical challenges and their important role in the care of students with mathematically talented students, and we insist on the possible roles that teachers can play. We stress the need for the math teacher achieve a specialized knowledge on formulating appropriate mathematical challenges, in order to identify and to encourage mathematically talented students in the classroom. We exemplify these ideas with specific challenges, showing teacher strategies used to formulate mathematical challenges around a specific content and how to sequence them.
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APPLEBAUM, M. y LEIKIN, R. (2007) Teachers’ conceptions of mathematical challenge in school mathematics. En J. W. Woo, H. C. Lew, K. S. Park y D. Y. Seo (eds.) Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, vol. 2 (pp. 9-16). Seoul, Korea: pme.
ASSOULINE, S. G. y LUPKOWSKI-SHOPLIK, A. (2005) Developing math talent: A guide for educating gifted and advanced learners in math. Waco, tx: Prufrock Press.
BARBEAU, E. J. y TAYLOR, P. J. (eds.) (2009) Challenging Mathematics In and Beyond the Classroom. The 16th icmi Study. New York: Springer.
BENAVIDES, M. (2008) Caracterización de sujetos con talento en resolución de problemas de estructura multiplicativa. Tesis doctoral. Universidad de Granada. Granada.
CASTRO, E. (1995) Niveles de comprensión en problemas verbales de comparación multiplicativa. Granada: Comares.
CASTRO, E.; BENAVIDES, M. y SEGOVIA, I. (2006) Cuestionario para caracterizar a niños con talento en resolución de problemas de estructura multiplicativa. Faisca. Revista de Altas Capacidades, 13, 4-22.
CHARLES, R. y LESTER, F. (1982) Teaching Problem Solving. What, Why y How. Palo Alto, ca: Dale Seymour Publications.
COLLINS, A.; BROWN, J. S. y NEWMAN, S. E. (1989) Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics. En L. B. Resnick (ed.) Knowing, learning, and instruction: Essays in honor of Robert Glaser (pp. 453-494). Hillsdale, nj: Erlbaum.
DEPARTMENT FOR EDUCATION AND EMPLOYMENT (2000) Mathematical challenges for able pupils. London (El autor).
DOYLE, W. (1988) Work in mathematics classes: The context of students’ thinking during instruction. Educational Psychologist, 23 (2), 167-180.
http://dx.doi.org/10.1207/s15326985ep2302_6
ELLERTON, N. (1986) Children’s Made-Up Mathematics Problems A New Perspective on Talented Mathematicians. Educational Studies in Mathematics, 17, 261-271. http://dx.doi.org/10.1007/BF00305073
FELDHUSEN, J. F. y KROLL, M. D. (1991) Boredom or challenge for the academically talented in school. Gifted Education International, 7, 80-81.
http://dx.doi.org/10.1177/026142949100700207
FREIMAN, V. (2006) Problems to discover and to boost mathematical talent in early grades: a challenging situations approach. The Montana Mathematics Enthusiast, 3, 51-75.
GREENES, C. (1981) Identifying the gifted student in mathematics. Aritmetic Teacher, 28 (8), 4-17.
GUZMÁN, M. (2002a) Una descripción del proyecto «Detección y estímulo del talento matemático precoz en la Comunidad de Madrid». Bordón. Revista de Pedagogía, 54, 255-268.
GUZMÁN, M. (2002b) Un programa para detectar y estimular el talento matemático precoz en la Comunidad de Madrid. Gaceta de la Real Sociedad Matemática Española, 5 (1), 131-144.
HENNINGSEN, M. y STEIN, M. K. (1997) Mathematical tasks and student cognition: classroombased factors that supports and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28 (5), 524-549.
http://dx.doi.org/10.2307/749690
HIEBERT, J.; CARPENTER, T.; FENNEMA, E.; FUSON, K.; WEARNE, D.; MURRAY, H.; OLIVIER, A. y HUMAN, P. (1997) Making Sense. Portsmouth, nh: Heinemann.
JOHNSON, D. T. (1994) Mathematics curriculum for the gifted. En J. VanTassel-Baska (ed.) Comprehensive curriculum for gifted learners. Boston: Allyn and Bacon.
KRUTETSKII, V. A. (1969) An analysis of the individual structure of mathematical abilities in schoolchildren. En J. Kilpatrick e I. Wirszup (eds.) Soviet Studies in the Psychology of Learning and Teaching Mathematics, vol. ii (pp. 59-104). The Structure of Mathematical Abilities. Chicago: University of Chicago Press.
LAMPERT, M. (1990) When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27 (1), 29-63.
http://dx.doi.org/10.3102/00028312027001029
LEIKIN, R. (2004) Towards High Quality Geometrical Tasks: Reformulation of a Proof Problem. En M. J. Hoines y A. B. Fuglestad (eds.) Proceedings of the 28th International Conference for the Psychology of Mathematics Education, vol. 3 (pp. 209-216).
MILLER, R. C. (1990) Discovering Mathematical Talent. eric Digest #E482.
Niederer, K. e Irwin, K. (2001) Using problem solving to identify mathematically gifted Students. En M. van den Heuvel-Panhuizen (ed.) Proceeding of the 25 th Conference of the International Group for the Psychology of Mathematics Education, vol. 3 (pp. 431-438). Utrecht.
NIEDERER, K.; IRWIN, R. C.; IRWIN, K. C. y REILLY, I. L. (2003) Identification of Mathematically Gifted Children in New Zealand. High Ability Studies, 14 (1), 71-84.
http://dx.doi.org/10.1080/13598130304088
PASARÍN, M. J.; FEIJOO, M.; DÍAZ, O. y RODRÍGUEZ, L. (2004) Evaluación del talento matemático en educación secundaria. Faisca. Revista de Altas Capacidades, 11, 88-103.
POLYA, G. (1973). Cómo plantear y resolver problemas. México: Trillas.
POWELL, A. B.; BORGE, I. C.; FIORITI, G. I.; KONDRATIEVA, M.; KOUBLANOVA, E. y SUKTHANKAR, N. (2009) Challenging tasks and mathematics learning. En Challenging Mathematics In and Beyond the Classroom (pp. 133-170). Springer us.
SCHOENFELD, A. H. (1985) Mathematical problem solving. Orlando, Fl: Academic Press.
SHEFFIELD, L. J. (ed.) (1999) Developing mathematically promising students. Reston, va: National Council of Teachers of Mathematics.
SHEFFIELD, L. J. (2003) Extending the Challenge in Mathematics: Developing Mathematical Promise in K-8 Students. Thousand Oaks, ca: Corwin Press.
SPAN, P. y OVERTOOM-CORSMIT, R. (1986) Information Processing by Intellectually Gifted Pupils Solving Mathematical Problems. Educational Studies in Mathematics, 17, 273-295.
http://dx.doi.org/10.1007/BF00305074
WATTERS, J. J. y DIEZMANN, C. M. (2000) Catering for mathematically gifted elementary students: Learning from challenging tasks. Gifted Child Today, 23 (4), 14-19.
ASSOULINE, S. G. y LUPKOWSKI-SHOPLIK, A. (2005) Developing math talent: A guide for educating gifted and advanced learners in math. Waco, tx: Prufrock Press.
BARBEAU, E. J. y TAYLOR, P. J. (eds.) (2009) Challenging Mathematics In and Beyond the Classroom. The 16th icmi Study. New York: Springer.
BENAVIDES, M. (2008) Caracterización de sujetos con talento en resolución de problemas de estructura multiplicativa. Tesis doctoral. Universidad de Granada. Granada.
CASTRO, E. (1995) Niveles de comprensión en problemas verbales de comparación multiplicativa. Granada: Comares.
CASTRO, E.; BENAVIDES, M. y SEGOVIA, I. (2006) Cuestionario para caracterizar a niños con talento en resolución de problemas de estructura multiplicativa. Faisca. Revista de Altas Capacidades, 13, 4-22.
CHARLES, R. y LESTER, F. (1982) Teaching Problem Solving. What, Why y How. Palo Alto, ca: Dale Seymour Publications.
COLLINS, A.; BROWN, J. S. y NEWMAN, S. E. (1989) Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics. En L. B. Resnick (ed.) Knowing, learning, and instruction: Essays in honor of Robert Glaser (pp. 453-494). Hillsdale, nj: Erlbaum.
DEPARTMENT FOR EDUCATION AND EMPLOYMENT (2000) Mathematical challenges for able pupils. London (El autor).
DOYLE, W. (1988) Work in mathematics classes: The context of students’ thinking during instruction. Educational Psychologist, 23 (2), 167-180.
http://dx.doi.org/10.1207/s15326985ep2302_6
ELLERTON, N. (1986) Children’s Made-Up Mathematics Problems A New Perspective on Talented Mathematicians. Educational Studies in Mathematics, 17, 261-271. http://dx.doi.org/10.1007/BF00305073
FELDHUSEN, J. F. y KROLL, M. D. (1991) Boredom or challenge for the academically talented in school. Gifted Education International, 7, 80-81.
http://dx.doi.org/10.1177/026142949100700207
FREIMAN, V. (2006) Problems to discover and to boost mathematical talent in early grades: a challenging situations approach. The Montana Mathematics Enthusiast, 3, 51-75.
GREENES, C. (1981) Identifying the gifted student in mathematics. Aritmetic Teacher, 28 (8), 4-17.
GUZMÁN, M. (2002a) Una descripción del proyecto «Detección y estímulo del talento matemático precoz en la Comunidad de Madrid». Bordón. Revista de Pedagogía, 54, 255-268.
GUZMÁN, M. (2002b) Un programa para detectar y estimular el talento matemático precoz en la Comunidad de Madrid. Gaceta de la Real Sociedad Matemática Española, 5 (1), 131-144.
HENNINGSEN, M. y STEIN, M. K. (1997) Mathematical tasks and student cognition: classroombased factors that supports and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28 (5), 524-549.
http://dx.doi.org/10.2307/749690
HIEBERT, J.; CARPENTER, T.; FENNEMA, E.; FUSON, K.; WEARNE, D.; MURRAY, H.; OLIVIER, A. y HUMAN, P. (1997) Making Sense. Portsmouth, nh: Heinemann.
JOHNSON, D. T. (1994) Mathematics curriculum for the gifted. En J. VanTassel-Baska (ed.) Comprehensive curriculum for gifted learners. Boston: Allyn and Bacon.
KRUTETSKII, V. A. (1969) An analysis of the individual structure of mathematical abilities in schoolchildren. En J. Kilpatrick e I. Wirszup (eds.) Soviet Studies in the Psychology of Learning and Teaching Mathematics, vol. ii (pp. 59-104). The Structure of Mathematical Abilities. Chicago: University of Chicago Press.
LAMPERT, M. (1990) When the problem is not the question and the solution is not the answer: Mathematical knowing and teaching. American Educational Research Journal, 27 (1), 29-63.
http://dx.doi.org/10.3102/00028312027001029
LEIKIN, R. (2004) Towards High Quality Geometrical Tasks: Reformulation of a Proof Problem. En M. J. Hoines y A. B. Fuglestad (eds.) Proceedings of the 28th International Conference for the Psychology of Mathematics Education, vol. 3 (pp. 209-216).
MILLER, R. C. (1990) Discovering Mathematical Talent. eric Digest #E482.
Niederer, K. e Irwin, K. (2001) Using problem solving to identify mathematically gifted Students. En M. van den Heuvel-Panhuizen (ed.) Proceeding of the 25 th Conference of the International Group for the Psychology of Mathematics Education, vol. 3 (pp. 431-438). Utrecht.
NIEDERER, K.; IRWIN, R. C.; IRWIN, K. C. y REILLY, I. L. (2003) Identification of Mathematically Gifted Children in New Zealand. High Ability Studies, 14 (1), 71-84.
http://dx.doi.org/10.1080/13598130304088
PASARÍN, M. J.; FEIJOO, M.; DÍAZ, O. y RODRÍGUEZ, L. (2004) Evaluación del talento matemático en educación secundaria. Faisca. Revista de Altas Capacidades, 11, 88-103.
POLYA, G. (1973). Cómo plantear y resolver problemas. México: Trillas.
POWELL, A. B.; BORGE, I. C.; FIORITI, G. I.; KONDRATIEVA, M.; KOUBLANOVA, E. y SUKTHANKAR, N. (2009) Challenging tasks and mathematics learning. En Challenging Mathematics In and Beyond the Classroom (pp. 133-170). Springer us.
SCHOENFELD, A. H. (1985) Mathematical problem solving. Orlando, Fl: Academic Press.
SHEFFIELD, L. J. (ed.) (1999) Developing mathematically promising students. Reston, va: National Council of Teachers of Mathematics.
SHEFFIELD, L. J. (2003) Extending the Challenge in Mathematics: Developing Mathematical Promise in K-8 Students. Thousand Oaks, ca: Corwin Press.
SPAN, P. y OVERTOOM-CORSMIT, R. (1986) Information Processing by Intellectually Gifted Pupils Solving Mathematical Problems. Educational Studies in Mathematics, 17, 273-295.
http://dx.doi.org/10.1007/BF00305074
WATTERS, J. J. y DIEZMANN, C. M. (2000) Catering for mathematically gifted elementary students: Learning from challenging tasks. Gifted Child Today, 23 (4), 14-19.
Castro, E., Ruiz-Hidalgo, J. F., & Castro-Rodríguez, E. (2015). Challenges, teachers and gifted learners in mathematics. Aula, 21, 85–104. https://doi.org/10.14201/aula20152185104
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