Desarrollo del conocimiento del profesor mediante el estudio de configuraciones epistémicas y cognitivas de la proporcionalidad.

Olivo Mauro Rivas, Godino Juan D.

Resumen


Este estudio tiene como objeto informar algunos avances teóricos sobre el constructo “conocimiento del profesor” de matemáticas referido en la literatura, y sobre la puesta en práctica de herramientas de análisis epistémico/cognitivo, concebidas y diseñadas con el fin de fomentar el desarrollo de esta forma de conocimiento en la formación de futuros profesores. Se presenta de manera esquemática el desarrollo de ese constructo en la literatura respectiva, se describen las herramientas de análisis utilizadas y se informa sobre la puesta en juego de tales herramientas en una muestra de 50 futuros profesores, al tratar con la resolución de un problema sobre proporcionalidad. Los resultados señalan la utilidad potencial del uso de dichas herramientas para fomentar el “Conocimiento Matemático para Enseñar” y se concluye con algunas implicaciones de este estudio en la formación de profesores.


Palabras clave


conocimiento matemático para enseñar; configuraciones epistémicas y cognitivas; proporcionalidad; formación de profesores.

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Referencias


Ball, Deborah Loewenberg (1990). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90, 449-466.

Ball, Deborah Loewenberg y Bass, Hyman (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. En J. Boaler (Ed.), Multiple perspectives of mathematics teaching y learning (pp. 83-104). Westport, CT: Greenwood Publishing Group Incorporated.

Ball, Deborah Loewenberg; Hill, Heather y Bass, Hyman (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29, 14-22.

Ball, Deborah Loewenberg; Lubienski, Sarah Theule y Mewborn, Denise Spangler (2001). Research on teaching mathematics: The insolved problem of teachers, mathematical knowledge. En V. Richarson (Ed.). Handbook of research on teaching. (pp. 433 – 456). New York: Macmillan.

Behr, Merlyn; Harel, Guershon; Post, Thomas y Lesh, Richard (1992). Rational number, ratio and proportion. En D. A. Grouws (Ed.). Handbook of research on mathematics teaching and learning. (pp. 296-333). New York: Macmillan.

Ben-Chaim, David; Fay, James; Fitzgerald, William; Benedetto, Catherine y Miller, Jane (1998). Proportional reasoning among 7th grade students with different curricular experience. Educational Studies in Mathematics, 36, 247–273.

Ben-Chaim, David; Keret, Yaffa e Ilany Bat-Sheva (2007) Designing and implementing authentic investigative proportional reasoning tasks: the impact on pre-service mathematics teachers’ content and pedagogical knowledge and attitudes. Journal of Mathematics Teacher Education, 10, 333–340.

Confrey, Jere y Smith, Erick (1995). Splitting, covariation and their role in the development of exponential functions. Journal for Research in Mathematics Education, 26, 66-86.

Dole, Shelly y Shield, Mal (2008). The capacity of two Australian eighth-grade textbooks for promoting proportional reasoning. Research in Mathematics Education, 10(1), 19-35.

Even, Ruhama (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24, 94-116.

Even, Ruhama y Tirosh, Dina (2002). Teachers’ knowledge and understanding of students’ mathematical learning. En L. English (Ed.), Handbook of international research in mathematics education, (pp. 219- 240). Mahwah, NJ: Erlbaum.

Fennema, Elizabeth y Franke, Megan Loef (1992). Teachers’ knowledge and its impact. En D. Grows (Ed.). Handbook of research on mathematics teaching and learning (pp. 147-164). New York: Macmillam.

Godino, Juan Díaz; Batanero, Carmen y Font, Vincenç (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39 (1-2), 127-135.

Godino, J. Díaz; Rivas, Mauro, Castro, Walter Fernando y Konic, Patricia. (2008). Epistemic and cognitive analysis of an arithmetic – algebraic problem solution. ICME 11, TSG 27: Mathematical knowledge for teaching. Recuperado el 12 de enero de 2009 en: http://tsg.icme11.org/document/get/391

Hernández Sampieri, Roberto; Fernández Collado, Carlos y Baptista Lucio, Pilar (2006). Metodología de la investigación (4ta ed.). México: McGraw-Hill.

Hill, Heather y Ball, Deborah Loewenberg (2004). Learning mathematics for teaching: Results fom California’s mathematics professional development institutes. Journal for Research in Mathematics Education, 35(5), 330-351.

Hill, Heather; Ball, Deborah Loewenberg y Schilling, Stephen (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39, 372-400.

Hill, Heather; Rowan, Brian y Ball, Deborah Loewenberg (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 317-406.

Hill, Heather; Sleep, Laurie; Lewis, Jennifer y Ball, Deborah Loewenberg (2007). Assessing teachers’ mathematical knowledge: What knowledge matters and what evidence counts? En F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 111-155). Charlotte, NC: Information Age Publishing.

Ilany, Bat-Sheva; Keret, Yaffa y Ben-Chaim, David (2004). Implementation of a model using authentic investigative activities for teaching ratio and proportion in pre-service elementary teacher education. En M. J. Høines y A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 81-88). Bergen, Norway: PME.

Kahan, Jeremy; Cooper, Duane y Bethea, Kimberly (2003). The role of mathematics teachers’ content knowledge in their teaching: A framework for research applied to a study of student teachers. Journal of Mathematics Teacher Education, 6, 223-252.

Kilpatrick, Jeremy; Swafford, Jane y Findell, Bradford (2001). Developing proficiency in teaching mathematics. En J. Kilpatrick, J. Swafford, y B. Findell (Eds.), Adding it up: Helping children learn mathematics (pp. 369-406). Washington, DC: National Academy Press.

Lamon, Susan (1993). Ratio and proportion: Connecting content and children’s thinking. Journal for Research in Mathematics Education, 24, 41-61.

Lamon, Susan (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. En F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 629-667). Charlotte, NC: Information Age Publishing.

León, Orfelio y Montero, Ignacio (2003). Diseño de Investigaciones. Madrid: McGraw-Hill.

Lesh, Richard, Post, Thomas y Behr, Merlyn (1988). Proportional reasoning. En J. Hiebert y M. Behr (Eds.). Number concepts and operations for the middle grades (pp. 93-118). Reston, VA: National Council of Teachers of Mathematics.

Lin, Pi-Jen. (2002). On enhancing teachers’ knowledge by constructing cases in classrooms. Journal of Mathematics Teacher Education, 5, 317–349.

Lo, Jane-Jane y Watanabe, Tad (1997). Developing ratio and proportion schemes: A story of a fifth grader. Journal for Research in Mathematics Education, 28, 216-236.

Ma, Liping (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.

Mason, John y Spence, Mary (1999). Beyond mere knowledge of mathematics: the importance of knowingto act in the moment. Educational Studies in Mathematics, 38, 135–161.

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

National Council of the Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.

Person, Axelle; Berenson, Sarah y Greenspon, Paula (2004). The role of number in proportional reasoning: a prospective teacher’s understanding. En M. J. Høines y A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 17-24). Bergen, Norway: PME

Ponte, Joao Pedro y Chapman, Olive (2006). Mathematics teachers’ knowledge and practice. En A.

Gutiérrez y P. Boero (Eds.). Handbook of research of the psychology of mathematics education: Past, present and future. (pp. 461-494). Roterdham: Sense Publishing.

Sanz, Angeles; Pozo, Juan Ignacio; Pérez Echeverría, María del Puy y Gómez Crespo, Miguel Ángel (1996). El razonamiento proporcional en expertos y novatos: El efecto del contenido. Revista de Psicología General y Aplicada, 49(2), 337-352.

Shulman, Lee (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 2-14.

Shulman, Lee (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.

Singer, J., Kohn, S. y Resnick, L. (1997). Knowing about proportions in different contexts. En T. Nunes y P. Bryant (Eds.). Learning and teaching mathematics: An international perspective (pp. 115-132). Hove: Psychology Press.

Smith, J. (2002). The development of students’ knowledge of fractions and ratios. En B. Litwiller y G. Bright. (Eds.). Making sense of fractions, ratios, and proportions. (pp. 87-99). Reston, Virginia: National Council of Teachers of Mathematics.

Sowder, J., Armstrong, B., Lamon, S., Simon, M., Sowder, L. y Tompson, A. (1998). Educating teachers to teach multiplicative structures in the middle grades. Journal of Mathematics Teacher Education, 1, 127–155.

Steele, M. D. (2005). Comparing knowledge bases and reasoning structures in discussions of mathematics and pedagogy. Journal of Mathematics Teacher Education, 8, 291-328.

Thompson, A. G., y Thompson, P. W. (1996). Talking about rates conceptually, Part II: Mathematical knowledge for teaching. Journal for Research in Mathematics Education, 27(1), 2-24.

Thompson, P. (1994). The development of the concept of speedy and its relationship to concept of rate. En G. Harel y J. Confrey (Eds.). The Development of Mutltiplicative Reasoning in the Learning of Mathematics (pp. 179-234). Albany, NY: State University of New York Press.

Tirosh, Dina; Even, Ruhama y Robinson, N. (1998). Simplifying algebraic expressions: Teacher awareness and teaching approaches. Educational Studies in Mathematics, 35, 51-64.

Tourniaire, F. y Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16, 181-204.

Vergnaud, G. (1988). Multiplicative structures. En J. Hiebert y M. Behr (Eds.). Number concepts and operations for the middle grades (pp. 141-161). Reston, VA: National Council of Teachers of Mathematics.




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Depósito legal electrónico: pp199702ME1927 

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