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Artículos

Vol. 11 No. 3 (2008): Noviembre

INTERPRETING MATHEMATICAL UNDERSTANDING IN BASIC CONTEXTS OF ASSESSMENT. A STUDY ON THE INTERFERENCES IN THE USE OF THE MEANINGS OF THE FRACTION

Submitted
May 21, 2024
Published
2008-10-31

Abstract

This work examines some aspects of the problem of interpretation of mathematical understanding. Starting with the specific configuration of one of the basic context where this problem arises, a proposal for the interpretation of learning for understanding is developed. The proposed model is based on an operational model of the value placed on the understanding of mathematical content. Its practical potential is revealed through its application, with pre-service teachers, in the context of fractions. The evidence obtained using some fraction meanings, support a characterization of the understanding based on different priorities and availability in the use of this mathematical object, within its phenomenological and epistemological field.

References

  1. Ainley, J. & Lowe, A. (1999). Can written questions differentiate between degrees of understanding? Mathematics Teacher 168, 32-35.
  2. Behr, M., Harel, G., Post, T. & Lesh, R. (1992). Rational number, ratio and proportion. En D. A.
  3. Grouws (Ed.) Handbook of Research on Mathematics Teaching and Learning (pp. 233-296), New York: MacMillan Publishing Company.
  4. Bender, P. (1996). Basic imagery and understandings for mathematical concepts. En C. Alsina, J. M. Álvarez, B. Hodgson, C. Laborde & A. Pérez. 8° Congreso Internacional de Educación Matemática (ICME). Selección de Conferencias (pp. 57-74). Sevilla, España: SAEM Thales.
  5. Brown, T. (2001). Mathematics Education and Language. Interpreting Hermeneutics and Post-Structuralism. Dordrecht: Kluwer Academic Publishers.
  6. Byers, V. & Erlwanger, S. (1985). Memory in mathematical understanding. Educational Studies in Mathematics 16, 259-281.
  7. Carpenter, T. & Lehrer, R. (1999). Teaching and learning mathematics with understanding. En E. Fennema & T.A. Romberg (Eds.) Mathematics classrooms that promote understanding (pp. 19 32). Mahwah, N.J.: Lawrence Erlbaum Associates.
  8. Carpenter, T., Fennema, E., Fuson, K., Hiebert, J., Human, P., Murray, H., Olivier, A. & Wearne, D. (1999). Learning basic number concepts and skills as problem solving. En E. Fennema & T.A. Romberg (Eds.) Mathematics classrooms that promote understanding (pp. 45-61). Mahwah, N.J.: Lawrence Erlbaum Associates.
  9. Castro, E., Rico, L. y Romero, I. (1997). Sistemas de representación y aprendizaje de estructuras numéricas. Enseñanza de las Ciencias 15 (3), 361-371.
  10. Clarke, D. M. & Sukenik, M. (2006). Assessing fraction understanding using task-based interviews. En J. Novotná, H. Moraová, M. Krátká & N. Stehlíková (Eds.). Proceedings 30th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 337-344). Praga: PME.
  11. Davis, R. B. (1992). Understanding "Understanding". Journal of Mathematical Behavior 11, 225-241.
  12. Dos Santos, A. (2005). O conceito de fração em seus diferentes significados: Um estudo diagnóstico junto a professores que atuam no encino fundamental. Tesis de Maestria. Sao Paulo, Brasil: Pontificia Universidad Católica de Sao Paulo.
  13. Duffin, J. M. & Simpson, A. P. (2000). A search for understanding. Journal of Mathematical Behavior 18 (4), 415-427.
  14. English, L.D. & Halford, G.S. (1995). Mathematics Education: Models and processes. Mahwah, N.J.: Lawrence Erlbaum Associates.
  15. Escolano, R. y Gairin, J. M. (2005). Modelos de medida para la enseñanza de números racionales en educación primaria. UNIÓN Revista Latinoamericana de Educación Matemática 1, 17-35. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel Publishing Company.
  16. gGairin, J. M. ( 1998). Sistemas de representación de números racionales positivos. Un estudio con maestros en formación. Tesis de doctorado no publicada, Universidad de Zaragoza, España.
  17. Gairin, J. M. y Sancho, J. (2002). Números y algoritmos. Madrid: Síntesis.
  18. Gallardo, J. (2004). Diagnóstico y evaluación de la comprensión del conocimiento matemático. El caso del algoritmo estándar escrito para la multiplicación de números naturales. Tesis de doctorado no publicada, Universidad de Málaga, España.
  19. Gallardo, J. & González, J. L. (2006a). Assessing understanding in mathematics: steps towards an operative model. For the Learning of Mathematics 26 (2), 10-15.
  20. Gallardo, J. y González, J. L. (2006b). Una aproximación operativa al diagnóstico y la evaluación de la comprensión del conocimiento matemático. PNA, 1, 1, 21-31.
  21. Gallardo, J. y González, J. L. (2007a). Fronteras en la investigación sobre comprensión en Educación Matemática. Números, 66.
  22. Gallardo, J. y González, J. L. (2007b). Diagnóstico y evaluación de la comprensión del conocimiento matemático: el caso del algoritmo estándar para la multiplicación de números
  23. naturales. En E. Castro y J. L. Lupiañez (Eds.) Investigaciones en Educación Matemática: Pensamiento numérico (pp. 157-184). Granada: Editorial Universidad de Granada.
  24. Godino, J. D. (2000). Significado y comprensión de los conceptos matemáticos. Uno 25, 77-87. Godino, J. D. (2002). Un enfoque semiótico y ontológico de la cognición matemática. Recherches en Didactique des Mathématiques 22 (2/3), 237-284.
  25. Godino, J. D. y Batanero, C. (1994). Significado personal e institucional de los objetos matemáticos. Recherches en Didactique des Mathématiques 14 (3), 325-355.
  26. Goldin, G. (2002). Representation in mathematical learning and problem solving. En L. D. English (Ed.) Handbook of international research in Mathematics Education (pp. 197-218). Mahwah, N. J.: Lawrence Erlbaum Associates.
  27. González, J. L. y Ortiz. A. (2000). La investigación en Educación Matemática en la Universidad de Málaga: Estructura y fundamentos. En L. C. Contreras, J. Carrillo, N. Climent y M. Sierra (Eds.) Actas del IV Simposio de la Sociedad Española de Investigación en Educación Matemática SEIEM (pp. 131-146). Huelva: Universidad de Huelva.
  28. Hiebert, J. & Carpenter, T. P. (1992). Learning and teaching with understanding. En D. A. Grouws (Ed.) Handbook of research on mathematics teaching and learning (pp. 65-97). New York: MacMillan Publishing Company.
  29. Hiebert, J. & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. En J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillsdale, N. J.: Lawrence Erlbaum Associates.
  30. Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K.C., Wearne, D., Murray, H., Olivier, A. & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding, Portsmouth, N. H.: Heinemann.
  31. Kieren, T. E. (1976). On the mathematical, cognitive and instructional foundations of rational numbers. In R. Lesh (Ed.), Number and measurement: Papers from a research workshop (pp. 101-144). Columbus, OH: ERIC/SMEAC.
  32. Kieren, T. (1988). Personal Knowledge of rational numbers: Its intuitive and formal development. En J. Hiebert & M. J. Behr (Eds.) Number concepts and operations in the middle grades (pp. 162-181). Reston, VA: National Council of Teachers of Mathematics.
  33. Kieren, T. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. En T. P. Carpenter, E. Fennema & T. A. Romberg (Eds.) Rational numbers: An integration of research (pp. 49-84). New Jersey: Lawrence Erlbaum Associates.
  34. Kieren, T., Pirie, S. & Calvert, L. G. (1999). Growing minds, growing mathematical understanding: mathematical understanding, abstraction and interaction. En L. Burton (Ed.) Learning mathematics: From hierarchies to networks (pp. 209-231). London: Routledge.
  35. Koyama, M. (2000). A research on the validity and efectiveness of "two-axes process model" of understanding mathematics at elementary school level. En T. Nakahara & M. Koyama (Eds.) Proceedings of the 24th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3 (pp. 159-166). Hiroshima, Japan: PME.
  36. Lamon, S. J. (2001). Presenting and representing: from fractions to rational numbers. En A.A.
  37. Couco y F. R. Curcio (Eds.) The roles of representation on school mathematics (pp. 146-165). Reston, Virginia: National Council of Teachers of Mathematics.
  38. NCTM (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  39. Niemi, D. (1996). Assessing conceptual understanding in mathematics: Representations, problem solutions, justifications, and explications. The Journal of Educational Research 89 (6), 351-363.
  40. Pirie, S. & Kieren, T. (1994). Growth in mathematical understanding: how can we characterise it and how can we represent it? Educational Studies in Mathematics 26, 165-190.
  41. Post, T., Cramer, K., Behr, M., Lesh, R. & Harel, G. (1993). Curriculum implications of research on the learning, teaching and assessing of rational number concepts. En T. P. Carpenter, E. Fennema & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 327-361). Hillsdale, NJ: Lawrence Erlbaum Associates.
  42. Puig, L. (1997). Análisis Fenomenológico. En L. Rico (Coord.) La Educación Matemática en la Enseñanza Secundaria (pp. 61-94). Barcelona: Horsori.
  43. Quispe, W. (2008). Interferencias en la comprensión de los significados del número racional. Tesis de maestría no publicada, Universidad Nacional de San Antonio Abad del Cusco-CUES, Perú.
  44. Sierpinska, A. (1994). Understanding in mathematics. London: The Falmer Press.
  45. Sierpinska, A. (2000). Mathematics classrooms that promote understanding (Book Review). ZDM 2, 45-50.
  46. Valdemoros, M. (2004). Lenguaje, fracciones y reparto. Revista Latinoamericana de Investigación en Matemática Educativa 7 (3), 235-256.
  47. Vergnaud, G. ( 1997). The nature of mathematical concepts. En T. Nunes & P. E. Bryant (Eds.) Learning and teaching mathematics (pp. 5-28). London: Psycology Press, Ltd.
  48. Warner, L. B., Alcock, L. J., Coppolo, J. & Davis, G. E. (2003). How does flexible mathematical thinking contribute to the growth of understanding? En N. A. Paterman, B. J. Dougherty & J. Zilliox (Eds.) Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4 (pp. 371-378). Honolulu, USA: PME.

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