A praxeological analysis of pre-service elementary teachers’ knowledge of rational numbers

• Autores: Zetra Hainul Putra
• Localización: Recherches en didactique des mathématiques, ISSN 0246-9367, Vol. 38, Nº 3, 2018, págs. 315-363
• Idioma: inglés
• Títulos paralelos:
  • Une analyse praxéologique de la connaissance des nombres rationnels de professeurs des écoles en formation initiale
  • Un análisis praxeológico del conocimiento sobre números racionales de maestros en formación inicial
• Texto completo no disponible (Saber más ...)
• Resumen
  • español

    La investigación reciente ha estudiado el conocimiento matemático y didáctico individual de los docentes a través de cuestionarios de opción múltiple. Este método es especialmente conveniente para un estudio a gran escala, pero no cubre el conocimiento matemático y didáctico colectivo de los docentes, incluido el conocimiento que pueden desarrollar juntos y compartir con otros. Para examinar esta pregunta en un caso concreto, usamos un método conocido como tareas hipotéticas de enseñanza (THE) para estudiar el conocimiento matemático y didáctico de los maestros en formación inicial (MFI) sobre los números racionales. Este método se basa en la teoría antropológica de lo didáctico, específicamente en la noción de modelo epistemológico de referencia. Se aplica para estudiar los conocimientos matemáticos y didácticos sobre los números racionales de treinta y dos MFI indonesios. A través de este método, encontramos que, para enseñar a los alumnos los números racionales, los MFI tienden a proponer una instrucción directa de las técnicas matemáticas, y a menudo tienen dificultades para construir técnicas didácticas apropiadas debido a la falta de Conocimiento matemático.

    Además, vemos cómo las THE Se pueden utilizar para estudiar los componentes colectivos del conocimiento matemático y didáctico de los futuros docentes.

  • English

    Recent research has studied teachers’ individual mathematical and didactical knowledge through multiple choice items. This method is especially convenient for a large-scale study, but it does not cover teachers’ collective mathematical and didactical knowledge, including knowledge they may develop together and share with others. To examine this question in a concrete case, we use a method known as hypothetical teacher tasks (HTTs) to study pre-service elementary teachers’ (PsETs) mathematical and didactical knowledge of rational numbers. This method is based on the anthropological theory of the didactic, specifically praxeological reference models. It is applied to study thirty-two Indonesian PsETs’ mathematical and didactical knowledge of rational numbers. Through this method, we found that the PsETs tend to propose a direct instruction of mathematical techniques to teach pupils about rational numbers, and they often struggle to construct appropriate didactical techniques due to a lack of mathematical knowledge. In addition, we see how HTTs can be used to study collective components of teachers’ mathematical and didactical knowledge.

  • français

    Des recherches récentes ont étudié les connaissances mathématiques et didactiques individuelles des enseignants à travers des items à choix multiples. Cette méthode est particulièrement pratique pour une étude à grande échelle, mais elle ne permet pas de rendre compte des connaissances mathématiques et didactiques collectives des enseignants, y compris les connaissances qu'ils sont susceptibles de développer ensemble et partager avec des collègues. Pour examiner cette question dans un cas concret, nous utilisons une méthode Connue sous le nom de tâches hypothétiques d’enseignants (THE) pour étudier les connaissances mathématiques et didactiques de professeurs des écoles en formation initiale (PE) sur les nombres rationnels. Cette méthode est basée Sur la théorie anthropologique du didactique, en particulier la notion de modèle praxéologique de référence. Cette notion est utilisée pour étudier les connaissances mathématiques et didactiques de 32 PE indonésiens, par rapport aux nombres rationnels. Grâce à cette méthode, nous montrons que les PE ont tendance à proposer une instruction directe des techniques mathématiques pour enseigner aux élèves les nombres rationnels, et qu’ils ont souvent du mal à construire des techniques didactiques appropriées en 3 raison de connaissances mathématiques insuffisantes. En outre, nous voyons comment les THE peuvent être utilisées pour étudier les composantes des connaissances mathématiques et didactiques collectives des futurs enseignants.

• Referencias bibliográficas
  • ARTIGUE, M., WINSLØW, C. (2010). International comparative studies on mathematics education: A viewpoint from the anthropological theory of...
  • BARBE, J., BOSCH, M., ESPINOZA, L., GASCON, J. (2005). Didactic restrictions on the teacher’s practice: The case of limits of functions in...
  • BILLSTEIN, R., LIBESKIND, S., LOTT, J. (2007). A problem solving to mathematics for elementary school teachers (9th edition). Boston: Pearson...
  • BROUSSEAU, G. (1997). Theory of didactical situations in mathematics (Edited and translated by N. Balacheff, M. Cooper, R. Sutherland, &...
  • BROUSSEAU, G., BROUSSEAU, N., WARFIELD, V. (2004). Rationals and decimals as required in the school curriculum: Part 1: Rationals as measurement....
  • BROUSSEAU, G., BROUSSEAU, N., WARFIELD, V. (2007). Rationals and decimals as required in the school curriculum: Part 2: From rationals to...
  • BROUSSEAU, G., BROUSSEAU, N., WARFIELD, V. (2008). Rationals and decimals as required in the school curriculum: Part 3. Rationals and decimals...
  • BROUSSEAU, G., BROUSSEAU, N., WARFIELD, V. (2009). Rationals and decimals as required in the school curriculum: Part 4: Problem solving, composed...
  • CHARALAMBOUS, C. Y., PITTA-PANTAZI, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational...
  • CHEVALLARD, Y. (1992). Fundamental concepts in didactics: perspectives provide by an anthropological approach. In R. Douady & A. Mercier...
  • CHEVALLARD, Y. (2006). Steps towards a new epistemology in mathematics education. In M. Bosch (Eds.), Proceedings of the IV Congress of the...
  • CHEVALLARD, Y. (2007). Readjusting didactics to changing epistemology, European Educational Research Journal, 6(2), 131-134.
  • DEPAEPE, F., TORBEYNS, J,. VERMEERSCH, N., JANSSENS, D., JANSSEN, R., KELCHTERMANS, G., VERSCHAFFEL, L., VAN DOOREN, W. (2015). Teachers’...
  • DURAND-GUERRIER, V., WINSLØW, C., YOSHIDA, H. (2010). A model of mathematics teacher knowledge and a comparative study in Denmark, France...
  • DUVAL, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational studies in mathematics, 61(1-2),...
  • HILL, H. C., SCHILLING, S. G., BALL, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching, The Elementary School...
  • LIU, C., XIN, Z., LI, X. (2011). The development of Chinese students’ understanding of the concept of fractions from fifth to eight grade....
  • MA, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States....
  • NI, Y., ZHOU, Y. D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational...
  • PUTRA, Z. H. (2017). Pre-service elementary teachers’ knowledge of comparing decimals based on anthropological theory of the didactic. Presented...
  • PUTRA, Z. H. (2016). Collective aspects of pre-service lower secondary teachers’ knowledge on density of rational numbers. In M. Achiam &...
  • PUTRA, Z. H. (submitted). Praxeological change and the density of rational numbers: The case of pre-service teachers in Denmark and Indonesia....
  • RODRÍGUEZ, E., BOSCH, M., GASCÓN, J. (2008). A networking method to compare theories: metacognition in problem solving reformulated within...
  • SHULMANN, L, S. (1986). Those who understand: Knowledge growth in teaching, Educational Researcher, 15(2), 4-14.
  • SONNABEND, T. (1997). Mathematics for elementary teachers (2nd edition). Orlando, Florida: Saunders College Publishing.
  • TATTO, M. T., SCHWILLE, J., SENK, S. L., INGVARSO, L., PECK, R., ROWLEY, G. (2008). Teacher education and development study in Mathematics...
  • VAMVAKOUSSI, X., VAN DOOREN, W., VERSCHAFFEL, L. (2012). Naturally biased? in search for reaction time evidence for a natural number bias...
  • VAMVAKOUSSI, X., VOSNIADOU, S. (2004). Understanding the structure of the set of rational numbers: a conceptual change approach. Learning...
  • VAN DOOREN, W., LEHTINEN, E., & VERSCHAFFEL, L. (2015). Unraveling the gap between natural and rational numbers. Learning and Instruction,...
  • WIJAYANTI, D., WINSLØW, C. (2017). Mathematical practice in textbooks analysis: Praxeological reference models, the case of proportion. REDIMAT,...
  • WINSLØW, C. (2015). Mathematical at university: The anthropological approach. In S.J. Cho (Eds.), Selected Regular Lecturer from the 12th...
  • WINSLØW, C., DURAND-GUERRIER, V. (2007). Education of lower secondary mathematics teachers in Denmark and France. Nordic Studies in Mathematics...