Developing secondary school teachers’ didactic–mathematical knowledge about probability

Referencias

Ball, D. L., Hill, H. H., & Bass, H. (2005). Knowing Mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, Fall, 14-46. Batanero, C., & Díaz, C. (2012). Training school teachers to teach probability: reflections and challenges. Chilean Journal of Statistics, 3 (1), 3-13. Batanero, C., Henry, M., & Parzysz, B. (2005).The nature of chance and probability. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp.16-42). New York, USA: Springer. DOI http://dx.doi. org/10.1007/0-387-24530-8_2 Batanero, C., Gómez, E., Gea, M. M., & Contreras, J. M. (2014). Assessing and developing prospective teachers’ understanding of random sequences. In U. Sproesser, S. Wessolowski, & C. Wörn (Eds.), Daten, Zufall und der Rest der Welt – Didaktische Perspektiven zur anwendungsbezogenen Mathematik, (pp.1- 11). Heidelberg: Springer Fachmedien Wiesbaden. DOI http://dx.doi.org/10.1007/978-3-658-04669-9_1 Contreras, J. M., Batanero, C., Díaz, C., & Arteaga, P. (2013). Evaluación de la falacia del eje temporal en futuros profesores de educación secundaria. Acta Scientiae, 14 (3), 346-362. Cordani, L. K., & Wechsler, S. (2006). Teaching independence and exchangeability. In A. Rossman, & B. Chance (Eds.), Proceedings of the Seventh International Conference on Teaching Statistics. Salvador, Brasil: International Association for Statistics Education. [CD-ROM]. Díaz, C., & De La Fuente, I. (2007). Assessing students’ difficulties with conditional probability and bayesian reasoning. International Electronic Journal of Mathematics Education, 2 (3), 128-148. Falk, R. (1986). Conditional probabilities: insights and difficulties. In Proceedings of the Second International Conference on Teaching Statistics.Victoria, Canada: International Association for Statistical Education. Retrieved from:http://iase-web.org/Conference_Proceedings. php?p=ICOTS_2_1986 Fischbein, E. (1993). The interaction between the formal, the algorithmic and the intuitive components in a mathematical activity. In R. Biehler, R. W. Scholz, R. Straser, & B. Winkelmann, (Eds.), Didactics of Mathematics as a Scientific Discipline, (pp. 231-245). Netherlands, Dordrecht: Kluwer. Font, V., Godino, J. D., & Gallardo, J. (2013). The emergence of objects from mathematical practices. Educational Studies in Mathematics, 82(1),97-124. doi: http://dx.doi.org/10.1007/ s10649-012-9411-0 Gal, I. (2005). Towards “probability literacy” for all citizens: building blocks and instructional dilemmas. In G. A. Jones, (Ed.), Exploring probability in school: Challenges for teaching and learning.(pp.39-63). New York, USA: Springer. doi http://dx.doi.org/10.1007/0-387-24530-8_3 Garfield, J. (2006). Assessment resource tools for improving statistical thinking - Artist. Retrieved from https://apps3. cehd.umn.edu/artist/ Godino, J. D. (2009). Categorías de análisis de los conocimientos del profesor de matemáticas. Unión Revista Iberoamericana de Educación Matemática, 20, 13-31. Godino, J. D., Batanero, C., Font, V., Giacomone, B. (2016). Articulando conocimientos y competencias del profesor de matemáticas: el modelo CCDM. In: Fernández, C. et al. (Ed.). Investigación en Educación Matemática XX, (pp288-297). Málaga: SEIEM. Godino, J. D., Batanero, C., Rivas, H., & Arteaga, P. (2013). Componentes e indicadores de idoneidad de programas de formación de profesores en didáctica de las matemáticas. Revemat – Revista Eletrônica de Educação Matemática, 8(1),46-74. doi http://dx.doi.org/10.5007/1981- 1322.2013v8n1p46 Godino, J. D., Ortiz, J. J., Roa, R. & Wilhelmi, M.R. (2011). Models for statistical pedagogical knowledge. In C. Batanero, G. Burrill, & C. Reading. Teaching statistics in school mathematics-challenges for teaching and teacher education: a joint ICMI/IASE Study.(pp.271-282). Berlin, Alemanha: Springer. Godino, J. D., Rivas, H., Arteaga, P., Lasa, A., & Wilhelmi, M. R. (2014). Ingeniería didáctica basada en el enfoque ontológico - semiótico del conocimiento y la instrucción matemáticos. Recherches en Didactique des Mathématiques, 34 (2/3), 167- 200. Gómez, E. (2014). Evaluación y desarrollo del conocimiento matemático para la enseñanza de la probabilidad en futuros profesores de educación primaria. (Tese doctoral) Facultad de Ciencias de la Educación, Departamento de Didáctica de la Matemática. Universidad de Granada. Gras, R., & Totohasina, A. (1995). Chronologie et causalité, conceptions sourcesd’ obstacles épistémologiques à la notion de probabilité conditionnelle. Educacional Studies in Mathematics, 28(4), 337-363. doi http://dx.doi.org/10.1007/ bf01274078 Green, D. R. (1983). A survey of probability concepts in 3000 pupils aged 11-16 years. In D. R. Grey, P. Holmes, V. Barnett & G. M. Constable, (Eds.), Proceedings of the First International Conference on Teaching Statistics. (pp.766- 783). Sheffield, UK: Teaching Statistics Trust. Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39 (4), 372- 400. Ives, S. E. (2009). Learning to teach probability: Relationships among preservice teachers’ beliefs and orientations, content knowledge, and pedagogical content knowledge of probability. (Doctor ship Thesis) Faculty of North Carolina State University. Kataoka, V. Y., Souza, A. A., Oliveira, A. de C. S., Fernandes, F., Paranaíba, P., & Oliveira, M. S. (2008).Probability Teaching in Brazilian Basic Education: Evaluation and Intervention. Anais do ICME 11, Monterrey, Mexico. Retrieved from http://tsg.icme11.org/tsg/show/14 Lecoutre, M. (1992).Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23 (6), 557-568. doi http://dx.doi.org/10.1007/ BF00540060 Brasil. MEC-SEF. (1998). Parâmetros curriculares nacionais: Matemática, 5ª a 8ª série. Brasília, Brasil: Ministério de Educação e Cultura – Secretaria de Ensino Fundamental. Mohr, M.J. (2008). Mathematics knowledge for teaching: The case of preservice teachers. In G. Kulm, (Ed.), Teacher knowledge and practice in middle grades mathematics. (pp.19-43). Rotterdam, The Netherlands: Sense Publishers. Nunes, T., Bryant, P., Evans, D., Gottardis, L., & Terlektsi, M. (2012). Teaching primary school children about probability. Teacher handbook. Education Department, Oxford University. Pietropaolo, R. C., Campos, T. M. M., Felisberto de Carvalho, J. I., & Teixeira, P. (2013). Um estudo sobre os conhecimentos necessários ao professor para ensinar noções concernentes à probabilidade nos anos iniciais. Anais do IV Seminário do Observatório da Educação da CAPES. Brasil. Retrived from http://seminarios.capes.gov.br/observatorio-da-educacao/ resumos/108-educacao-basica Pietropaolo, R. C., Campos, T. M. M., & Silva, A. F. G. (2012). Formação continuada de professores de matemática da Educação Básica em um contexto de implementação de inovações curriculares. Ensino de Ciências e da Matemática, 8 (2), 377-399. Sánchez, E. (2000). Investigaciones didácticas sobre el concepto de eventos independientes em probabilidad. Recherches en Didactique des Mathématics, 2(3), 305-330. Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1),1-22. doi http://dx.doi.org/10.17763/haer.57.1.j463w79r56455411 Tversky, A., & Kahneman, D. (1982). Causal schemas in judgment under uncertainty. In D. Kahneman, P.Slovic, & A. Tversky. Judgement under uncertainty: Heuristics and biases (pp.117-128). Cambridge, Inglaterra: Cambridge University Press. doi http://dx.doi.org/10.1017/CBO9780511809477