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Topics and Trends in Current Statistics Education Research pp 225–244Cite as

Necessary Knowledge for Teaching Statistics: Example of the Concept of Variability

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Part of the book series: ICME-13 Monographs ((ICME13Mo))

Abstract

This chapter explores teachers’ statistical knowledge in relation to the concept of variability. Twelve high school mathematics teachers were asked to respond to scenarios describing students’ strategies, solutions, and misconceptions when presented with a task based on the concept of variability. The teachers’ responses primarily helped us analyze their comprehension and practices associated with the concept of variability and gain insight into how to teach this concept. Secondly, the study shows that students and high school teachers share the same conceptions on this subject.

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Notes

  1. 1.

    Adapted from Canada (2004).

  2. 2.

    Adapted from Meletiou-Mavrotheris and Lee (2005).

References

  • Baillargeon, N. (2005). Petit cours d’autodéfense intellectuelle (Short intellectual self-defense course). Montreal: Lux Publisher.

    Google Scholar 

  • Bargagliotti, A., Anderson, C., Casey, S., Everson, M., Franklin, C., Gould, R., et al. (2014). Project-set materials for the teaching and learning of sampling variability and regression. In K. Makar, B. de Sousa, & R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9), Flagstaff, Arizona, USA. Voorburg, The Netherlands: International Statistical Institute.

    Google Scholar 

  • Bednarz, N., & Proulx, J. (2009). Connaissance et utilisation des mathématiques dans l’enseignement: Clarifications conceptuelles et épistémologiques (Knowledge and use of mathematics in teaching: Conceptual and epistemological clarifications). For the Learning of Mathematics, 29(3), 11–17.

    Google Scholar 

  • Bednarz, N., & Proulx, J. (2010). Processus de recherche-formation et développement professionnel des enseignants de mathématiques: Exploration de mathématiques enracinées dans leurs pratiques. (Research-training process and professional development of mathematics teachers: Exploration of mathematics rooted in their practice). Éducation et Formation (Education and Training), 293, 21–36.

    Google Scholar 

  • Blais, M., & Martineau, S. (2006). L’analyse inductive générale: Description d’une démarche visant à donner un sens à des données brutes. (General inductive analysis: Description of a process aiming at giving meaning to raw data). Recherches qualitatives (Qualitative Researches), 26(2), 1–18.

    Google Scholar 

  • Bloch, I. (2009). Les interactions mathématiques entre professeurs et élèves. Comment travailler leur pertinence en formation? (Mathematical interactions between teachers and students. How to make them relevant in training?). Petit x, 81, 25–52.

    Google Scholar 

  • Borim da Sina, C., & Coutinho, C. (2008). In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference.

    Google Scholar 

  • Brousseau, G. (1998). Théorie des situations didactiques (Theory of didactial situations). Paris: La pensée sauvage Publishers.

    Google Scholar 

  • Canada, D. (2004). Elementary preservice teachers’ conceptions of variation (Doctoral dissertation). Portland State University, Portland, OR.

    Google Scholar 

  • Canada, D. (2006). Elementary pre-service teachers’ conceptions of variation in a probability context. Statistics Education Research Journal, 5(1), 36–63.

    Google Scholar 

  • Cooper, L., & Shore, F. (2008). Students’ misconceptions in interpreting center and variability of data represented via histograms and stem-and-leaf plots. Journal of Statistics Education, 15(2), 1–13.

    Google Scholar 

  • Cooper, L., & Shore, F. (2010). The effects of data and graph type on concepts and visualizations of variability. Journal of Statistics Education, 18(2), 1–16.

    Article  Google Scholar 

  • Dabos, M. (2011). Two-year college mathematics instructors’ conceptions of variation (Doctorate in education thesis). University of California, Santa Barbara, CA.

    Google Scholar 

  • Davis, B., & Simmt, E. (2006). Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need to) know. Educational Studies in Mathematics, 61(3), 293–319.

    Article  Google Scholar 

  • delMas, R., & Liu, Y. (2005). Exploring students’ conceptions of the standard deviation. Statistics Education Research Journal, 4(1), 55–82.

    Google Scholar 

  • Dodge, Y. (1993). Statistics: encyclopedic dictionary. Switzerland: Université de Neuchâtel.

    Google Scholar 

  • Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94–116.

    Article  Google Scholar 

  • Even, R., & Tirosh, D. (1995). Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject-matter. Educational Studies in Mathematics, 29(1), 1–20.

    Article  Google Scholar 

  • Garfield, J., & Ben-Zvi, D. (2005). A framework for teaching and assessing reasoning about variability. Statistics Education Research Journal, 4(1), 92–99.

    Google Scholar 

  • Garfield, J., delMas, R., & Chance, B. (2007). Using students’ informal notions of variability to develop an understanding of formal measures of variability. In M. C. Lovett & P. Shah (Eds.), Thinking with data (pp. 117–147). New York, NY: Lawrence Erlbaum Associates.

    Google Scholar 

  • Gattuso, L., & Vermette, S. (2013). L’enseignement de statistique et probabilités au Canada et en Italie (The teacing of statistics and probability in Canada and Italy). Statistique et Enseignement, 4(1), 107–129.

    Google Scholar 

  • Green, J. L., & Blankenship, E. E. (2014). Beyond calculations: Fostering conceptual understanding in statistics graduate teaching assistants. In K. Makar, B. de Sousa, & R. Gould (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9), Flagstaff, Arizona, USA. Voorburg, The Netherlands: International Statistical Institute and International Association for Statistical Education.

    Google Scholar 

  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.

    Article  Google Scholar 

  • Holm, J., & Kajander, A. (2012). Interconnections of knowledge and beliefs in teaching mathematics. Canadian Journal of Science, Mathematics and Technology Education, 12(1), 7–21.

    Article  Google Scholar 

  • Konold, C., & Higgins, T. (2003). Reasoning about data. In J. Kilpatrick, W. G. Martin, & D. E. Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 193–215). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Margolinas, C. (2014). Concepts didactiques et perspectives sociologiques? (Didactical concepts and sociological perspectives?). Revue Française de Pédagogie,188, 13–22.

    Google Scholar 

  • Meletiou-Mavrotheris, M., & Lee, C. (2005). Exploring introductory statistics students’ understanding of variation in histograms. In Proceedings of the 4th Congress of the European Society for Research in Mathematics Education, Sant Feliu de Guíxols, Spain.

    Google Scholar 

  • Ministry of Education and Higher Education. (2004). Quebec education program (QEP) secondary: Cycle one. In Mathematics. Quebec: Government of Quebec.

    Google Scholar 

  • Ministry of Education and Higher Education. (2007). Quebec education program (QEP), secondary: Cycle two. In Mathematics. Quebec: Government of Quebec.

    Google Scholar 

  • Moreira, P., & David, M. (2005). Mathematics in teacher education versus mathematics in teaching practice: A revealing confrontation. Paper presented at the conference of the 15th ICMI study on the Professional Education and Development of Teachers of Mathematics, Águas de Lindóia, Brazil.

    Google Scholar 

  • Moreira, P., & David, M. (2008). Academic mathematics and mathematical knowledge needed in school teaching practice: Some conflicting elements. Journal for Mathematics Teacher Education, 11(1), 23–40.

    Article  Google Scholar 

  • Peters, S. (2011). Robust understanding of statistical variation. Statistics Education Research Journal, 10(1), 52–88.

    Google Scholar 

  • Peters, S. (2014). Developing understanding of statistical variation: Secondary statistics teachers’ perceptions and recollections of learning factors. Journal of Mathematics Teacher Education, 17(6), 539–582.

    Article  Google Scholar 

  • Proulx, J. (2008). Exploring school mathematics as a source for pedagogic reflections in teacher education. Canadian Journal of Science, Mathematics and Technology Education, 8(4), 331–354.

    Article  Google Scholar 

  • Proulx, J. & Bednarz, N. (2010). Formation mathématique des enseignants du secondaire. Partie 1: Réflexions fondées sur une analyse des recherches (High school mathemematics teacher training. Part 1: Reflexions based on a research analysis). Revista de Educação Matemática e Tecnologica Ibero-Americana, 1(1). http://emteia.gente.eti.br/index.php/emteia.

  • Proulx, J. & Bednarz, N. (2011). Formation mathématique des enseignants du secondaire. Partie 2: Une entrée potentielle par les mathématiques professionnelles de l’enseignant (High school mathemematics teacher training. Part 2: A potential entry by the teacher’s professional mathematics). Revista de Educação Matemática e Tecnologica Ibero-Americana, 1(2). http://emteia.gente.eti.br/index.php/emteia.

  • Reading, C., & Shaughnessy, J. M. (2004). Reasoning about variation. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 201–226). Dordrecht: Kluwer Academic Publishers.

    Chapter  Google Scholar 

  • Sanchez, E., Borim da Sina, C., & Coutinho, C. (2011). Teachers’ understanding of variation. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics—Challenges for teaching and teacher education (pp. 211–221). Dordrecht, Germany: Springer.

    Chapter  Google Scholar 

  • Savard, A. (2014). Developing probabilistic thinking: What about people’s conceptions? In E. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (Vol. 2, pp. 283–298). Berlin: Springer.

    Chapter  Google Scholar 

  • Shulman, L. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.

    Article  Google Scholar 

  • Shulman, L. (1988). Paradigms and research programs in the study of teaching: A contemporary perspective. In M. C. Whittrock (Ed.), Handbook of research on teaching (pp. 3–35). New York, NY: Macmillan Publishers.

    Google Scholar 

  • Silva, C. B., & Coutinho, C. Q. S. (2006). The variation concept: A study with secondary school mathematics teachers. In A. Rossman & B. Chance (Eds), Proceedings of the Seventh International Conference on Teaching Statistics. Voorburg: International Statistical Institute and International Association for Statistical Education.

    Google Scholar 

  • Vergne, C. (2004). La notion de variabilité dans les programmes de seconde (2000)-Étude de conditions de viabilité didactique (The concept of variability in secondary programs (2000)—A study of conditions for the viability of didactics). In Actes des XXXVIèmes journées de Statistique, Société Française de Statistique (Acts from the XXXVIst days of Statistics, French Society for Statistics), Montpellier, France.

    Google Scholar 

  • Wozniak, F. (2005). Conditions et contraintes de l’enseignement de la statistique en classe de seconde générale. Un repérage didactique (Conditions and constraints of teaching statistics in general secondary classes. A didactical identification) (Doctoral dissertation). Université Claude Bernard Lyon 1, Lyon.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Université du Québec à Trois-Rivières, Trois-Rivières, Québec, Canada

    Sylvain Vermette

  2. McGill University, Montréal, Québec, Canada

    Annie Savard

Authors
  1. Sylvain Vermette
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  2. Annie Savard
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Correspondence to Sylvain Vermette .

Editor information

Editors and Affiliations

  1. Program in Mathematics Education, Michigan State University, East Lansing, MI, USA

    Gail Burrill

  2. Faculty of Education, University of Haifa, Haifa, Israel

    Dani Ben-Zvi

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Vermette, S., Savard, A. (2019). Necessary Knowledge for Teaching Statistics: Example of the Concept of Variability. In: Burrill, G., Ben-Zvi, D. (eds) Topics and Trends in Current Statistics Education Research. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-03472-6_10

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  • DOI: https://doi.org/10.1007/978-3-030-03472-6_10

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