Teachers’ Professional Knowledge: The case of Variability
Abstract
In this research, we explore teachers’ statistical knowledge in relation with variability. Several high school mathematics teachers were presented with situations describing how students dealt with tasks based on the concept of variability. The teachers’ responses primarily helped us to analyze their comprehension and practices associated with the concept of variability and also to gain insight on how to teach this concept. Secondly, the study shows that students and high school teachers share the same conceptions on this subject.
Keywords
Full Text:
PDFReferences
Allmond, S. and Makar, K. (2014). From hat plots to box plots in tinkerplots: supporting students to write conclusions which account for variability in data. In K. Makar, B. de Sousa and 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.
Ball, D.L., Thames, M.H. and Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389-407.

Bednarz, N. and Proulx, J. (2009). Connaissance et utilisation des mathématiques dans l'enseignement: Clarifications conceptuelles et épistémologiques. For The Learning of Mathematics, 29(3), 11-17.
Bednarz, N. and Proulx, J. (2010). Processus de recherche-formation et développement professionnel des enseignants de mathématiques : Exploration de mathématiques enracinées dans leurs pratiques. Éducation et Formation, e-293, 21-36.
Behr, M. and Harel, G. (1990). Students’ Errors, Misconceptions, and Cognitive Conflict in Application of Procedures. Focus on Learning Problems in Mathematics 12 (3-4), 75–84.
Blais, M. and Martineau, S. (2006). L’analyse inductive générale: description d’une démarche visant à donner un sens à des données brutes. Recherches qualitatives, 26(2), 1-18.
Bloch, I. (2009). Les interactions mathématiques entre professeurs et élèves. Comment travailler leur pertinence en formation? Petit x, 81, 25-52.
Brousseau, G. (1998). Théorie des Situations Didactiques, La pensée sauvage.
Canada, D. (2004). Elementary Preservice Teachers’ Conceptions of Variation. Doctoral dissertation, Portland State University, Portland, OR.
Clivaz, S. (2014). Des mathématiques pour enseigner? Quelle influence les connaissances mathématiques des enseignants ont-elles sur leur enseignement à l’école primaire? Grenoble: La Pensée Sauvage.
Cooper, L. and 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.
Davis, B. and 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.
Delmas, R. and Liu, Y. (2005). Exploring Students’ Conceptions of the Standard Deviation. Statistics Education Research Journal, 4(1), 55-82.
Depaepe, F., Verschaffel, L. and Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12-25.
Even, R. and Tirosh, D. (1995). Subject-Matter Knowledge and Knowledge about Students as Sources of Teacher Presentations of the Subject-Matter. Educational Studies in Mathematics, 29, 1-20.
Gattuso, L. (2011). L’enseignement de la statistique : où, quand, comment, pourquoi pas? Statistique et Enseignement, 2(1), 5-30.
González, O. (2014). Secondary mathematics teachers’ professional competencies for effective teaching of variability-related ideas : a japanese case study. Statistique et Enseignement, 5(1), 31-51.
Hauk, S., Toney, A., Jackson, B., Nair, R. and Tsay, J.-J. (2013). Illustrating a theory of pedagogical content knowledge for secondary and post-secondary mathematics instruction. In S. Brown (Ed.), Proceedings of the 16th Conference on Research in Undergraduate Mathematics Education (Denver, CO).
Hauk, S., Toney, A., Jackson, B., Nair, R. and Tsay, J.-J. (2014). Developing a Model of Pedagogical Content Knowledge for Secondary and Post- Secondary Mathematics Instruction. Dialogic Pedagogy, 2, 16-40.
Hill, H.C., Ball, D.L. and Schilling, S.G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39, 372-400.
Holm, J. and Kajander, A. (2012). Interconnections of Knowledge and Beliefs in Teaching Mathematics. Canadian Journal of Science, Mathematics and Technology Education, 12(1), 7-21.
Konold, C. and Higgins, T. (2003). Reasoning about data. In J. Kilpatrick, W.G. Martin and D.E. Schifter (Eds.), A research companion to principles and standards for school mathematics (p. 193-215). Reston, VA: NCTM.
Meletiou-Mavrotheris, M. and Lee, C. (2005). Exploring Introductory Statistics Students' Understanding of Variation in Histograms. Proceedings of the 4th Congress of the European Society for Research in Mathematics Education, Sant Feliu de GuÃxols, Spain.
Moreira, P. and David, M. (2005). Mathematics in teacher education versus mathematics in teaching practice. ICMI-15 study.
Pratt, D. (1998). The co-ordination of meanings for randomness. For the Learning of Mathematics, 18(3), 2–11.
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.
Proulx, J. and Bednarz, N. (2010). Formation mathématique des enseignants du secondaire. Partie 1 : Réflexions fondées sur une analyse des recherches. Revista de Educação MatemaÌtica e Tecnologica Ibero-americana, 1(1), http://emteia.gente.eti.br/index.php/emteia.
Proulx, J. and Bednarz, N. (2011). Formation mathématique des enseignants du secondaire. Partie 2: Une entrée potentielle par les mathématiques professionnelles de l’enseignant. Revista de Educação MatemaÌtica e Tecnologica Ibero-americana, 1(2), http://emteia.gente.eti.br/index.php/emteia.
Reading, C. and Shaughnessy, J.M. (2004). Reasoning about variation. In Ben-Zvi and J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (p. 201-226). Dordrecht: Kluwer Academic Publishers.
Sánchez, E., da Silva, C.B. and Coutinho, C. (2011). Teachers’ understanding of variation. In C. Batanero, G. Burrill and C. Reading (Eds.), Teaching Statistics in School Mathematics- Challenges for Teaching and Teacher Education, Springer, New York, 211–221.
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 (p. 3- 35). New York, NY: Macmillan Publishers.
Skemp, R.R. (1978). Relational Understanding and Instrumental Understanding. The Arithmetic Teacher, 26(3), 9-15.
Steffe, L.P. (1990). Inconsistencies And Cognitive Conflict: A Constructivist’s View. Focus on Learning Problems in Mathematics, 12 (3-4), 99–109.
Vergne, C. (2004). La notion de variabilité dans les programmes de seconde (2000)-Étude de conditions de viabilité didactique. Actes des XXXVIèmes journées de Statistique, Société Française de Statistique, Montpellier, France.
Watson, J.M. (2007). The Role of Cognitive Conflict in Developing Students’ Understanding of Average. Educational Studies in Mathematics, 65, 21-47.
Watson, J.M., Kelly, B.A., Callingham, R.A. and Shaughnessy, J.M. (2003). The measurement of school students’ understanding of statistical variation. International Journal of Mathematical Education in Science and Technology, 34(1), 1-29.
Wozniak, F. (2005). Conditions et contraintes de l’enseignement de la statistique en classe de seconde générale. Un repérage didactique. Doctoral dissertation. Université Claude Bernard Lyon 1, Lyon.
Yin, R.K. (2003). Case study research: Design and methods (3rd ed.). Thousand Oaks, CA: Sage.
Refbacks
- There are currently no refbacks.
e-ISSN: 1694-2116
p-ISSN: 1694-2493