An important use of statistical models and modeling in education stems from the potential to involve students more deeply with conceptions of distribution, variation and center. As models are key to statistical thinking, introducing students to modeling early in their schooling will likely support the statistical thinking that underpins later, more advanced work with increasingly sophisticated statistical models. In this case study, a class of 10–11 year-old students are engaged in an authentic task designed to elicit modeling. Multiple data sources were used to develop insights into student learning: lesson videotape, work samples and field notes. Through the use of dot plots and hat plots as data models, students made comparisons of the data sets, articulated the sources of variability in the data, sought to minimize the variability, and then used their models to both address the initial problem and to justify the effectiveness of their attempts to reduce induced variation. This research has implications for statistics curriculum in the early formal years of schooling.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
Ainley, J., & Pratt, D. (2017). Computational modelling and children’s expressions of signal and noise. Statistics Education Research Journal, 16(2), 15–37.
Australian Curriculum, Assessment and Reporting Authority (2017). Australian Curriculum: mathematics v8.3. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics. Accessed 23 Nov 2017.
Ben-Zvi, D., & Amir, Y. (2005). How do primary school students begin to reason about distributions? In K. Makar (Ed.), Reasoning about distribution: a collection of current research studies. Proceedings of the fourth international research forum on statistical reasoning, thinking, and literacy (SRTL-4), University of Auckland, New Zealand, 2–7 July. Brisbane: University of Queensland.
Ben-Zvi, D., & Arcavi, A. (2001). Junior high school students’ construction of global views of data and data representations. Educational Studies in Mathematics, 45, 35–65.
Ben-Zvi, D., Aridor, K., Makar, K., & Bakker, A. (2012). Students’ emergent articulations of uncertainty while making informal statistical inferences. ZDM, 44(7), 913–925.
Cobb, G. W. (2007). The introductory statistics course: a Ptolemaic curriculum? Technology Innovations in Statistics Education, 1(1), 1–15.
Common Core State Standards Initiative (2010). Common Core State Standards for mathematics. http://www.corestandards.org/Math. Accessed 30 Nov 2017.
Crouch, R. M., & Haines, C. R. (2004). Mathematical modeling: transitions between the real world and the mathematical model. International Journal of Mathematics Education in Science and Technology, 35(2), 197–206.
Doerr, H. M., DelMas, B., & Makar, K. (2017). A modeling approach to the development of students’ informal inferential reasoning. Statistics Education Research Journal, 16(2), 86–115.
English, L. D. (2010). Young children’s early modeling with data. Mathematics Education Research Journal, 22(2), 24–47.
English, L. D. (2012). Data modeling with first-grade students. Educational Studies in Mathematics, 81(1), 15–30.
English, L. D. (2013). Modeling with complex data in the primary school. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 287–299). Dordrecht: Springer.
Garfield, J., & Ben-Zvi, D. (2007). How students learn statistics revisited: a current review of research on teaching and learning statistics. International Statistical Review, 75(3), 372–396.
Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: connecting research and teaching practice. Dordrecht: Springer.
Graham, A. (2006). Developing thinking in statistics. London: Paul Chapman.
Konold, C., Higgins, T., Russell, J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325.
Konold, C., & Kazak, S. (2008). Reconnecting data and chance. Technology Innovations in Statistics Education, 2(1). http://escholarship.org/uc/item/38p7c94v.
Konold, C., & Miller, C. D. (2005). TinkerPlots: dynamic data exploration. Emeryville: Key Curriculum Press.
Konold, C., & Pollatsek, A. (2002). Data analysis as the search for signals in noisy processes. Journal for Research in Mathematics Education, 33(4), 259–289.
Larson, C., Harel, G., Oehrtman, M., Zandieh, M., Rasmussen, C., Speiser, R., & Walter, C. (2013). Modeling perspectives in math education research. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. 61–71). Dordrecht: Springer.
Lehrer, R., & English, L. (2018). Introducing children to modeling variability. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), The international handbook of research in statistics education (pp. 229–260). Switzerland: Springer International.
Lehrer, R., & Schauble, L. (2010). What kind of explanation is a model? In M. Stein & L. Kucan (Eds.), Instructional explanations in the disciplines (pp. 9–22). Boston: Springer.
Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical Thinking and Learning, 5(2), 157–189.
Makar, K., Bakker, A., & Ben-Zvi, D. (2015). Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom. ZDM, 47(7), 1107–1120.
Makar, K., & Rubin, A. (2018). Learning about statistical inference. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 261–294). Switzerland: Springer International.
McPhee, D., & Makar, K. (2014). Exposing young children to activities that develop emergent inferential practices in statistics. In K. Makar, B. de Sousa, & R. Gould (Eds.), International Conference on Teaching Statistics (ICOTS9), Flagstaff, Arizona, USA. Voorburg: International Statistical Institute.
Mokros, J., & Russell, S. J. (1995). Children’s concepts of average and representativeness. Journal for Research in Mathematics Education, 26(1), 20–39.
Noll, J., & Kirin, D. (2017). TinkerPlots model construction approaches for comparing two groups: student perspectives. Statistics Education Research Journal, 16(2), 213–243.
Pfannkuch, M., & Reading, C. (2006). Reasoning about distribution: a complex process. Statistics Education Research Journal, 5(2), 4–9.
Powell, A. B., Francisco, J. M., & Maher, C. A. (2003). An analytical model for studying the development of learners’ mathematical ideas and reasoning using videotape data. Journal of Mathematical Behavior, 22(4), 405–435.
Pratt, D. (2011). Re-connecting probability and reasoning about data in secondary school teaching. In Proceedings of the 58th World Statistics Conference, Dublin. http://2011.isiproceedings.org/papers/450478.pdf. Accessed on 21 June 2018.
Rubin, A., Hammerman, J. K. L., & Konold, C. (2006). Exploring informal inference with interactive visualization software. In Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil. Voorburg, The Netherlands: International Statistical Institute.
Shaughnessy, J. M. (2007). Research on statistics learning and reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957–1010). Charlotte: Information Age.
Stake, R. E. (2006). Multiple case study analysis. New York: Guilford.
Watson, J., & Moritz, J. (2000). The longitudinal development of understanding of average. Mathematical Thinking and Learning, 2(1–2), 11–50.
Watson, J. M. (2006). Statistical literacy at school: growth and goals. New Jersey: Lawrence Erlbaum Associates.
Wild, C. J. (2006). The concept of distribution. Statistics Education Research Journal, 5(2), 10–26.
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–265.
Yin, R. (2014). Case study research: design and methods (5th edn.). Beverly Hills: Sage.
THIS work was supported by funding from the Australian Research Council under DP170101993. The author wishes to gratefully acknowledge the contributions of the teacher and students engaged in this research.
About this article
Cite this article
Fielding-Wells, J. Dot plots and hat plots: supporting young students emerging understandings of distribution, center and variability through modeling. ZDM Mathematics Education 50, 1125–1138 (2018). https://doi.org/10.1007/s11858-018-0961-1
- Statistical model
- Statistical modeling
- Statistical inquiry
- Model eliciting activities