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Modelling with authentic data in sixth grade

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Abstract

This article explores 6th-grade students’ modelling with data in generating models for selecting an Australian swimming team for the (then) forthcoming 2016 Olympics, using data on swimmers’ times at various previous events. We propose a modelling framework comprising four components: working in shared problem spaces between mathematics and statistics; interpreting and reinterpreting problem contexts and questions; interpreting, organising and operating on data in model construction; and drawing informal inferences. In studying students’ model generation, consideration is given to how they interpreted, organised, and operated on the problem data in constructing and documenting their models, and how they engaged in informal inferential reasoning. Students’ responses included applying mathematical and statistical operations and reasoning to selected variables, identifying how variation and trends in swimmers’ performances inform model construction, recognising limitations in using only one performance variable, and acknowledging uncertainty in model creation and model application due to chance variation.

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References

  • Bakker, A., & Gravemeijer, K.P.E. (2004). Learning to reason about distribution. In The challenge of developing statistical literacy. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy (pp. 147–168). Dordrecht: Springer.

    Chapter  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Blum, W., & Leiss, D. (2007). How do students and teachers deal with mathematical modelling problems? The example Sugarloaf and the DISUM project. In C. Haines, P. L. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modelling (ICTMA12): Education, engineering and economics (pp. 222–231). Chichester: Horwood.

    Chapter  Google Scholar 

  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.

    Article  Google Scholar 

  • Doerr, H. M., delMas, R., & Makar, K. (2017). A modeling approach to the development of students’ informal inferential reasoning. Statistics Education Research Journal (in press).

  • Doerr, H. M., & English, L. D. (2003). A modelling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136.

    Article  Google Scholar 

  • Engel, J. (2017). Statistical literacy for active citizenship: A call for data science education. Statistics Education Research Journal, 16(1), 44–49. https://iase-web.org/documents/SERJ/SERJ16(1)_Engel.pdf.

  • English, L., Watson, J., & Fitzallen, N. (2017). Fourth-graders’ meta-questioning in statistical investigations. In A. Downton, S. Livy, & J. Hall (Eds.), 40 years on: We are still learning! (Proceedings of the 40th annual conference of the Mathematics Education Research Group of Australasia, pp. 229–236). Melbourne: MERGA.

  • English, L. D. (2013). Reconceptualising statistical learning in the early years. In L.D. English & J. Mulligan (Eds.), Reconceptualising early mathematics learning (pp. 67–82). Dordrecht: Springer.

    Chapter  Google Scholar 

  • English, L. D. (2014). Promoting statistical literacy through data modelling in the early school years. In E. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: presenting plural perspectives (pp. 441–458). Dordrecht: Springer.

    Chapter  Google Scholar 

  • English, L. D., Arleback, J. B., & Mousoulides, N. (2016). Reflections on progress in mathematical modelling research. In A. Gutierrez, G. Leder & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education (pp. 383–413). Rotterdam: Sense Publishers.

    Chapter  Google Scholar 

  • English, L. D., & Lesh, R. A. (2003). Ends-in-view problems. In R. A. Lesh & H. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 297–316). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines for assessment and instruction in statistics education [GAISE) report. Alexandria, VA: American Statistical Association. http://www.amstat.org/education/gaise/GAISEPreK-12_Full.pdf.

  • Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht: Kluwer.

    Google Scholar 

  • Gal, I. (2004). Adults’ statistical literacy: Meanings, components, responsibilities. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 47–78). Dordrecht: Kluwer.

    Chapter  Google Scholar 

  • 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: Springer.

  • Gould, R. (2017). Data literacy is statistical literacy. Statistics Education Research Journal, 16(1), 22–25. https://iase-web.org/documents/SERJ/SERJ16(1)_Gould.pdf.

  • Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1, 155–177.

    Article  Google Scholar 

  • Groth, R. (2015). Research commentary: Working at the boundaries of mathematics education and statistics education communities of practice. Journal for Research in Mathematics Education, 46(1), 4–16.

    Article  Google Scholar 

  • Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. L. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 110–119). Chichester: Horwood.

    Chapter  Google Scholar 

  • Konold, C., Finzer, W., & Kreetong, K. (2015). Modeling as a core component of structuring data. Paper presented at the 9th International Research Forum on Statistical Reasoning, Thinking, and Literacy (SRTL9), Paderborn, Germany.

  • Konold, C., & Higgins, T. L. (2003). Reasoning about data. In J. Kilpatrick, W. G. Martin & D. 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 

  • Konold, C., & Miller, C. D. (2011). TinkerPlots: dynamic data exploration [Computer software, Version 2.2]. Emeryville, CA: Key Curriculum Press.

    Google Scholar 

  • Langman, C. N., Zawojewski, J. S., & Whitney, S. R. (2016). Five principles for supporting design activity. In L. A. Annetta & J. Minogue (Eds.), Connecting science and engineering education practices in meaningful ways: Building bridges (pp. 59–106). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Langrall, C., Nisbet, S., Mooney, E., & Jansem, S. (2011). The role of context in developing reasoning about informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 47–67.

    Article  Google Scholar 

  • Lavigne, N. C., & Lajoie, S. P. (2007). Statistical reasoning of middle school children engaged in survey inquiry. Contemporary Educational Psychology, 32, 630–666.

    Article  Google Scholar 

  • Leavy, A., & Hourigan, M. (2017). Inscriptional capacities of young children engaged in statistical investigations. In A. Leavy, M. Meletiou-Mavrotheris & E. Paparistodemou (Eds.), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking. Dordrecht: Springer (forthcoming).

    Google Scholar 

  • Lehrer, R., & &, English, L. D. (In press). Introducing children to modeling variability. In D. Ben-Zvi, J. Garfield & K. Makar (Eds.), International handbook of research in statistics education. Dordrecht: Springer.

  • Lehrer, R., Kim, M. J., & Jones, R. S. (2011). Developing conceptions of statistics by designing measures of distribution. ZDM—The International Journal on Mathematics Education, 43(5), 723–736.

    Google Scholar 

  • Lehrer, R., & Romberg, T. (1996). Exploring children’s data modeling. Cognition and Instruction, 14(1), 69–108.

    Article  Google Scholar 

  • Lehrer, R., & Schauble, L. (2000). Inventing data structures for representational purposes: Elementary grade students’ classification models. Mathematical Thinking and Learning, 2, 49–72.

    Article  Google Scholar 

  • Lehrer, R., & Schauble, L. (2002). (Eds.). Investigating real data in the classroom: Expanding children’s understanding of math and science. New York: Teachers College Press. (Spanish Translation, Publicaciones M.C.E.P, Sevilla, Spa.

    Google Scholar 

  • Lehrer, R., & Schauble, L. (2010). What kind of explanation is a model? In M. K. Stein & L. Kucan (Eds.), Instructional explanation in the disciplines (pp. 9–22). New York: Springer.

    Chapter  Google Scholar 

  • Lesh, R., & Lehrer, R. (2000). Iterative refinement cycles for videotape analyses of conceptual change. In R. Lesh & A. Kelly (Eds.), Research design in mathematics and science education (pp. 665–708). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Lesh, R. A., & Doerr, H. (2003). (Eds.). Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning, and teaching. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Lesh, R. A., & Zawojewski, J. (2007). Problem solving and modelling. In F. K. Lester Jr.. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763–804). Charlotte, NC: Information Age.

    Google Scholar 

  • Makar, K. (2016). Developing young children’s emergent inferential practices in statistics. Mathematical Thinking and Learning, 16(1), 1–24.

    Article  Google Scholar 

  • Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The role of context and evidence in informal inferential reasoning. Mathematical Thinking and Learning, 13(1–2), 1–4.

    Article  Google Scholar 

  • Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105. http://iase-web.org/documents/SERJ/SERJ8(1)_Makar_Rubin.pdf.

  • Moore, D. S. (1990). Uncertainty. In L. Steen (Ed.), On the shoulders of giants: New approaches to numeracy (pp. 95–137). Washington, DC: National Academy Press.

    Google Scholar 

  • Niss, M. (2010). Modeling a crucial aspect of students’ mathematical modeling. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 43–60). New York: Springer.

    Chapter  Google Scholar 

  • Patton, M. (2002). Qualitative research and evaluation methods (3rd edn.). Thousand Oaks, CA: Sage.

    Google Scholar 

  • Pfannkuch, M. (2011). The role of context in developing informal statistical inferential reasoning: A classroom study. Mathematical Thinking and Learning, 13(1–2), 27–46.

    Article  Google Scholar 

  • Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Watson, J. M., & English, L. D. (2015). Introducing the practice of statistics: Are we environmentally friendly? Mathematics Education Research Journal, 27(4), 585–613.

    Article  Google Scholar 

  • Watson, J. M., & English, L. D. (in press). Statistical problem posing, problem refining, and further reflection in Grade 6. Canadian Journal of Science, Mathematics, and Technology Education.

  • Whitin, D. J., & Whitin, P. E. (2011). Learning to read numbers: Integrating critical literacy and critical numeracy in K-8 classrooms. New York, NY: Routledge.

    Google Scholar 

  • Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248. doi:10.1111/j.1751-5823.1999.tb00442.x.

    Article  Google Scholar 

  • Zawojewski, J. S. (2010). Problem solving versus modeling. In R. Lesh, P. L. Galbraith, C. R. Haines & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 237–243). New York: Springer.

    Chapter  Google Scholar 

  • Zawojewski, J. S., Lesh, R., & English, L. D. (2003). A models and modelling perspective on the role of small group learning. In R. A. Lesh & H. Doerr (Eds.), Beyond constructivism: A models and modelling perspective on mathematics problem solving, learning, and teaching (pp. 337–358). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

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Acknowledgements

This study was supported by research funding from the Australian Research Council (ARC) Discovery Grant DP20100158. Any opinions, findings, and conclusions or recommendations expressed are those of the authors and do not necessarily reflect the views of the ARC. We wish to acknowledge the enthusiastic participation of the students and teachers, together with the excellent support of our senior research assistant, Jo Macri, and research assistant Joanna Smeed.

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  1. Faculty of Education, Queensland University of Technology, Victoria Park Road, Kelvin Grove, Brisbane, QLD, 4059, Australia

    Lyn D. English

  2. Faculty of Education, University of Tasmania, Hobart, Australia

    Jane Watson

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  1. Lyn D. English
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Correspondence to Lyn D. English.

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English, L.D., Watson, J. Modelling with authentic data in sixth grade. ZDM Mathematics Education 50, 103–115 (2018). https://doi.org/10.1007/s11858-017-0896-y

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