Abstract
Data modelling develops the skills and competencies necessary for real-world problem solving and the evaluation of evidence. In the early years, data modelling involves posing questions, identifying attributes of phenomena, measuring and structuring these attributes and then composing, revising, making inferences and communicating the outcomes. Many of these processes, particularly making inference and predictions, are fundamental to mathematical modelling. In this chapter, we focus on the latter stages of the data modelling process – making informal inferences about data. We explore the approaches used by 5–6-year-old children when presented with a situation requiring them to make informal inferences about data presented within the context of a data modelling activity. We identify the strategies young children use to make inferences about data and discuss what these strategies communicate about early understandings of statistical inference. The findings suggest that making inferences can be challenging for younger students primarily due to the powerful influence of their developing understandings of number. However, there is evidence that children possess some of the building blocks of informal inference most notably in the approaches that point to a pre-aggregate view of data. We present evidence suggesting that situating data modelling activities within interesting and relevant contexts, alongside good teacher questioning and opportunities to listen to the reasoning of their peers, contributes to the creation of environments that support and develop early understandings of inference.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. In A. Rossman & B. Chance (Eds.), Working cooperatively in statistics education: Proceedings of the Seventh International Conference on Teaching Statistics, Salvador, Brazil. [CDROM]. Voorburg, The Netherlands: International Statistical Institute. [Online: http://www.stat.auckland.ac.nz/~iase/publications/17/2D1_BENZ.pdf].
Cobb, P. (1999). Individual and collective mathematical development: The case of statistical data analysis. Mathematical Thinking and Learning, 1(1), 5–43.
English, L., & Sriraman, B. (2010). Problem solving for the 21st century. In B. Sriraman & L. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 263–290). Heidelberg, Germany: Springer.
English, L. D. (2010). Young children’s early modelling with data. Mathematics Education Research Journal, 22(2), 24–47.
English, L. D. (2012). Data modelling with first-grade students. Educational Studies in Mathematics, 81, 15–30.
English, L. D. (2018). Young children’s statistical literacy in modelling with data and chance. In A. M. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking. Singapore, Singapore: Springer Nature. https://doi.org/10.1007/978-981-13-1044-7
Ertle, B., Chokshi, S., & Fernandez, C. (2001). Lesson planning tool. Retrieved from www.tc.columbia.edu/centers/lessonstudy/doc/Lesson_Planning_Tool.pdfon November 28, 2016.
Garfunkel, S., & Montgomery, M. (Eds.). (2016). Guidelines for assessment and instruction in mathematical modeling education (GAIMME) report. Boston, MA: Consortium for Mathematics and Its Applications (COMAP)/Society for Industrial and Applied Mathematics (SIAM).
Hancock, C., Kaput, J. J., & Goldsmith, L. T. (1992). Authentic inquiry with data: Critical barriers to classroom implementation. Educational Psychologist, 27(3), 337–364.
Hurst, C., & Hurrell, D. (2016). Investigating children’s multiplicative thinking: Implications for teaching. European Journal of STEM Education, 1(3), 56.
Kinnear, V. (2013). Young children’s statistical reasoning: A tale of two contexts (Unpublished PhD dissertation). Queensland University of Technology.
Kinnear, V., & Clarke, J. (2016). Young children’s abductive reasoning about data. In Proceedings of the13th International Congress on Mathematical Education. Hamburg, July 24–31.
Konold, C., Higgins, T., Russell, S. J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88, 305–325.
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.
Konold, C., Pollatsek, A., Well, A., & Gagnon, A. (1997). Students analyzing data: Research of critical barriers. In J. B. Garfield & G. Burrill (Eds.), Research on the role of technology in teaching and learning statistics: 1996 Proceedings of the 1996 IASE Round Table Conference (pp. 151–167). Voorburg, The Netherlands: International Statistical Institute. Retrieved from http://www.dartmouth.edu/~chance/teaching_aids/IASE/IASE.book.pdf
Leavy, A., & Hourigan, M. (2016). Crime Scenes and Mystery Players! Using interesting contexts and driving questions to support the development of statistical literacy. Teaching Statistics, 38(1), 29–35. https://doi.org/10.1111/test.12088
Leavy, A. M., & Hourigan, M. (2018a). Inscriptional capacities of young children engaged in statistical investigations. In Leavy, A.M. Meletiou-Mavrotheris, M & Paparistodemou, E. (Editors). Statistics in Early Childhood and Primary Education: Supporting early statistical and probabilistic thinking. Springer. ISBN 978-981-13-1043-0
Leavy, A., & Hourigan, M. (2018b). The role of perceptual similarity, data context and task context when selecting attributes: Examination of considerations made by 5–6 year olds in data modelling environments. Educational Studies in Mathematics, 97(2), 163–183. https://doi.org/10.1007/s10649-017-9791-2
Leavy, A. M. (2017). Insights into the approaches of young children when making informal inferences about data. In Paper presented at the Congress of European Research in Mathematics Education (CERME10). Dublin, Ireland.
Lesh, R. (2010). Tools, researchable issues & conjectures for investigating what it means to understand statistics (or other topics) meaningfully. Journal of Mathematical Modeling and Application, 1(2), 16–48.
Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching (pp. 3–34). Mahwah, NJ: Lawrence Erlbaum.
Lesh, R., & Fennewald, T. (2013). Introduction to part I modeling: What is it? Why do it? In R. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 5–10). New York, NY: Springer.
Lesh, R., & Kelly, A. (2000). Multitiered teaching experiments. In A. Kelly & R. Lesh (Eds.), Research design in mathematics and science education (pp. 197–230). Mahwah, NJ: Lawrence Erlbaum Associates.
Makar, K., Bakker, A., & Ben-Zvi, D. (2015). Scaffolding norms of argumentation-based inquiry in a primary mathematics classroom. ZDM – The International Journal on Mathematics Education, 47, 1107. https://doi.org/10.1007/s11858-015-0732-1
Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105. [Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ8(1)_Makar_Rubin.pdf].
Paparistodemou, E., & Meletiou-Mavrotheris, M. (2008). Enhancing reasoning about statistical inference in 8 year-old students. Statistics Education Research Journal, 7(2), 83–106.
Rubin, A., Hammerman, J. K. L., & Konold, C. (2006). Exploring informal inference with interactive visualization software. In A. Rossman & B. Chance (Eds.), Working cooperatively in statistics education: Proceedings of the Seventh International Conference on Teaching Statistics. Salvador, Brazil. [CDROM]. Voorburg, The Netherlands.
Watson, J. (2018). Variation and expectation for six-year-olds. In A. M. Leavy, M. Meletiou-Mavrotheris, & E. Paparistodemou (Eds.), Statistics in early childhood and primary education: Supporting early statistical and probabilistic thinking (pp. 55–73). Springer Nature: Singapore, Singapore. https://doi.org/10.1007/978-981-13-1044-7_3
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry (with discussion). International Statistical Review, 67(3), 223–265.
Zawojewski, J. S. (2013). 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, NY: Springer.
Zieffler, A., Garfield, J., delMas, R., & Reading, C. (2008). A framework to support research on informal inferential reasoning. Statistics Education Research Journal, 7(2), 40–58. [Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ7(2)_Zieffler.pdf].
Funding
This work was supported by Mary Immaculate College Faculty Seed Funding.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix
Appendix
The giraffe task 
The wolf task 
The monkey task 
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Leavy, A., Hourigan, M. (2021). Data Modelling and Informal Inferential Reasoning: Instances of Early Mathematical Modelling. In: Suh, J.M., Wickstrom, M.H., English, L.D. (eds) Exploring Mathematical Modeling with Young Learners. Early Mathematics Learning and Development. Springer, Cham. https://doi.org/10.1007/978-3-030-63900-6_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-63900-6_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-63899-3
Online ISBN: 978-3-030-63900-6
eBook Packages: EducationEducation (R0)