Educational Studies in Mathematics

, Volume 88, Issue 3, pp 385–404 | Cite as

Developing students’ reasoning about samples and sampling in the context of informal inferences

Article

Abstract

The expanding use of data in modern society for prediction and decision-making makes it a priority for mathematics instruction to help students build sound foundations of inferential reasoning at a young age. This study contributes to the emerging research literature on the early development of informal inferential reasoning through the conduct of a two-phase exploratory study carried out in an urban upper elementary school (Grades 4 to 6) in Cyprus. In Phase I, Grade 6 (11-year-old) students’ initial understandings of samples and sampling were examined through an open-ended written assessment (n = 69), and follow-up interviews (n = 5). In Phase II, a teaching experiment guided by a hypothetical learning trajectory (HLT) was implemented in a Grade 6 classroom (n = 19). The HLT aimed to support the emergence of children’s reasoning about sampling issues through the provision of an inquiry-based learning environment designed to offer ample opportunities for informal, data-based inferences. Findings indicate that the efforts of the teaching experiment to integrate the existing body of research into a HLT that starts with children’s initial understandings supported students in moving towards more nuanced forms of reasoning about sampling.

Keywords

Samples and sampling Sampling method Statistical reasoning Informal inferential reasoning Informal statistical inference Hypothetical learning trajectory 

References

  1. Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. (Doctoral dissertation). Utrecht University.Google Scholar
  2. Bakker, A., & Hoffmann, M. (2005). Diagrammatic reasoning as the basis for developing concepts: A semiotic analysis of students’ learning about statistical distribution. Educational Studies in Mathematics, 60, 333–358.CrossRefGoogle Scholar
  3. Clements, D., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York: Routledge.Google Scholar
  4. Confrey, J., Maloney, A., Nguyen, K., Mojica, G., & Myers, M. (2009). Equipartitioning/splitting as a foundation of rational number reasoning using learning trajectories. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33 rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 345–352). Thessaloniki: PME.Google Scholar
  5. Daro, P., Mosher, F., & Cocoran, T. (2011). Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction. Philadelphia: Consortium for Policy Research in Education.CrossRefGoogle Scholar
  6. English, L. (2012). Data modelling with first-grade students. Educational Studies in Mathematics, 81, 15–30.CrossRefGoogle Scholar
  7. Gil, E., & Ben-Zvi, D. (2011). Explanations and context in the emergence of students’ informal inferential reasoning. Mathematical Thinking and Learning, 13, 87–108.CrossRefGoogle Scholar
  8. Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory. Chicago: Aldine Publishing Company.Google Scholar
  9. Jacobs, V. R. (1999). How do students think about statistical sampling before instruction? Mathmatics Teacher Middle School, 5, 240–263.Google Scholar
  10. Konold, C., & Miller, C. D. (2005). TinkerPlots: Dynamic Data Explorations. Emeryville: Key Curriculum Press.Google Scholar
  11. Makar, K., & Ben-Zvi, D. (2011). The role of context in developing reasoning about informal statistical inference. Mathematical Thinking and Learning, 13, 1–4.CrossRefGoogle Scholar
  12. Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8, 82–105.Google Scholar
  13. Makar, K., Fielding-Wells, J., & Allmond, S. (2011). Is this game 1 or game 2? Primary children’s reasoning about samples in an inquiry classroom. Paper presented at the Seventh International Forum for Research on Statistical Reasoning, Thinking, & Literacy. Texel, The Netherlands.Google Scholar
  14. McClain, K., & Cobb, P. (2001). Supporting students’ ability to reason about data. Educational Studies in Mathematics, 45, 103–129.CrossRefGoogle Scholar
  15. Meletiou-Mavrotheris, M., Lee, C., & Fouladi, R. (2007). Introductory statistics, college student attitudes and knowledge—A Qualitative Analysis of the Impact of Technology-Based Instruction. International Journal of Mathematics Education in Science and Technology, 38, 65–83.CrossRefGoogle Scholar
  16. Paparistodemou, E., & Meletiou-Mavrotheris, M. (2008). Developing young children’s informal inference skills in data analysis. Statistics Education Research Journal, 7, 83–106.Google Scholar
  17. Pratt, D., Johnston-Wilder, P., Ainley, J., & Mason, J. (2008). Local and global thinking in statistical inference. Statistics Education Research Journal, 7, 107–129.Google Scholar
  18. Rubin, A., Bruce, B., & Tenney, Y. (1991). Learning about sampling: Trouble at the core of statistics. In D. Vere-Jones (Ed.), Proceedings of the Third International Conference on Teaching Statistics (Vol. 1, pp. 314–319). Voorburg: International Statistical Institute.Google Scholar
  19. Simon, M. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145.CrossRefGoogle Scholar
  20. Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Mahwah: Lawrence Erlbaum Associates.Google Scholar
  21. Watson, J., & Moritz, J. B. (1998). The beginning of statistical inference: Comparing two data sets. Educational Studies in Mathematics, 37, 145–168.CrossRefGoogle Scholar
  22. Watson, J., & Moritz, J. (2000). Developing concepts of sampling. Journal for Research in Mathematics Education, 31, 44–70.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Maria Meletiou-Mavrotheris
    • 1
  • Efi Paparistodemou
    • 2
  1. 1.European University CyprusNicosiaCyprus
  2. 2.Cyprus Pedagogical InstituteNicosiaCyprus

Personalised recommendations