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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. (Doctoral dissertation). Utrecht University.
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.
Clements, D., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York: Routledge.
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.
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.
English, L. (2012). Data modelling with first-grade students. Educational Studies in Mathematics, 81, 15–30.
Gil, E., & Ben-Zvi, D. (2011). Explanations and context in the emergence of students’ informal inferential reasoning. Mathematical Thinking and Learning, 13, 87–108.
Glaser, B. G., & Strauss, A. L. (1967). The discovery of grounded theory. Chicago: Aldine Publishing Company.
Jacobs, V. R. (1999). How do students think about statistical sampling before instruction? Mathmatics Teacher Middle School, 5, 240–263.
Konold, C., & Miller, C. D. (2005). TinkerPlots: Dynamic Data Explorations. Emeryville: Key Curriculum Press.
Makar, K., & Ben-Zvi, D. (2011). The role of context in developing reasoning about informal statistical inference. Mathematical Thinking and Learning, 13, 1–4.
Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8, 82–105.
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.
McClain, K., & Cobb, P. (2001). Supporting students’ ability to reason about data. Educational Studies in Mathematics, 45, 103–129.
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.
Paparistodemou, E., & Meletiou-Mavrotheris, M. (2008). Developing young children’s informal inference skills in data analysis. Statistics Education Research Journal, 7, 83–106.
Pratt, D., Johnston-Wilder, P., Ainley, J., & Mason, J. (2008). Local and global thinking in statistical inference. Statistics Education Research Journal, 7, 107–129.
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.
Simon, M. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26, 114–145.
Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Mahwah: Lawrence Erlbaum Associates.
Watson, J., & Moritz, J. B. (1998). The beginning of statistical inference: Comparing two data sets. Educational Studies in Mathematics, 37, 145–168.
Watson, J., & Moritz, J. (2000). Developing concepts of sampling. Journal for Research in Mathematics Education, 31, 44–70.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Meletiou-Mavrotheris, M., Paparistodemou, E. Developing students’ reasoning about samples and sampling in the context of informal inferences. Educ Stud Math 88, 385–404 (2015). https://doi.org/10.1007/s10649-014-9551-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10649-014-9551-5