Abstract
The practice of statistics is the focus of the world in which professional statisticians live. To understand meaningfully what this practice is about, students need to engage in it themselves. Acknowledging the limitations of a genuine classroom setting, this study attempted to expose four classes of year 5 students (n = 91) to an authentic experience of the practice of statistics. Setting an overall context of people’s habits that are considered environmentally friendly, the students sampled their class and set criteria for being environmentally friendly based on questions from the Australian Bureau of Statistics CensusAtSchool site. They then analysed the data and made decisions, acknowledging their degree of certainty, about three populations based on their criteria: their class, year 5 students in their school and year 5 students in Australia. The next step was to collect a random sample the size of their class from an Australian Bureau of Statistics ‘population’, analyse it and again make a decision about Australian year 5 students. At the end, they suggested what further research they might do. The analysis of students’ responses gives insight into primary students’ capacity to appreciate and understand decision-making, and to participate in the practice of statistics, a topic that has received very little attention in the literature. Based on the total possible score of 23 from student workbook entries, 80 % of students achieved at least a score of 11.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Allmond, S., & Makar, K. (2010). Developing primary students’ ability to pose questions in statistical investigations. In C. Reading (Ed.), Data and context in statistics education: towards an evidence-based society (Proceedings of the 8th International Conference on the Teaching of Statistics, Ljubljana, Slovenia, July (pp. 11–16). Voorburg, The Netherlands: International Statistical Institute. Retrieved from http://iase-web.org/documents/papers/icots8/ICOTS8_8A1_ALLMOND.pdf.
Arnold, P. (2008). What about the P in the PPDAC cycle? An initial look at posing questions for statistical investigation. Proceedings of the 11th International Congress of Mathematics Education, Monterrey, Mexico, 6–13 July, 2008. Online: http://tsg.icme11.org/tsg/show/15
Australian Curriculum, Assessment and Reporting Authority (ACARA). (2015). Australian Curriculum: mathematics, Version 7.4, 30 March 2015. Sydney, NSW: ACARA.
Ben-Zvi, D., Aridor, K., Makar, K., & Bakker, A. (2012). Students’ emergent articulations of uncertainty while making informal statistical inferences. ZDM Mathematics Education, 44, 913–925.
Ben-Zvi, D., Bakker, A., & Makar, K. (2015). Learning to reason from samples. Educational Studies in Mathematics, 88, 291–303.
Biggs, J. B., & Collis, K. F. (1982). Evaluating the quality of learning: the SOLO taxonomy. New York: Academic.
Bohan, J. (2006). Using regression to connect algebra to the real world. In G. F. Burrill (Ed.), Thinking and reasoning with data and chance (pp. 195–208). Reston, VA: National Council of Teachers of Mathematics.
Bush, S. B., Karp, K. S., Albanese, J., & Dillon, F. (2014). The oldest person you’ve known. Mathematics Teaching in the Middle School, 20, 278–285.
Chin, S., & Kayalvizhi, G. (2002). Posing questions for open investigations: what questions do pupils ask? Research in Science & Technology Education, 20, 269–287.
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.
Cobb, P., Jackson, K., & Munoz, C. (2016). Design research: a critical analysis. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (3rd ed., pp. 481–503). New York: Routledge.
Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Washington, DC: National Governors Association for Best Practices and the Council of Chief State School Officers. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.
English, L. D. (2014). Statistics at play. Teaching Children Mathematics, 21, 37–44.
English, L., & Watson, J. (2015a). Exploring variation in measurement as a foundation for statistical thinking in the elementary school. International Journal of STEM Education, 2(3). doi:10.1186/s40594-015-0016-x
English, L., & Watson, J. (2015b). Making decisions with data: are we environmentally friendly? Australian Primary Mathematics Classroom. In press.
English, L., & Watson, J. (2015c). Statistical literacy in the elementary school: opportunities for problem posing. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Problem posing: from research to effective practice (pp. 241–256). New York: Springer.
English, L., & Watson, J. (2015d). Development of probabilistic understanding in fourth grade. Journal for Research in Mathematics Education. In press.
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: a preK-12 curriculum framework. Alexandria, VA: American Statistical Association.
Friel, S. N., & Bright, G. W. (1998). Teach-Stat: a model for professional development in data analysis and statistics for teachers K-6. In S. P. Lajoie (Ed.), Reflections on statistics: learning, teaching, and assessment in grades K-12 (pp. 89–117). Mahwah, NJ: Lawrence Erlbaum.
Friel, S. N., O’Connor, W., & Mamer, J. D. (2006). More than “Meanmedianmode” and a bar graph: what’s needed to have a statistical conversation? In G. F. Burrill (Ed.), Thinking and reasoning with data and chance (pp. 117–137). Reston, VA: National Council of Teachers of Mathematics.
Holmes, P. (1980). Teaching statistics 11–16. Slough, UK: Schools Council and Foulsham Educational.
Jacobs, V. R. (1999). How do students think about statistical sampling before instruction? Mathematics in the Middle School, 5(4), 240–263.
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.
Konold, C., & Miller, C. D. (2011). TinkerPlots: dynamic data exploration [computer software, Version 2.0]. Emeryville, CA: Key Curriculum Press.
Lavigne, N. C., & Lajoie, S. P. (2007). Statistical reasoning of middle school children engaging in survey inquiry. Contemporary Educational Psychology, 32, 630–666.
Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105. Retrieved from http://iase-web.org/documents/SERJ/SERJ8(1)_Makar_Rubin.pdf.
Meletiou-Mavrotheris, M., & Paparistodemou, E. (2015). Developing students’ reasoning about samples and sampling in the context of informal inferences. Educational Studies in Mathematics, 88, 385–404.
Ministry of Education. (2007). The New Zealand curriculum. Wellington, NZ: Author. Retrieved from http://nzcurriculum.tki.org.nz/The-New-Zealand-Curriculum.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
Rubin, A., Bruce, B., & Tenney, Y. (1990). Learning about sampling: trouble at the core of statistics. In D. Vere-Jones (Ed.), School and general issues (Proceedings of the 3rd International Conference on the Teaching of Statistics). Voorburg, The Netherlands: International Statistical Institute. Retrieved from http://iase-web.org/documents/papers/icots3/BOOK1/A9-4.pdf.
Saldanha, L., & Thompson, P. (2002). Conceptions of sample and their relationship to statistical inference. Educational Studies in Mathematics, 51, 257–270.
Watson, J. M. (2006). Statistical literacy at school: growth and goals. Mahwah, NJ: Lawrence Erlbaum.
Watson, J. M. (2009). The development of statistical understanding at the elementary school level. Mediterranean Journal for Research in Mathematics Education, 8(1), 89–109.
Watson, J., & English, L. (2015). Repeated random sampling in grade 5. Manuscript submitted for publication.
Watson, J. M., & Moritz, J. B. (2000). Developing concepts of sampling. Journal for Research in Mathematics Education, 31, 44–70.
Wild, C., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248.
Acknowledgments
This study was funded by Australian Research Council project number DP120100158. The authors acknowledge the excellent organisational support by the Senior Research Assistant, Jo Macri.
Author information
Authors and Affiliations
Corresponding author
Appendices
Appendix A
Appendix B
Rights and permissions
About this article
Cite this article
Watson, J.M., English, L.D. Introducing the practice of statistics: are we environmentally friendly?. Math Ed Res J 27, 585–613 (2015). https://doi.org/10.1007/s13394-015-0153-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13394-015-0153-z