Abstract
Researchers have recently started focusing on the development of informal statistical inference (ISI) skills by primary school students. However, primary school teachers generally lack knowledge of ISI. In the literature, the growing samples heuristic is proposed as a way to learn to reason about ISI. The aim of this study was to explore pre-service teachers’ reasoning processes about ISI when they are engaged in a growing samples activity. Three classes of first-year pre-service teachers were asked to generalize to a population and to predict the graph of a larger sample during three rounds with increasing sample sizes . The content analysis revealed that most pre-service teachers described only the data and showed limited understanding of how a sample can represent the population.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
All the participants’ names are pseudonyms.
References
Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Utrecht, The Netherlands: CD-Ăź Press, Center for Science and Mathematics Education.
Bakker, A., & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13(2), 5–26.
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
Batanero, C., & DĂaz, C. (2010). Training teachers to teach statistics: What can we learn from research? Statistique et enseignement, 1(1), 5–20.
Ben-Zvi, D. (2006). Scaffolding students’ informal inference and argumentation. Paper presented at the Seventh International Conference on Teaching Statistics, Salvador, Brazil.
Ben-Zvi, D., Aridor, K., Makar, K., & Bakker, A. (2012). Students’ emergent articulations of uncertainty while making informal statistical inferences. ZDM—Mathematics Education, 44(7), 913–925.
Ben-Zvi, D., Bakker, A., & Makar, K. (2015). Learning to reason from samples. Educational Studies in Mathematics, 88(3), 291–303.
Ben-Zvi, D., Gil, E., & Apel, N. (2007). What is hidden beyond the data? Young students reason and argue about some wider universe. In D. Pratt & J. Ainley (Eds.), Proceedings of the Fifth International Forum for Research on Statistical Reasoning, Thinking and Literacy (SRTL-5). Warwick, UK: University of Warwick.
Burgess, T. (2009). Teacher knowledge and statistics: What types of knowledge are used in the primary classroom? Montana Mathematics Enthusiast, 6(1&2), 3–24.
Canada, D., & Ciancetta, M. (2007). Elementary preservice teachers’ informal conceptions of distribution. Paper presented at the 29th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Stateline, NV.
Cobb, P., & Tzou, C. (2009). Supporting students’ learning about data creation. In W.-M. Roth (Ed.), Mathematical representation at the interface of body and culture (pp. 135–171). Charlotte, NC: IAP.
De Vetten, A., Schoonenboom, J., Keijzer, R., & Van Oers, B. (2018). Pre-service primary school teachers’ knowledge of informal statistical inference. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-018-9403-9.
Garfield, J., & Ben-Zvi, D. (2007). How students learn statistics revisited: A current review of research on teaching and learning statistics. International Statistical Review, 75(3), 372–396.
Garfield, J., & Ben-Zvi, D. (2008). Developing students’ statistical reasoning: Connecting research and teaching practice. Dordrecht, The Netherlands: Springer.
Garfield, J., Le, L., Zieffler, A., & Ben-Zvi, D. (2015). Developing students’ reasoning about samples and sampling variability as a path to expert statistical thinking. Educational Studies in Mathematics, 88(3), 327–342.
Groth, R. E., & Bergner, J. A. (2006). Preservice elementary teachers’ conceptual and procedural knowledge of mean, median, and mode. Mathematical Thinking and Learning, 8(1), 37–63.
Harradine, A., Batanero, C., & Rossman, A. (2011). Students and teachers’ knowledge of sampling and inference. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICMI/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference (pp. 235–246). Dordrecht, The Netherlands: Springer.
Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., et al. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511.
Jacobbe, T., & Carvalho, C. (2011). Teachers’ understanding of averages. In C. Batanero, G. Burrill, C. Reading, & A. Rossman (Eds.), Joint ICMI/IASE study: Teaching statistics in school mathematics. Challenges for teaching and teacher education. Proceedings of the ICMI Study 18 and 2008 IASE Round Table Conference (pp. 199–209). Dordrecht, The Netherlands: Springer.
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.
Leavy, A. M. (2006). Using data comparison to support a focus on distribution: Examining preservice teacher’s understandings of distribution when engaged in statistical inquiry. Statistics Education Research Journal, 5(2), 89–114.
Leavy, A. M. (2010). The challenge of preparing preservice teachers to teach informal inferential reasoning. Statistics Education Research Journal, 9(1), 46–67.
Liu, Y., & Grusky, D. B. (2013). The payoff to skill in the third industrial revolution. American Journal of Sociology, 118(5), 1330–1374.
Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 152–173.
Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.
Makar, K., & Rubin, A. (2014). Informal statistical inference revisited. Paper presented at the Ninth International Conference on Teaching Statistics (ICOTS 9), Flagstaff, AZ.
Meletiou-Mavrotheris, M., Kleanthous, I., & Paparistodemou, E. (2014). Developing pre-service teachers’ technological pedagogical content knowledge (TPACK) of sampling. Paper presented at the Ninth International Conference on Teaching Statistics (ICOTS9), Flagstaff, AZ.
Meletiou-Mavrotheris, M., & Paparistodemou, E. (2015). Developing students’ reasoning about samples and sampling in the context of informal inferences. Educational Studies in Mathematics, 88(3), 385–404.
Mooney, E., Duni, D., VanMeenen, E., & Langrall, C. (2014). Preservice teachers’ awareness of variability. In K. Makar, B. De Sousa, & R. Gould (Eds.), Proceedings of the Ninth International Conference on Teaching Statistics (ICOTS9). Voorburg, The Netherlands: International Statistical Institute.
Rivkin, S. G., Hanushek, E. A., & Kain, J. F. (2005). Teachers, schools, and academic achievement. Econometrica, 73(2), 417–458.
Schön, D. A. (1983). The reflective practitioner: How professionals think in action. London, UK: Temple Smith.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Watson, J. M. (2001). Profiling teachers’ competence and confidence to teach particular mathematics topics: The case of chance and data. Journal of Mathematics Teacher Education, 4(4), 305–337.
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
de Vetten, A., Schoonenboom, J., Keijzer, R., van Oers, B. (2019). Pre-service Teachers and Informal Statistical Inference: Exploring Their Reasoning During a Growing Samples Activity. In: Burrill, G., Ben-Zvi, D. (eds) Topics and Trends in Current Statistics Education Research. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-03472-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-03472-6_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-03471-9
Online ISBN: 978-3-030-03472-6
eBook Packages: EducationEducation (R0)