Statistical inquiry, teacher education, statistical questions, collaborative work, peer feedback, expert feedback, Posing questions, prospective primary teachers


Recent approaches to statistics education situate the teaching and learning of statistics within cycles of statistical inquiry. Learners pose questions, plan, and collect, represent, analyse and interpret data. We focus on the first step – posing statistical questions. Posing statistical questions is a critical step as questions inform the types of data collected, determine the representations used, and influence the interpretations that can be made. We report on an investigation of 158 prospective elementary teachers as they design statistical questions to support group comparisons. Support was provided through implementation of three phases of question development (think, peer-feedback, and expert-feedback). We describe the features of initial statistical questions posed, examine refinements made to statistical questions, and evaluate the effectiveness of both peer and expert feedback. Our study reveals that generating adequate statistical questions is particularly complex and requires considerable time, targeted feedback, and support. With appropriate support, in the form of peer and expert feedback provided within a three-phase question design scenario, prospective elementary teachers could generate adequate statistical questions suitable for use in primary classrooms. While this study provides compelling evidence to support the use of expert feedback, further research is required to identify the best ways to support prospective teachers in both providing and implementing peer-feedback.


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 Eight International Conference on Teaching Statistics, Ljubljana, Slovenia, July 11-16.

Arnold, P. M. (2013). Statistical investigative questions: An enquiry into posing and answering investigative questions from existing data [Doctoral dissertation, University of Auckland].

Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools [Doctoral dissertation, University of Utrecht].

Bakker, A., & Gravemeijer, K. (2004). Learning to reason about distributions. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 147–168). Kluwer Academic Publishers.

Bargagliotti, A., Franklin, C., Arnold, P., Gould, R., Johnson, S., Perez, L., & Spangler, D. (2020). Pre-K–12 Guidelines for Assessment and Instruction in Statistics Education (GAISE) report II. American Statistical Association and National Council of Teachers of Mathematics.

Ben-Zvi, D. (2004). Reasoning about variability in comparing distributions. Statistics Education Research Journal, 3(2), 42–63.

Biehler, R. (2001). Statistische kompetenz von schülerinnen und schülern: Konzepte und ergebnisse empirischer studien am beispiel des vergleichens empirischer verteilungen. In M. Borovcnik, J. Engel, & D. Wickmann (Eds.), Anregungen Zum Stochastikunterricht (pp. 97–114). Franz Becker.

Bitchener, J., Young, S., & Cameron, D. (2005). The effect of different types of corrective feedback on ESL student writing. Journal of Second Language Writing, 14, 191–205.

Burrill, G., & Biehler, R. (2011). Fundamental statistical ideas in the school curriculum and in training teachers. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics: Challenges for teaching and teacher education. A joint ICMI/IASE study (pp. 57–69). Springer.

Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83, 57–69.

Cai, J., & Hwang., S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, 102.

Chapman, O. (2004). Helping pre-service elementary teachers develop flexibility in using word problems in their teaching. In D. McDougall & A. Ross (Eds.) Proceedings of the 26th North American Chapter of PME, 3, 1175–1182.

Cho, Y. H., & Cho, K. (2011). Peer reviewers learn from giving comments. Instructional Science, 39(5), 629–43.

Cho, K., & MacArthur. C. (2010). Student revision with peer and expert reviewing. Learning and Instruction, 20(4), 328–38.

Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’ practices. Educational Studies in Mathematics, 52(3), 243–270.

Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415.

Crespo, S. & Harper, F. K. (2020). Learning to pose collaborative mathematics problems with secondary prospective teachers. International Journal of Educational Research, 102.

Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: Development of an active learning framework. Educational Studies in Mathematics, 83, 87–101.

Falchikov, N., & Goldfinch, J. (2000). Student peer assessment in higher education: A meta-analysis comparing peer and teacher marks. Review of Educational Research, 70(3), 287–322.

Ferris, D. R. (1997). The influence of teacher commentary on student revision. TESOL Quarterly, 31(2), 315–339.

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. American Statistical Association.

Frischemeier, D. (2019). Primary school students´ reasoning when comparing groups using modal clumps, medians and hatplots. Mathematics Education Research Journal, 31(4), 485–505.

Frischemeier, D., & Biehler, R. (2018). Stepwise development of statistical literacy and thinking in a statistics course for elementary preservice teachers. In: T. Dooley, & G. Gueudet (Eds.), Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (pp. 756–763). DCU Institute of Education and ERME.

Frischemeier, D., & Leavy, A. (2020). Improving the quality of statistical questions posed for group comparison situations. Teaching Statistics, 42(2), 58–65.

Kluger, A. N., & DeNisi, A. (1996). The effects of feedback interventions on performance: A historical review, a meta-analysis, and a preliminary feedback intervention theory. Psychological Bulletin, 119(2), 254–284.

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. Garfield & G. Burrill (Eds.), Research on the Role of Technology in Teaching and Learning Statistics: Proceedings of the 1996 IASE Round Table Conference (pp. 151–167). International Statistical Institute.

Konold, C., Robinson, A., Khalil, K., Pollatsek, A., Well, A., Wing, R., & Mayr, S. (2002). Students' use of modal clumps to summarize data. In Proceedings of the Sixth International Conference on Teaching Statistics (ICOTS6), Cape Town, South Africa.

Kuckartz, U. (2012). Qualitative inhaltsanalyse. Methoden, praxis, computerunterstüzung. Beltz Juventa.

Leavy, A. M. & Hourigan, M. (2019). Posing mathematically worthwhile problems: Developing the problem posing skills of prospective teachers. Journal of Mathematics Teacher Education, 23, 341–361.

Leavy, A. M. & Hourigan, M. (2021). Enhancing the mathematical problem posing skills of prospective teachers through a mathematical letter writing initiative. Journal of Mathematics Teacher Education.

Matsumura, L. C., Patthey-Chavez, G. G., Valdes, R., & Garnier, H. (2002). Teacher feedback, writing assignment quality, and third-grade students’ revision in lower- and higher-achieving urban schools. The Elementary School Journal, 103(1), 3–25.

Mayring, P. (2015). Qualitative content analysis: Theoretical background and procedures. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 365–380). Springer.

National Council of Teachers of Mathematics (1989). Curriculum and evaluation standards for school mathematics. Author.

National Council of Teachers of Mathematics. (2000). The principles and standards for school mathematics [PSSM]. Author.

Nelson, M. M., & Schunn, C. D. (2009). The nature of feedback: How different types of peer feedback affect writing performance. Instructional Science, 37 (4), 375–401.

Nilson, L. B. (2003). Improving student peer feedback. College Teaching, 51(1), 34–38.

Pfannkuch, M., & Horring, J. (2004). Developing statistical thinking in a secondary school: A collaborative curriculum development. In G. Burrill & M. Camden (Eds.), Curricular development in statistics education: International Association for Statistics Education 2004 Roundtable (pp. 204–218). International Statistical Institute.

Silver, E. A. (2013). Problem-posing research in mathematics education: looking back, looking around, and looking ahead. Educational Studies in Mathematics, 83, 157–162.

Sugita, Y. (2006). The impact of teachers’ comment types on students’ revision. ELT Journal, 60(1), 34–41.

Topping, K. J. (2009). Peer assessment. Theory into Practice, 48(1), 20–7.

Watson, J. M. & English, L. D. (2017). Statistical problem posing, problem refining, and further reflection in grade 6. Canadian Journal of Science, Mathematics and Technology Education, 17(4), 347–365.

Watson, J. M., & Moritz, J. B. (1999). The beginning of statistical inference: Comparing two data sets. Educational Studies in Mathematics, 37(2), 145–168.

Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248.






Regular Articles