Preparing prospective primary school teachers in teaching informal statistical inference
DOI:
https://doi.org/10.7146/nomad.v30i1.152931Keywords:
mathematicsAbstract
In recent decades, the statistics education community has focused extensively on research aimed at modernising mathematics curricula by integrating powerful statistical concepts relevant to the 21st century. As a result, the professional development needs of statistics teachers are evolving. There is an increasing demand for teachers to be well-equipped to teach foundational statistical concepts, including inferential statistics, and gaining these insights has become essential. This paper presents findings from an educational design research study conducted with participants in primary teacher education. The study outlines a design principle with three sub-components, intended to guide teacher training in statistical inference. The conclusion highlights the importance of statistical inference as a central theme in statistics education, with significant implications for school statistics and curriculum evaluation.
References
Akker, J. van den (1999). Principles and methods of development research. In J. van den Akker, R. M. Branch, K. Gustafson, N. Nieveen & T. Plomp (Eds.), Design approaches and tools in education and training (pp. 1–14). Springer. https://doi.org/10.1007/978-94-011-4255-7_1
Arnold, P. & Franklin, C. (2021). What makes a good statistical question? Journal of Statistics and Data Science Education, 29 (1), 122–130.
https://doi.org/10.1080/26939169.2021.1877582
Bakker, A. (2018). Design research in education: a practical guide for early career researchers. Routledge. https://doi.org/10.4324/9780203701010
Batanero, C. (2011). Measuring levels of statistical pedagogical content knowledge. 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. 295–298). Springer.
https://doi.org/10.1007/978-94-007-1131-0
Bargagliotti, A., Franklin, C., Arnold, P., Gould, R., Johnson, S. et al. (2020). Pre-K-12 guidelines for assessment and instruction in statistics education II (GAISE II). A framework for statistics and data science education. A. S. Association. https://www.amstat.org/asa/files/pdfs/GAISE/GAISEIIPreK-12_Full.pdf
Ben-Zvi, D., Gravemeijer, K. & Ainley, J. (2018). Design of statistics learning environments. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 473–502). Springer. https://doi.org/10.1007/978-3-319-66195-7_16
Bergman Ärlebäck, J., Blomberg, P. & Nilsson, P. (2015). An instructional design perspective on data-modelling for learning statistics and modelling. I O. Helenius, A. Engström, T. Meaney, P. Nilsson, E. Norén et al. (Eds.), Proceedings of MADIF 9 (pp. 37–46). SMDF.
Bertram, A. (2014). CoRes and PaP-eRs as a strategy for helping beginning primary teachers develop their pedagogical content knowledge. Educación Química, 25 (3), 292–303. https://doi.org/10.1016/S0187-893X(14)70545-2
Biehler, R. & Pratt, D. (2012). Research on the reasoning, teaching and learning of probability and uncertainty. ZDM, 44, 819–823. https://doi.org/10.1007/s11858-012-0468-0
Blomberg, P. (2015). Informell statistisk inferens i modelleringssituationer – en studie om utveckling av ett ramverk för att analysera hur elever uttrycker inferenser [Informal statistical inference in modeling situations – a study of developing a framework for analysing how students express inferences]. [Licentiate dissertation]. Linnaeus University.https://lnu.diva-portal.org/smash/get/diva2:843625/FULLTEXT02.pdf
Blomberg, P., Högström, P. & Liljekvist, Y. (2022, 2–7 February). Learning opportunities for pre-service teachers to develop pedagogical content knowledge for statistical inference. Twelfth Congress of the European Society for Research in Mathematics Education (CERME12). https://hal.science/hal-03751811/file/TWG05_06_Blomberg%20.pdf
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 (pp. 57–69). Springer. https://doi.org/10.1007/978-94-007-1131-0_10
Carlson, J., Daehler, K. R., Alonzo, A. C., Barendsen, E., Berry, A. et al. (2019). The refined consensus model of pedagogical content knowledge in science education. In A. Hume, R. Cooper & A. Borowski (Eds.), Repositioning pedagogical content knowledge in teachers’ knowledge for teaching science (pp. 77–94). Springer. https://doi.org/10.1007/978-981-13-5898-2_2
Carpendale, J. & Hume, A. (2019). Investigating practising science teachers’ pPCK and ePCK development as a result of collaborative CoRe design. In A. Hume, R. Cooper & A. Borowski (Eds.), Repositioning pedagogical content knowledge in teachers’ knowledge for teaching science (pp. 225–252). Springer. https://doi.org/10.1007/978-981-13-5898-2_10
Cobb, G. W., & Moore, D. S. (1997). Mathematics, statistics, and teaching. The American Mathematical Monthly, 104 (9), 801–823. https://doi.org/10.2307/2975286
Cobb, P., Jackson, K. & Dunlap Charpe, C. (2017). Conducting design studies to investigate and support mathematics students’ and teachers’ learning. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 208–233). NCTM.
Cobb, P., Zhao, Q. & Dean, C. (2009). Conducting design experiments to support teachers’ learning: a reflection from the field. Journal of the Learning Sciences, 18 (2), 165–199. https://doi.org/10.1080/10508400902797933
Danish Ministry of Education (2019). Matematik fælles mål 2019. Børne- og undervisningsministeriet. https://emu.dk/sites/default/files/2020-09/GSK_F%C3%A6llesM%C3%A5l_Matematik.pdf
Doerr, H. M. & Lesh, R. A. (2003). A modeling perspective on teacher development. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 125–140). Lawrence Erlbaum.
Groth, R. E. (2017). Developing statistical knowledge for teaching during designbased research. Statistics Education Research Journal, 16 (2), 376–396. https://doi.org/10.52041/serj.v16i2.197
Groth, R. E. (2013). Characterizing key developmental understandings and pedagogically powerful ideas within a statistical knowledge for teaching framework. Mathematical Thinking and Learning, 15 (2), 121–145. https://doi.org/10.1080/10986065.2013.770718
Heaton, R. M. & Mickelson, W. T. (2002). The learning and teaching of statistical investigation in teaching and teacher education. Journal of Mathematics Teacher Education, 5 (1), 35–59. https://doi.org/10.1023/A:1013886730487
Hill, H. C., Ball, D. L. & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39 (4), 372–400. https://doi.org/10.5951/jresematheduc.39.4.0372
Hume, A. & Berry, A. (2011). Constructing CoRes – a strategy for building PCK in pre-service science teacher education. Research in Science Education, 41 (3), 341–355. https://doi.org/10.1007/s11165-010-9168-3
Hußmann, S. & Prediger, S. (2016). Specifying and structuring mathematical topics: a four-level approach for combining formal, semantic, concrete, and empirical levels exemplified for exponential growth. J Math Didakt, 37 (1), 33–67. https://doi.org/10.1007/s13138-016-0102-8
Langrall, C. W., Makar, K., Nilsson, P. & Shaughnessy, J. M. (2017). Teaching and learning probability and statistics: an integrated perspective. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 490–525). NCTM.
Landtblom, K. & Sumpter, L. (2021). Teachers and prospective teachers’ conceptions about averages. Journal of Adult Learning, Knowledge and Innovation, 4 (1), 1–8. https://doi.org/10.1556/2059.03.2019.02
Leavy, A. M. (2010). The challenge of preparing preservice teachers to teach informal inferential reasoning. Statistics Education Research Journal, 9 (1), 46–67. https://doi.org/10.52041/serj.v9i1.387
Lehrer, R. & English, L. (2018). Introducing children to modeling variability. In D. Ben-Zvi, K. Makar & G. J. (Eds.), International handbook of research in statistics education (pp. 229–260). Springer. https://doi.org/10.1007/978-3-319-66195-7_7
Lehrer, R. & Schauble, L. (2004). Modeling natural variation through distribution. American Educational Research Journal, 41 (3), 635–679.
https://doi.org/10.3102/00028312041003635
Lesh, R. & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5 (2-3), 109–129. https://doi.org/10.1080/10986065.2003.9679996
Lesh, R. A. & Doerr, H. M. (2003). In what ways does a models and modeling perspective move beyond constructivism? In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 519–556). Lawrence Erlbaum.
Loughran, J., Mulhall, P. & Berry, A. (2004). In search of pedagogical content knowledge in science: developing ways of articulating and documenting professional practice. Journal of Research in Science Teaching, 41 (4), 370–391. https://doi.org/10.1002/tea.20007
Makar, K. & Fielding-Wells, J. (2011). Teaching teachers to teach statistical investigations. 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. 347–358). Springer. https://doi.org/10.1007/978-94-007-1131-0_33
Makar, K. & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8 (1), 82–105.
https://doi.org/10.52041/serj.v8i1.457
Makar, K. & Rubin, A. (2018). Learning about statistical inference. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 261–294). Springer. https://doi.org/10.1007/978-3-319-66195-7_8
McKenney, S. & Reeves, T. C. (2018). Conducting educational design research (2nd ed.). Routledge. https://doi.org/10.4324/9781315105642
Nilsson, P., Schindler, M. & Bakker, A. (2018). The nature and use of theories in statistics education. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 359–386). Springer. https://doi.org/10.1007/978-3-319-66195-7_11
Oliveira, H. & Henriques, A. (2019). Teachers’ perspectives about statistical reasoning: opportunities and challenges for its development. In G. Burrill & D. Ben-Zvi (Eds.), Topics and trends in current statistics education research: international perspectives (pp. 309–328). Springer.
https://doi.org/10.1007/978-3-030-03472-6_14
Paparistodemou, E. & Meletiou-Mavrotheris, M. (2008). Developing young students’ informal inference skills in data analysis. Statistics Education Research Journal, 7 (2), 83–106. https://doi.org/10.52041/serj.v7i2.471
Petocz, P., Reid, A. & Gal, I. (2018). Statistics education research. In D. Ben-Zvi, K. Makar & G. J. (Eds.), International handbook of research in statistics education (pp. 71–98). Springer. https://doi.org/10.1007/978-3-319-66195-7
Pfannkuch, M. (2005). Probability and statistical Inference: How can teachers enable learners to make the connection? In G. A. Jones (Ed.), Exploring probability in school: challenges for teaching and learning (pp. 267–294). Springer. https://doi.org/10.1007/0-387-24530-8_12
Ponte, J. P. da & Noll, J. (2018). Building capacity in statistics teacher education. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 433–456). Springer. https://doi.org/10.1007/978-3-319-66195-7_14
Pratt, D. & Ainley, J. (2008). Introducing the special issue on informal inferential reasoning. Statistics Education Research Journal, 7 (2), 3–4. https://doi.org/10.52041/serj.v7i2.466
Prediger, S., Bikner-Ahsbahs, A. & Arzarello, F. (2008). Networking strategies and methods for connecting theoretical approaches: first steps towards a conceptual framework. ZDM, 40 (2), 165–178. https://doi.org/10.1007/s11858-008-0086-z
Prediger, S., Roesken-Winter, B. & Leuders, T. (2019). Which research can support PD facilitators? Strategies for content-related PD research in the Three-tetrahedron model. Journal of Mathematics Teacher Education, 22 (4), 407–425. https://doi.org/10.1007/s10857-019-09434-3
Rossman, A. J. (2008). Reasoning about informal statistical inference: one statistician’s view. Statistics Education Research Journal, 7 (2), 5–19.
https://doi.org/10.52041/serj.v7i2.467
Runesson, U. (2006). What is it possible to learn? On variation as a necessary condition for learning. Scandinavian Journal of Educational Research, 50 (4), 397–410. https://doi.org/10.1080/00313830600823753
Shaughnessy, J. M. (2019, 5–10 may). The Big Ideas in the statistics education of our students: Which ones are the biggest? XV Inter-American Conference on Mathematics Education. https://conferencia.ciaem-redumate.org/index.php/xvciaem/xv/paper/viewFile/1091/603
Swedish National Agency for Education (2024). Curriculum for compulsory school, preschool class and school-age educare – Lgr22. Skolverket. https://www.skolverket.se/publikationer?id=12435
Vetten, A. de, Schoonenboom, J., Keijzer, R. & Oers, B. van (2019a). Pre-service primary school teachers’ knowledge of informal statistical inference. Journal of Mathematics Teacher Education, 22(6), 639–661. https://doi.org/10.1007/s10857-018-9403-9
Vetten, A. de, Schoonenboom, J., Keijzer, R. & Oers, B. van (2019b). Pre-service teachers and informal statistical inference: exploring their reasoning during a growing samples activity. In G. Burrill & D. Ben-Zvi (Eds.), Topics and trends in current statistics education research: international perspectives (pp. 199–224). Springer. https://doi.org/10.1007/978-3-030-03472-6_9
Watson, J. & Callingham, R. (2003). Statistical literacy: a complex hierarchical construct. Statistics Education Research Journal, 2 (2), 3–46.
https://doi.org/ 10.52041/serj.v2i2.553
Watson, J., Fitzallen, N., Fielding-Wells, J. & Madden, S. (2018). The practice of statistics. In D. Ben-Zvi, K. Makar & J. Garfield (Eds.), International handbook of research in statistics education (pp. 105–137). Springer. https://doi.org/10.1007/978-3-319-66195-7_4
Wild, C. J., Pfannkuch, M., Regan, M. & Horton, N. J. (2011). Towards more accessible conceptions of statistical inference. Journal of the Royal Statistical Society Series A: Statistics in Society, 174 (2), 247–295. https://doi.org/10.1111/j.1467-985X.2010.00678.x
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Per Blomberg

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.