Variability in statistical problem-solving: The case of Sweden

Authors

DOI:

https://doi.org/10.52041/serj.897

Keywords:

Statistics education research, Variability, School mathematics, Textbook analysis, Statistical problem-solving

Abstract

Understanding variability is key to statistical reasoning, yet research indicates that it receives insufficient attention in school mathematics textbooks. This study investigates how primary school textbooks for grades 4–6 (age 10–12 years) in Sweden present variability within the statistical problem-solving process. Using the Guidelines for Assessment and Instruction in Statistics Education and established variability practices, the analysis of two widely used textbooks reveals a strong emphasis on analyzing data, particularly tasks that involve reading data displays or calculating measures of central tendency. However, other practices, such as formulating statistical questions and interpreting results, are underrepresented. Tasks predominantly encourage implicit noticing and representation rather than deeper reasoning through explanation or investigation. Variability is predominantly introduced through descriptive statistics rather than as a fundamental concept for understanding data distribution and uncertainty. The findings underscore the need for textbooks to integrate all components of statistical problem-solving more evenly, thereby enhancing students’ statistical reasoning and engagement with variability.

References

Bargagliotti, A., Franklin, C., Arnold, P., Gould, R., Johnson, S., Perez, L., & Spangler, D. (2020). Pre-K-12 guideline for assessment and instruction in statistics education II (GAISE II). A framework for statistics and data science education. American Statistical Association; National Council of Teachers of Mathematics. https://www.amstat.org/asa/files/pdfs/GAISE/GAISEIIPreK-12_Full.pdf

Ben-Zvi, D. (2004). Reasoning about variability in comparing distributions. Statistics Education

Research Journal, 3(2), 42–63. https://doi.org/10.52041/serj.v3i2.547

Biehler, R., Frischemeier, D., Reading, C., & Shaughnessy, M. (2018). Reasoning about data. In: Ben-Zvi, D. Makar, K., & garfield, J. (Eds.) International Handbook of Research in Statistics Education. Springer, Dordrecht pp. 139- 192. https://doi.org/10.1007/978-3-319-66195-7_5

Burrill, G., & Biehler, R. (2011). Fundamental statistical ideas in the school curriculum and in training teachers. In Batanero, C., Burrill, G., & Reading, C. (Eds.) Teaching Statistics in School Mathematics. Challenges foor Teaching and Teacher Education. New ICMI study Series, vol 14, Springer Dordrecht pp. 57 -69. https://doi.org/10.1007/978-94-007-1131-0_10

Büscher, C. (2022). Learning opportunities for statistical literacy in German middle school mathematics textbooks. In Twelfth Congress of the European Society for Research in Mathematics Education. https://hal.science/hal-03751814v1

Cobb, P., McClain, K. (2004). Principles of Instructional Design for Supporting the Development of Students’ Statistical Reasoning. In: Ben-Zvi, D., Garfield, J. (eds) The Challenge of Developing Statistical Literacy, Reasoning and Thinking. Springer, Dordrecht. pp. 375–395 https://doi.org/10.1007/1-4020-2278-6_16

delMas, R., & Liu, Y. (2005). Exploring students' conceptions of the standard deviation. Statistics Education Research Journal, 4(1), 55–82. https//doi.org/10.52041/serj.v4i1.525

Dierdorp, A., Bakker, A., Ben-zvi, D., & Makar, K. (2017). Secondary Students’ Considerations of variability in measurement activities based on authentic practices. Statistics Education Research Journal: International Association for Statistical Education, 16, (2), 397- 418. Available in: http://iase-web.org/Publications.ph p?p=SERJ.

Dolor, J., & Noll, J. (2015). Using guided reinvention to develop teachers' understanding of hypothesis testing concepts. Statistics Education Research Journal, 14(1), 60–89. https://doi.org/10.52041/serj.v14i1.269

English, L. D. & Watson, J. M. (2015). Exploring variation in measurement as a foundation for statistical thinking in the elementary school. International Journal of STEM Education doi: 10.1186/s40594-015-0016-x

Fischbein, E. (1975). The intuitive sources of probabilistic thinking in children. Dordrecht, The Netherlands: Reidel

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 Pre-K-12 Curriculum Framework Alexandria, VA: American Statistical Association. https://www.amstat.org/asa/files/pdfs/gaise/gaiseprek-12_full.pdf

Friel, S. N., Curcio, F. R., & Bright, G. W. (2001) Making sense of graphs: critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 32, (2), 124 - 158. doi: https://doi.org/10.2307/749671

Garfield, J., & Ben-Zvi, D. (2005). A framework for teaching and assessing reasoning about vari-

ability. Statistics Education Research Journal, 4(1), 92–99. http://www.stat.auckland.ac.nz/serj

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. https://doi.org/10.1111/j.1751-5823.2007.00029.x

Garfield, J.B., Ben-Zvi, D., Chance, B., Medina, E., Roseth, C., Zieffler, A. (2008). Learning to reason about variability. In: Garfield, J. & Ben-Zvi, D (Eds.) Developing Students’ Statistical Reasoning: Connecting Research and Teaching Practice. Springer, Dordrecht pp. 201-214. https://doi.org/10.1007/978-1-4020-8383-9_10

Gould, R. (2004). Variability: one statistician’s view. Statistics Education Research Journal, (3), 2 doi: https://doi.org/10.52041/serj.v3i2.537

Haggarty, L. & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French and German classrooms: who gets an opportunity to learn what? British Educational Research Journal, 28, (4), pp. 567-590. https://doi.org/10.1080/0141192022000005832

Holsti, O. R. Content Analysis for the Social Sciences and Humanities. Addison-Wesley, Reading, MA. https://doi.org/10.1177/000169937001300209

Hsieh, H-F., & Shannon, S. E. (2005) Three approaches to content analysis. Qualitative Health Research. 15(9) https://doi.org/10.1177/1049732305276687

Jones, D. L., & Basyal, D. (2019). An analysis of the statistics content in Nepali school textbooks. Mathematics Education Forum Chitwan, 4 (4), 21 – 34. doi: 10.3126/mefc.v4i4.26356

Jones, D. L., Brown, M., Dunkle, A., Hixon, L., Yoder, N., & Silbernick, Z. (2015). The statistical content of elementary school mathematics textbooks. Journal of Statistics Education, 23(3). https://doi.org/10.1080/10691898.2015.11889748

Jones, D. L., & Jacobbe, T. (2014). An analysis of the statistical content in textbooks for prospective elementary teachers. Journal of Statistics Education, 22(3). https://doi.org/10.1080/10691898.2014.11889713

Ko, E. S., & Lee, K. H. (2011). A study on levels of thinking of elementary and middle school students on the task of explaining and dealing with variability. Journal of Educational Research in Mathematics, 21(2) pp. 201-220. http://scholar.kyobobook.co.kr/article/detail/4010047431259

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., Higgins, T., Russell, S. J., & Khalil, K. (2014). Data seen through different lenses. Educational Studies in Mathematics doi:10.1007/s10649-013-9529-8

Landtblom, K. (2023). Opportunities to learn mean, median, and mode afforded by textbook tasks. Statistics Education Research Journal, 22(3), 1–17. https://doi.org/10.52041/serj.v22i3.655

Langrall, C., 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. NCM, pp. 490-525

Lehrer, R. & English, L. (2018). Introducing children to modeling variability. In Makar, K, Ben-Zvi, D, & Garfield, J (Eds.) International handbook of research in statistics education. Springer, pp. 229-260.

Lehrer, R., Kim, M., & Schauble, L. (2007). Supporting the development of conceptions of sta-

tistics by engaging students in measuring and modeling variability. International Journal of Computers for Mathematical Learning, 12(3), 195–216. https://doi.org/10.1007/s10758-007-9122-2

Makar, K. (2016). Developing young children’s emergent inferential practices in statistics. Mathematical Thinking and Learning, 18(1), 1-24. https://doi.org/10.1080/10986065.2016.1107820

Makar, K., & Rubin, A. (2014). Informal statistical inference revisited. In Makar, K., de Sousa, B. & Gould, R. (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics, Flagstaff, Arizona, USA. Voorburg, The Netherlands: International Statistical Institute. https://icots.info/9/proceedings/pdfs/ICOTS9_8C1_MAKAR.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, (3), 385 - 404. https://doi.org/10.1007/s10649-014-9551-5

Mooney, E., Duni, D., VanMeenen, E., & Langrall, C. (2014). Preservice teachers’ awareness of variability. In Makar, K., de Sousa, B. & Gould, R. (Eds.), Sustainability in statistics education. Proceedings of the Ninth International Conference on Teaching Statistics, pp. 1-6. Flagstaff, Arizona, USA. Voorburg, The Netherlands: International Statistical Institute. https://iase-web.org/icots/9/proceedings/pdfs/ICOTS9_C149_MOONEY.pdf?1405041831

Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College.

Nilsson, P. (2020). Students’ informal hypothesis testing in a probability context with concrete random generators. Statistics Education Research Journal, 19(3), 53-73. https://doi.org/10.52041/serj.v19i3.56

Nilsson, P. (2023). Hypothetical learning trajectory on informal hypothesis testing in a probability context. Statistics Education Research Journal, 22(2), 11-11. https://doi.org/doi.org/10.52041/serj.v22i2.425

Nilsson, P., & Eckert, A. (2023). Design principles for simulation-based learning of hypothesis testing in secondary school. Mathematical Thinking and Learning, 1-23. https://doi.org/10.1080/10986065.2022.2161288[PN1]

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

Pfannkuch, M., & Wild, C. J. (2004). Towards and understanding of statistical thinking. In: Ben-Zvi, D. & Garfield, J. (Eds.) The challenge of developing statistical literacy, reasoning and thinking (pp. 17-46). Springer.

Reading, C., & Shaughnessy, J. M. (2004). Reasoning about variation. In: Ben-Zvi, D. & Garfield, J. (Eds.) The challenge of developing statistical literacy, reasoning and thinking (pp. 201-226). Springer.

Remillard, J. T., & Heck, D. J. (2014). Conceptualizing the curriculum enactment process in mathematics education. ZDM Mathematics Education, 46, 705 – 718. doi: 10.1007/s11858-014-0600-4

Shaughnessy, J. M. (2007). Research on statistics learning and reasoning. In Lester, F.K. (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 2. pp. 957–1010). Charlotte, NC: Information Age.

Skolverket. (2022). Läroplan för grundskolan, förskoleklassen och fritidshemmet: Lgr22. https://www.skolverket.se/getFile?file=9718

Son, J. W., & Diletti, J. (2017). What can we learn from textbook Analysis? What matters? Research trends in international comparative studies in mathematics education, 3-32. doi:10.1007/978-3-319-51187-0_1

Van den Ham, A-K., & Heinze, A. (2018). Does the textbook matter? Longitudinal effects of textbook choice on primary school students’ achievement in mathematics. Studies in Education Evaluation, 59, pp 133-140 https://doi.org/10.1016/j.stueduc.2018.07.005

Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223-248. https://iase-web.org/documents/intstatreview/99.Wild.Pfannkuch.pdf

Zieffler, A., Garfield, J., Alt, S., Dupuis, D. N., Holleque, K., & Chang, B. (2008). What does the research suggest about the teaching and learning of introductory statistics at the college level? A review of the literature. Journal of Statistics Education, 16,(2) doi: 10.1080/10691898.2008.11889566

Downloads

Published

2026-10-26

Issue

Section

Regular Articles