Which measure of central tendency is most useful? Grade 6 students’ expressed statistical literacy
DOI:
https://doi.org/10.52041/serj.v24i2.811Keywords:
Conceptions, Mean, median, and mode, Measures of central tendency, Primary students, Statistical literacyAbstract
Recently, the importance of statistical literacy has been stressed, and three central concepts in statistical literacy are the measures of central tendency: mean, median, and mode. This study explores aspects of statistical literacy expressed by 12–13-year-old students, focusing on mean, median, and mode. Their responses were analysed using a framework of statistical literacy that includes knowledge and dispositional elements. The results showed that students’ descriptions of the measures were mainly based on mathematical and vocabulary knowledge. When discussing what measure was easiest or hardest to explain, a variety of conceptions were expressed. Some explanations about the usefulness of the measures were related to context knowledge. Here, the median was an exception as students gave neither examples of contexts nor found the median useful outside the classroom.
References
Arnold, P., & Pfannkuch, M. (2022). Engaging novice statisticians in statistical communications. Mathematics Education Research Journal, 36(Suppl 1), 1–27. https://doi.org/10.1007/s13394-022-00442-w
Batanero, C., Valenzuela-Ruiz, S. M., & Gea, M. M. (2020). Significados institucionales y personales de los estadísticos de orden en la Educación Secundaria. [Institutional and personal meaning of order statistics in secondary education] Matemáticas, Educación y Sociedad, 3(2), 21–39. https://journals.uco.es/mes/article/view/12912/11744
Bond, M. E., Perkins, S. N., & Ramirez, C. (2012). Students’ perceptions of statistics: An exploration of attitudes, conceptualizations, and content knowledge of statistics. Statistics Education Research Journal, 11(2), 6–25. https://doi.org/10.52041/serj.v11i2.325
Braun, V., Clarke, V., Boulton, E., Davey, L., & McEvoy, C. (2020). The online survey as a qualitative research tool. International Journal of Social Research Methodology, 24(6), 641–654. https://doi.org/10.1080/13645579.2020.1805550
Büscher, C. (2019). Students’ development of measures. In G. Burrill, & D. Ben-Zvi (Eds.), Topics and trends in current statistics education research (pp. 27–50). Springer. https://doi.org/10.1007/978-3-030-03472-6_2
Callingham, R., & Watson, J. M. (2017). The development of statistical literacy at school. Statistics Education Research Journal, 16(1), 181–201. https://doi.org/10.52041/serj.v16i1.223
Carmichael, C., Callingham, R., Hay, I., & Watson, J. (2010). Statistical literacy in the middle school: The relationship between interest, self-efficacy and prior mathematics achievement. Australian Journal of Educational & Developmental Psychology, 10, 83–93.
Çatman Aksoy, E., & I??ksal Bostan, M. (2021). Seventh graders’ statistical literacy: An investigation on bar and line graphs. International Journal of Science and Mathematics Education, 19(2), 397–418. https://doi.org/10.1007/s10763-020-10052-2
Chick, H. L., & Pierce, R. (2012). Teaching for statistical literacy: Utilising affordances in real-world data. International Journal of Science and Mathematics Education, 10(2), 339–362. https://doi.org/10.1007/s10763-011-9303-2
Clark, J., Kraut, G., Mathews, D., & Wimbish, J. (2007). The fundamental theorem of statistics: Classifying student understanding of basic statistical concepts. [Unpublished manuscript].
Denscombe, M. (2017). The good research guide: For small-scale social research projects (6th ed.). Open University Press.
Diego-Mantecón, J. M., Blanco, T. F., Chamoso, J. M., & Cáceres, M. J. (2019). An attempt to identify the issues underlying the lack of consistent conceptualisations in the field of student mathematics-related beliefs. Plos One, 14(11), Article e0224696. https://doi.org/10.1371/journal.pone.0224696
Fry, K., English, L., & Makar, K. (2024). Cognitive tuning in the STEM classroom: Communication processes supporting children’s changing conceptions about data. Mathematics Education Research Journal, 36(Suppl 1), 67–89. https://doi.org/10.1007/s13394-023-00465-x
Gal, I. (2002). Adults’ statistical literacy: Meaning, components, responsibilities. International Statistical Review, 70(1), 1–52. https://doi.org/10.2307/1403713
Gal, I., Nicholson, J., & Ridgway, J. (2023). A conceptual framework for civic statistics and its educational applications. In J. Ridgway (Ed.), Statistics for empowerment and social engagement: Teaching civic statistics to develop informed citizens (pp. 37– 66). Springer. https://doi.org/10.1007/978-3-031-20748-8_3
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
Goldin, G. A. (2002). Affect, meta-affect, and mathematical belief structures. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education (pp. 59–72). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47958-3_4
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. https://doi.org/10.1207/s15327833mtl0801_3
Groth, R. E., & Bergner, J. A. (2013). Mapping the structure of knowledge for teaching nominal categorical data analysis. Educational Studies in Mathematics, 83(2), 247–265. https://doi.org/10.1007/s10649-012-9452-4
Groth, R., & Meletiou-Mavrotheris, M. (2018). Research on statistics teachers’ cognitive and affective characteristics. In D. Ben-Zvi, K. Makar, & J. Garfield (Eds.), International Handbook of Research in Statistics Education (pp. 327–355). Springer. https://doi.org/10.1007/978-3-319-66195-7_10
Jacobbe, T. (2012). Elementary school teachers’ understanding of the mean and median. International Journal of Science and Mathematics Education, 10(5), 1143–1161. https://doi.org/10.1007/s10763-011-9321-0
Konold, C., Higgins, T., Russell, S. J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325. https://doi.org/10.1007/s10649-013-9529-8
Landtblom, K. K. (2018). Prospective teachers’ conceptions of the concepts mean, median and mode. In H. Palmér & J. Skott (Eds.), Students’ and teachers’ values, attitudes, feelings and beliefs in mathematics classrooms (pp. 43–52). Springer. https://doi.org/10.1007/978-3-319-70244-5_5
Landtblom, K. (2023). Opportunities to learn mean, median, and mode afforded by textbook tasks. Statistics Education Research Journal, 22(3), Article 6. https://doi.org/10.52041/serj.v22i3.655
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., & O’Loughlin, N. (2006). Preservice teachers’ understanding of the mean: Moving beyond the arithmetic average. Journal of Mathematics Teacher Education, 9(1), 53–90. https://doi.org/10.1007/s10857-006-9003-y
Leavy, A., & Hourigan, M. (2016). Crime scenes and mystery players! Using driving questions to support the development of statistical literacy. Teaching Statistics, 38(1), 29–35. https://doi.org/10.1111/test.12088
Lesser, L. M., Wagler, A. E., & Abormegah, P. (2014). Finding a happy median: Another balance representation for measures of center. Journal of Statistics Education, 22(3), 1–27. https://doi.org/10.1080/10691898.2014.11889714
Madrid-García, A. E., Valenzuela-Ruiz, S. M., & Batanero, C. (2023). Is the calculation of the median for university students simple? In L. Gómez Chova, C. González Martínez, & J. Lees (Eds.), INTED2023 Proceedings: 17th International technology, education and development conference (pp. 1253–1257). IATED Academy. https://doi.org/10.21125/inted.2023.0362
Mason, J. (2018). Qualitative researching (3rd ed.). Sage.
Makar, K., & Confrey, J. (2005). “Variation-talk”: Articulating meaning in statistics. Statistics Education Research Journal, 4(1), 27–54. https://doi.org/10.52041/serj.v4i1.524
Mathews, D., & Clark, J. (2003). Successful students’ conceptions of mean, standard deviation, and the central limit theorem. [Unpublished manuscript].
Mayén, S., Díaz, C., & Batanero, C. (2009). Students’ semiotic conflicts in the concept of median. Statistics Education Research Journal, 8(2), 74–93. https://doi.org/10.52041/serj.v8i2.396
Mokros, J., & Russell, S. J. (1995). Children’s concepts of average and representativeness. Journal for Research in Mathematics Education, 26(1), 20–39. https://doi.org/10.2307/749226
Nowell, L. S., Norris, J. M., White, D. E., & Moules, N. J. (2017). Thematic analysis: Striving to meet the trustworthiness criteria. International Journal of Qualitative Methods, 16(1). https://doi.org/10.1177/1609406917733847
Philipp, R. A. (2007). Mathematics teacher’s beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–315). Information Age Publishing.
Ramirez, C., Schau, C., & Emmioglu, E. (2012). The importance of attitudes in statistics education. Statistics Education Research Journal, 11(2), 57–71. https://doi.org/10.52041/serj.v11i2.329
Schnell, S., & Frischemeier, D. (2019). Primary school students’ reasoning about and with the median when comparing distributions. In U.T. Jankvist, M. van den Heuvel-Panhuizen, & M. Veldhuis (Eds.), Proceedings of the Eleventh Congress of the European Society for Research in Mathematics Education (pp. 1075–2082). Freudenthal Group & Freudenthal Institute, Utrecht University, and ERME.
Sharma, S. (2017). Definitions and models of statistical literacy: A literature review, Open Review of Educational Research 4(1), 118–133. http://doi.org/10.1080/23265507.2017.1354313
Sproesser, U., Engel, J., & Kuntze, S. (2016). Fostering self-concept and interest for statistics through specific learning environments. Statistics Education Research Journal, 15(1), 28–54. https://doi.org/10.52041/serj.v15i1.256
Strauss, S., & Bichler, E. (1988). The development of children’s concepts of the arithmetic average. Journal for Research in Mathematics Education, 19(1), 64–80. https://doi.org/10.2307/749111
Sumpter, L., Eriksson, H., Hedefalk, M., & Markkanen, P. (2024). Ethical reasoning as part of mathematical modelling: young children’s work with sharing and division. In P. Ernest (Ed.). Ethics and Mathematics Education: the Good, the Bad and the Ugly. (pp. 443–462). Springer. https://doi.org/10.1007/978-3-031-58683-5_21
Swedish Research Council (2017). Good research practice. https://www.vr.se/english/analysis/reports/our-reports/2017-08-31-good-research-practice.html
Usiskin, Z. (2012). What does it mean to understand some mathematics? In S. J. Cho (Ed.), Selected regular lectures from the 12th International Congress on Mathematical Education (pp. 821–841). Springer. https://doi.org/10.1007/978-3-319-17187-6_46
Watson, J. M. (2006). Statistical literacy at school: Growth and goals. Routledge.
Watson, J. M. (2007). The role of cognitive conflict in developing students’ understanding of average. Educational Studies in Mathematics, 65(1), 21–47. http://doi.org/10.1007/s10649-006-9043-3
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
Weiland, T. (2017). Problematizing statistical literacy: An intersection of critical and statistical literacies. Educational Studies in Mathematics, 96(1), 33–47. https://doi.org/10.1007/s10649-017-9764-5
Weiland, T. (2019). Critical mathematics education and statistics education: Possibilities for transforming the school mathematics curriculum. In G. Burrill & D. Ben-Zvi (Eds.), Topics and Trends in Current Statistics Education Research (pp. 391–411). Springer. https://doi.org/10.1007/978-3-030-03472-6_18
