Students’ Development of Measures

Part of the ICME-13 Monographs book series (ICME13Mo)


Knowledge is situated, and so are learning processes. Although contextual knowledge has always played an important role in statistics education research, there exists a need for a theoretical framework for describing students’ development of statistical concepts. A conceptualization of measure is introduced that links concept development to the development of measures, which consists of the three mathematizing activities of structuring phenomena, formalizing communication, and creating evidence. In a qualitative study in the framework of topic-specific design research, learners’ development of measures is reconstructed on a micro level. The analysis reveals impact of the context of a teaching-learning arrangement for students’ situated concept development.


Concept development Design research Situativity of knowledge Statistical measures Statistical reasoning 


  1. Abelson, R. P. (1995). Statistics as principled argument. Hillsdale, NJ: Erlbaum.Google Scholar
  2. Bakker, A., Biehler, R., & Konold, C. (2004). Should young students learn about boxplots? In G. Burrill & M. Camden (Eds.), Curricular development in statistics education (pp. 163–173). Voorburg, The Netherlands: International Statistical Institute.Google Scholar
  3. Bakker, A., & Gravemeijer, K. P. E. (2004). Learning to reason about distribution. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 147–168). Dordrecht: Springer Netherlands.CrossRefGoogle Scholar
  4. Ben-Zvi, D., Bakker, A., & Makar, K. (2015). Learning to reason from samples. Educational Studies in Mathematics, 88(3), 291–303.CrossRefGoogle Scholar
  5. Büscher, C. (2017, February). Common patterns of thought and statistics: Accessing variability through the typical. Paper presented at the Tenth Congress of the European Society for Research in Mathematics Education, Dublin, Ireland.Google Scholar
  6. Büscher, C. (2018). Mathematical literacy on statistical measures: A design research study. Wiesbaden: Springer.CrossRefGoogle Scholar
  7. Büscher, C., & Schnell, S. (2017). Students’ emergent modelling of statistical measures—A case study. Statistics Education Research Journal, 16(2), 144–162.Google Scholar
  8. Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.CrossRefGoogle Scholar
  9. Corbin, J. M., & Strauss, A. (1990). Grounded theory research: Procedures, canons, and evaluative criteria. Qualitative Sociology, 13(1), 3–21.CrossRefGoogle Scholar
  10. Fetterer, F., Knowles, K., Meier, W., & Savoie, M. (2002, updated daily). Sea ice index, version 1: Arctic Sea ice extent. NSIDC: National Snow and Ice Data Center.Google Scholar
  11. Fischer, R. (1988). Didactics, mathematics, and communication. For the Learning of Mathematics, 8(2), 20–30.Google Scholar
  12. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, The Netherlands: Reidel.Google Scholar
  13. Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht, The Netherlands: Kluwer Academic Publishers.Google Scholar
  14. Gravemeijer, K. (2007). Emergent modeling and iterative processes of design and improvement in mathematics education. In Plenary lecture at the APEC-TSUKUBA International Conference III, Innovation of Classroom Teaching and Learning through Lesson Study—Focusing on Mathematical Communication . Tokyo and Kanazawa, Japan.Google Scholar
  15. Greeno, J. G. (1998). The situativity of knowing, learning, and research. American Psychologist, 53(1), 5–26.CrossRefGoogle Scholar
  16. Hußmann, S., & Prediger, S. (2016). Specifying and structuring mathematical topics. Journal für Mathematik-Didaktik, 37(S1), 33–67.CrossRefGoogle Scholar
  17. Konold, C., Higgins, T., Russell, S. J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325.CrossRefGoogle Scholar
  18. Konold, C., Robinson, A., Khalil, K., Pollatsek, A., Well, A., Wing, R., et al. (2002, July). Students’ use of modal clumps to summarize data. Paper presented at the Sixth International Conference on Teaching Statistics, Cape Town, South Africa.Google Scholar
  19. Konold, C., & Miller, C. D. (2011). Tinkerplots: Dynamic data exploration. Emeryville, CA: Key Curriculum Press.Google Scholar
  20. Lehrer, R., & Schauble, L. (2004). Modeling natural variation through distribution. American Educational Research Journal, 41(3), 645–679.CrossRefGoogle Scholar
  21. Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.Google Scholar
  22. Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 152–173.CrossRefGoogle Scholar
  23. Mayring, P. (2000). Qualitative content analysis. Forum Qualitative Social Sciences, 1(2). Retrieved from
  24. Porter, T. M. (1995). Trust in numbers: The pursuit of objectivity in science and public life. Princeton, NJ: Princeton University Press.Google Scholar
  25. Prediger, S., Gravemeijer, K., & Confrey, J. (2015). Design research with a focus on learning processes: An overview on achievements and challenges. ZDM Mathematics Education, 47(6), 877–891.CrossRefGoogle Scholar
  26. Prediger, S., Link, M., Hinz, R., Hußmann, S., Thiele, J., & Ralle, B. (2012). Lehr-Lernprozesse initiieren und erforschen—fachdidaktische Entwicklungsforschung im Dortmunder Modell [Initiating and investigating teaching-learning processes—topic-specific didactical design research in the Dortmund model]. Mathematischer und Naturwissenschaftlicher Unterricht, 65(8), 452–457.Google Scholar
  27. Prediger, S., & Zwetzschler, L. (2013). Topic-specific design research with a focus on learning processes: The case of understanding algebraic equivalence in grade 8. In T. Plomp & N. Nieveen (Eds.), Educational design research—Part A: An introduction (pp. 409–423). Enschede, The Netherlands: SLO.Google Scholar
  28. Schnell, S., & Büscher, C. (2015). Individual concepts of students Comparing distribution. In K. Krainer & N. Vondrová (Eds.), Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education (pp. 754–760).Google Scholar
  29. Stroeve, J. & Shuman, C. (2004). Historical Arctic and Antarctic surface observational data, version 1. Retrieved from
  30. Vergnaud, G. (1990). Epistemology and psychology of mathematics education. In P. Nesher (Ed.), ICMI study series. Mathematics and cognition: A research synthesis by the International Group for the Psychology of Mathematics Education (pp. 14–30). Cambridge: Cambridge University Press.Google Scholar
  31. Vergnaud, G. (1996). The theory of conceptual fields. In L. P. Steffe (Ed.), Theories of mathematical learning (pp. 219–239). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.TU Dortmund UniversityDortmundGermany

Personalised recommendations