Skip to main content

Students’ Development of Measures

  • Chapter
  • First Online:
  • 920 Accesses

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

Abstract

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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Abelson, R. P. (1995). Statistics as principled argument. Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • 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 

  • 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.

    Chapter  Google Scholar 

  • Ben-Zvi, D., Bakker, A., & Makar, K. (2015). Learning to reason from samples. Educational Studies in Mathematics, 88(3), 291–303.

    Article  Google Scholar 

  • 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 

  • Büscher, C. (2018). Mathematical literacy on statistical measures: A design research study. Wiesbaden: Springer.

    Book  Google Scholar 

  • Büscher, C., & Schnell, S. (2017). Students’ emergent modelling of statistical measures—A case study. Statistics Education Research Journal, 16(2), 144–162.

    Google Scholar 

  • Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.

    Article  Google Scholar 

  • Corbin, J. M., & Strauss, A. (1990). Grounded theory research: Procedures, canons, and evaluative criteria. Qualitative Sociology, 13(1), 3–21.

    Article  Google Scholar 

  • 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 

  • Fischer, R. (1988). Didactics, mathematics, and communication. For the Learning of Mathematics, 8(2), 20–30.

    Google Scholar 

  • Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, The Netherlands: Reidel.

    Google Scholar 

  • Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • 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 

  • Greeno, J. G. (1998). The situativity of knowing, learning, and research. American Psychologist, 53(1), 5–26.

    Article  Google Scholar 

  • Hußmann, S., & Prediger, S. (2016). Specifying and structuring mathematical topics. Journal für Mathematik-Didaktik, 37(S1), 33–67.

    Article  Google Scholar 

  • Konold, C., Higgins, T., Russell, S. J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325.

    Article  Google Scholar 

  • 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 

  • Konold, C., & Miller, C. D. (2011). Tinkerplots: Dynamic data exploration. Emeryville, CA: Key Curriculum Press.

    Google Scholar 

  • Lehrer, R., & Schauble, L. (2004). Modeling natural variation through distribution. American Educational Research Journal, 41(3), 645–679.

    Article  Google Scholar 

  • Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.

    Google Scholar 

  • Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 152–173.

    Article  Google Scholar 

  • Mayring, P. (2000). Qualitative content analysis. Forum Qualitative Social Sciences, 1(2). Retrieved from http://www.qualitative-research.net/index.php/fqs/issue/view/28

  • Porter, T. M. (1995). Trust in numbers: The pursuit of objectivity in science and public life. Princeton, NJ: Princeton University Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • Stroeve, J. & Shuman, C. (2004). Historical Arctic and Antarctic surface observational data, version 1. Retrieved from http://nsidc.org/data/nsidc-0190.

  • 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 

  • 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 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christian Büscher .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Büscher, C. (2019). Students’ Development of Measures. In: Burrill, G., Ben-Zvi, D. (eds) Topics and Trends in Current Statistics Education Research. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-03472-6_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-03472-6_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03471-9

  • Online ISBN: 978-3-030-03472-6

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics