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.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Abelson, R. P. (1995). Statistics as principled argument. Hillsdale, NJ: Erlbaum.
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.
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.
Ben-Zvi, D., Bakker, A., & Makar, K. (2015). Learning to reason from samples. Educational Studies in Mathematics, 88(3), 291–303.
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.
Büscher, C. (2018). Mathematical literacy on statistical measures: A design research study. Wiesbaden: Springer.
Büscher, C., & Schnell, S. (2017). Students’ emergent modelling of statistical measures—A case study. Statistics Education Research Journal, 16(2), 144–162.
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9–13.
Corbin, J. M., & Strauss, A. (1990). Grounded theory research: Procedures, canons, and evaluative criteria. Qualitative Sociology, 13(1), 3–21.
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.
Fischer, R. (1988). Didactics, mathematics, and communication. For the Learning of Mathematics, 8(2), 20–30.
Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht, The Netherlands: Reidel.
Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht, The Netherlands: Kluwer Academic Publishers.
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.
Greeno, J. G. (1998). The situativity of knowing, learning, and research. American Psychologist, 53(1), 5–26.
Hußmann, S., & Prediger, S. (2016). Specifying and structuring mathematical topics. Journal für Mathematik-Didaktik, 37(S1), 33–67.
Konold, C., Higgins, T., Russell, S. J., & Khalil, K. (2015). Data seen through different lenses. Educational Studies in Mathematics, 88(3), 305–325.
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.
Konold, C., & Miller, C. D. (2011). Tinkerplots: Dynamic data exploration. Emeryville, CA: Key Curriculum Press.
Lehrer, R., & Schauble, L. (2004). Modeling natural variation through distribution. American Educational Research Journal, 41(3), 645–679.
Makar, K., & Rubin, A. (2009). A framework for thinking about informal statistical inference. Statistics Education Research Journal, 8(1), 82–105.
Makar, K., Bakker, A., & Ben-Zvi, D. (2011). The reasoning behind informal statistical inference. Mathematical Thinking and Learning, 13(1–2), 152–173.
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.
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.
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.
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.
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).
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.
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
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)