Abstract
In this chapter, we highlight the importance not only of an understanding of place value, but the importance of a flexible understanding. We describe the principles of our decimal place value system and the development processes of children. Embedded in artefact-centric activity theory, we present an education-oriented design of a virtual place value chart and its potential to support this development and understanding. We also present results of a qualitative study with second graders as well as results of a quantitative study with third graders that can guide further research in that area.
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Notes
- 1.
In the German version, Z stands for “Zehner” (instead of T for tens) and E for “Einer” (instead of O for ones). This reduces the risk of confusing “O” (the letter capital o) with a “0” (the digit zero).
- 2.
The digital tool is available at http://kortenkamps.net/index.php/Place_Value_Chart.
References
Askew, M. (2012). Transforming primary mathematics. Abingdon: Routledge.
Bartolini Bussi, Maria G. (2011). Artefacts and utilization schemes in mathematics teacher education: place value in early childhood education. J Math Teacher Educ (2011), 14:93–112, DOI 10.1007/s10857-011-9171-2.
Gras, R., Suzuki, F., Guillet, F., & Spagnolo, F. (2008). Statistical implicative analysis. New York: Springer.
Kortenkamp, U., & Ladel, S. (2014). Flexible use and understanding of place value via traditional and digital tools. Research report. In P. Liljedahl, C. Nicol, S. Oesterle, & D. Allan (Eds.), Proceedings of PME 38 (Vol. 4, pp. 33–40). Vancouver, Canada: PME.
Ladel, S., & Kortenkamp, U. (2011). Finger-symbol-sets and multi-touch for a better understanding of numbers and operations. In Proceedings of CERME 7. Rzeszów.
Ladel, S., & Kortenkamp, U. (2013). Designing a technology based learning environment for place value using artifact-centric Activity Theory. In A. M. Lindmaier & A. Heinze (Eds.), Proceedings of PME 37 (Vol. 1, pp. 188–192). Kiel, Germany: PME.
Ladel, S., & Kortenkamp, U. (2014). Handlungsorientiert zu einem flexiblen Verständnis von Stellenwerten—ein Ansatz aus Sicht der Artifact-Centric Activity Theory. In: S. Ladel & Chr. Schreiber (Hrsg.), Von Audiopodcast bis Zahlensinn. Band 2 der Reihe Lernen, Lehren und Forschen mit digitalen Medien in der Primarstufe. Münster: WTM.
Resnick, L. B., Bill, V., Lesgold, S., & Leer, M. (1991). Thinking in arithmetic class. In B. Means, C. Chelemer, & M. S. Knapp (Eds.), Teaching advanced skills to at-risk students: Views from research and practice (pp. 27–53). San Francisco: Jossey-Bass.
Ross, S. H. (1989). Parts. Wholes, and place value: A developmental view. The Arithmetic Teacher, 36(6), 47–51.
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Ladel, S., Kortenkamp, U. (2016). Development of a Flexible Understanding of Place Value. In: Meaney, T., Helenius, O., Johansson, M., Lange, T., Wernberg, A. (eds) Mathematics Education in the Early Years. Springer, Cham. https://doi.org/10.1007/978-3-319-23935-4_16
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DOI: https://doi.org/10.1007/978-3-319-23935-4_16
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