Sharpening the Focus on Numbers and Counting: Preschool Educators Differentiating Aspects of Mathematical Knowledge for Teaching
Keywords:
mathematical knowledge for teaching, numbers and counting, preschool educators, professional development, variation theoryAbstract
This article reports a study of educators differentiating aspects of mathematical knowledge for teaching in preschool as part of a further-education programme. Eight Swedish preschool educators participated in focus group discussions about documentations from their own practice during a school year, to enhance their awareness of their mathematics education practice. The object of learning for the participants is more specifically how numbers and counting are made content for learning in preschool practice. The educators’ authentic documentations are reflected upon in focus group meetings and further analysed by the researchers to find out what aspects the educators differentiate during the programme. Results show that educators’ learning about content for children’s learning in preschool is a complex process. This process involves several aspects necessary to discern for a professional development to occur, but the collaborative approach seems prosperous in that new aspects are brought to the fore, influencing their reflective practice.
References
Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59(5), 389–407.
Baroody, A., Torbeyns, J., & Verschaffel, L. (2009). Young children’s understanding and application of subtraction-related principles. Mathematical Thinking and Learning, 11, 2–9.
Bertram, C. & Christiansen, I. (2012). Editorial. In: Teacher knowledge and learning – Perspectives and reflections. Special issue. Journal of Education, 56, 1–16.
Björklund, C. & Barendregt, W. (2016). Teachers’ mathematical awareness in Swedish early childhood education. Scandinavian Journal of Educational Research, 60(3), 359–377. doi:10.1080/00313831.2015.1066426
Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., . . . & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446.
Gelman, R., & Gallistel, C. (1978). The child’s understanding of number. Cambridge, Mass.: Harvard University.
Hargreaves, A. (2000). Four ages of professionalism and professional learning. Teachers and Teaching, 6(2), 151-182. doi:10.1080/713698714
Hill, C.H., Blunk, M.L. Charalambos, C.Y., Lewis, J.M., Phelps, G.C., Sleep, L. & Leowenberg Ball, D. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430-511. doi:10.1080/0737000802177235
Kennedy, A. (2005). Models of continuing professional development: A framework for analysis. Journal of In-service Education, 31(2), 235-250.
Klette, K. (2007). Trends in research on teaching and learning in schools: Didactics meets classroom studies. European Educational Research Journal, 6(2), 147-160.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum.
Math and Science Partnership (MSP). (2010). Knowledge reviews: Deepening teachers’ content knowledge. Knowledge management and dissemination. Retrieved from: http://www.mspkmd.net/blasts/tck.php
Marton, F. (2015). Necessary conditions of learning. New York: Routledge.
Marton, F. & Booth, S. (1997). Learning and awareness. Mahwah, NJ.: Lawrence Erlbaum.
McCrink, K., & Wynn, K. (2004). Large-number addition and subtraction by 9-month-old infants. Psychological Science, 15(11), 776–81.
McIntosh, A., Reys, B., & Reys, P. (1992). A proposed framework for examining basic number sense. For the Learning of Mathematics, 12(3), 2-8.
Neuman, D. (1987). The origin of arithmetic skills: A phenomenographic approach. Gothenburg: University of Gothenburg.
Neuman, D. (2013). Att ändra arbetssätt och kultur inom den inledande aritmetikundervisningen. Nordisk Matematikdidaktik, 18(2), 3–46.
National Agency for Education (2011). Curriculum for the Preschool Lpfö98. Revised 2010. Stockholm: Fritzes.
Oppermann, E., Anders, Y., & Hachfeld, A. (2016). The influence of preschool teachers’ content knowledge and mathematical ability beliefs on their sensitivity to mathematics in children’s play. Teaching and Teacher Education, 58, 174–184. doi: 10.1016/j.tate.2016.05.004
Östergren, R. & Träff, U. (2013). Early number knowledge and cognitive ability affect early arithmetic ability. Journal of Experimental Child Psychology, 115(3), 405–421.
Pramling, N., & Pramling Samuelsson, I. (Eds.). (2011). Educational encounters: Nordic studies in early childhood didactics. Dordrecht: Springer.
Pramling Samuelsson, I., & Pramling, N. (2013). Orchestrating and studying children’s and teachers’ learning: Reflections on developmental research approaches. Education Inquiry, 4(3), 519–536. doi:10.3402/edui.v4i3.22624
Sheridan, S., Williams, P., Sandberg, A., & Vuorinen, T. (2011). Preschool teaching in Sweden – a profession in change. Educational Research, 53(4), 415 – 437. doi:10.1080/00131881.2011.625153
Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
Siegler, R. & Braithwaite, D. (2017). Numerical development. Annual Review of Psychology, 68(1), 187-213.
Swedish Schools Inspectorate (2016). Förskolans pedagogiska uppdrag – Om undervisning, lärande och förskollärares ansvar. Report nr. 2015:5671.
The Ministry of Education (2010). Education Act SFS 2010:800. Stockholm: The Ministry of Education.
Timperley, H. (2008). Teacher Professional Learning and Development. Brussels: International Academy of Education.
Venkat, H., & Askew, M. (2012). Mediating early number learning: Specialising across teacher talk and tools? In: Teacher knowledge and learning – Perspectives and reflections. Special issue. Journal of Education, 56, 67–90.
Wynn, K. (1998). Numerical competence in infants. In C. Donlan (Ed.), The development of mathematical skills. (pp. 3–25). Hove: Psychology Press.