Abstract
In this paper, teacher educators’ stories about young children engaging in mathematical activities are discussed. There has been little previous research about teacher educators, without experiences as kindergarten teachers, reflecting on their own understandings about how to engage children in mathematical situations. The teacher educators’ stories were categorised in regard to the mathematics and the pedagogical practices that were evident. Bishop’s six mathematical activities, which are Explaining, Playing, Designing, Locating, Measuring and Counting, were used to identify the mathematics that children engaged in. The stories were also analysed in regard to pedagogical practices, related to construction and instruction. Travel guide, travel agent and travel companion were used as metaphors to clarify the pedagogical roles that the teacher educators adopted when they interacted with children. Understanding our own practices with young children has implications for how to support kindergarten student teachers to connect their theoretical understandings about mathematics education in kindergarten with practical experiences from working with children.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We thank Götz Krummheuer for this point.
- 2.
In order to focus on the pedagogical mathematical knowledge and not on the participants, we have chosen to describe all adults as females and children as males and to give each an identification number. A1 stands for Adult 1 and C3 stands for Child 3.
- 3.
When used as an analytical category, we capitalise the names of the roles.
- 4.
After citing a list of characterisations of play , Bishop (1988a, p. 43) remarked:
Clearly playing is a form of social activity which is different in character from any other kind of social intercourse which has been mentioned so far – playing takes place in the context of a game, and people become players. The real/not real boundary is well established and players can only play with other players if everyone agrees not to behave ‘normally’.
Could these characteristics be at the root of hypothetical thinking? Could playing represent the first stage of distancing oneself from reality in order to reflect on and perhaps to imagine modifying that reality? Certainly, Vygotsky (1978) argued that ‘the influence of play on a child’s development is enormous’ (p. 96) in that action and meaning can become separated and abstract thinking can thereby begin.
References
Aarsand, P. (2012). Family members as co-researchers: Reflections on practice-reported data. Nordic Journal of Digital Literacy, 7(3), 186–203.
Ainley, J. (1999). Who are you today? Complementary and conflicting roles in school-based research. For the Learning of Mathematics, 19(1), 39–47.
Anders, Y., & Rossbach, H.-G. (2015). Preschool teachers’ sensitivity to mathematics in children’s play: The influence of math-related school experiences, emotional attitudes, and pedagogical beliefs. Journal of Research in Childhood Education, 29(3), 305–322. https://doi.org/10.1080/02568543.2015.1040564.
Anthony, G., McLachlan, C., & Poh, R. L. H. (2015). Narrative assessment: Making mathematics learning visible in early childhood settings. Mathematics Education Research Journal, 27(3), 385–400. https://doi.org/10.1007/s13394-015-0142-2.
Bennett, J. (2005). Curriculum issues in national policy-making. European Early Childhood Education Research Journal, 13(2), 5–23. https://doi.org/10.1080/13502930585209641.
Benz, C. (2014). Learning to see: Representing, perceiving, and judging quantities of numbers as a task for in-service education for pre-school teachers. Journal of Mathematics Education, 7(2), 1–15.
Bishop, A. J. (1988a). Mathematical enculturation: A cultural perspective on mathematics education. Dordrecht, The Netherlands: Kluwer.
Bishop, A. J. (1988b). Mathematics education in its cultural context. Educational Studies in Mathematics, 19, 179–191. Available from: http://www.jstor.org/stable/3482573.
Bishop, A. J. (2002). Mathematical acculturation, cultural conflict, and transition. In G. de Abreu, A. J. Bishop, & N. C. Presmeg (Eds.), Transitions between contexts of mathematical practices (pp. 193–212). Dordrecht, The Netherlands: Springer.
Björklund, C., & Barendregt, W. (2016). Teachers’ pedagogical mathematical awareness in Swedish early childhood education. Scandinavian Journal of Educational Research, 60(3), 359–377. https://doi.org/10.1080/00313831.2015.1066426.
Brouwer, N., & Korthagen, F. (2005). Can teacher education make a difference? American Educational Research Journal, 42(1), 153–224.
Clarke, B., & Robbins, J. (2004). Numeracy enacted: Preschool families’ conceptions of their children’s engagements with numeracy. In I. Putt, R. Faragher, & M. McLean (Eds.), Mathematics education for the third millenium, towards 2010. Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australia (pp. 175–182). Sydney, Australia: MERGA.
Dinkelman, T., Margolis, J., & Sikkenga, K. (2006). From teacher to teacher educator: Experiences, expectations, and expatriation. Studying Teacher Education: A Journal of Self-study of Teacher Education Practices, 2(1), 5–23. https://doi.org/10.1080/17425960600557447.
Dunekacke, S., Jenßen, L., Eilerts, K., & Blömeke, S. (2016). Epistemological beliefs of prospective preschool teachers and their relation to knowledge, perception, and planning abilities in the field of mathematics: A process model. ZDM, 48(1), 125–137. https://doi.org/10.1007/s11858-015-0711-6.
Erfjord, I., Hundeland, P. S., & Carlsen, M. (2012). Kindergarten teachers’ accounts of their developing mathematical practice. ZDM, 44(5), 653–664. https://doi.org/10.1007/s11858-012-0422-1.
Fosse, T., & Lossius, M. H. (2015, April 10). Barnehagelæreres arbeid med matematikk (Kindergarten teachers’ work with mathematics). Paper presented at FoU i praksis, Dronning Mauds Minne Høgskole for barnehagelærerutdanning, 2015.
Franzén, K. (2015). Being a tour guide or travel companion on the children’s knowledge journey. Early Child Development and Care, 185(11–12), 1928–1943. https://doi.org/10.1080/03004430.2015.1028401.
Ginsburg, H. P., & Amit, M. (2008). What is teaching mathematics to young children? A theoretical perspective and case study. Journal of Applied Developmental Psychology, 29(4), 274–285. https://doi.org/10.1016/j.appdev.2008.04.008.
Helenius, O., Johansson, M., Lange, T., Meaney, T., Riesbeck, E., & Wernberg, A. (2016). When is preschool children’s play mathematical? In T. Meaney, O. Helenius, M. Johansson, T. Lange, & A. Wernberg (Eds.), Mathematics education in the early years: Results from the POEM2 conference, 2014 (pp. 139–156). New York: Springer International Publishing. https://doi.org/10.1007/978-3-319-23935-4.
Helenius, O., Johansson, M. L., Lange, T., Meaney, T., Riesbeck, E., & Wernberg, A. (2015, February 4–5). Preschool teachers’ awareness of mathematics. In O. Helenius, A. Engström, T. Meaney, P. Nilsson, E. Norén, J. Sayers, & M. Österholm (Eds)., Development of mathematics teaching: Design, scale, effects. Proceedings from Madif9: The Ninth Swedish Mathematics Education Research Seminar, Umeå, 2014 (pp. 67–76). Linköping, Sweden: SMDF. Available from: http://ncm.gu.se/media/smdf/Published/No10_Madif9/067076-Helenius_etal_B.pdf.
James, A., & Prout, A. (Eds.). (2001). Constructing and reconstructing childhood: Contemporary issues in the sociological study of childhood (2nd ed.). London: Falmer.
Johansson, M. L., Lange, T., Meaney, T., Riesbeck, E., & Wernberg, A. (2012, July 8–15). What maths do children engage with in Swedish preschools? Paper presented at TSG 1 Mathematics education at preschool level at the 12th International Congress on Mathematics Education (ICME 12), Seoul, Korea, 2012. Available from http://www.diva-portal.org/smash/get/diva2:1006107/FULLTEXT01.pdf.
Kunnskapsdepartementet. (2011). Framework plan for the content and tasks of kindergarten. Oslo, Norway: Author. [The Norwegian Ministry of Education and Research].
Lee, J. (2010). Exploring kindergarten teachers’ pedagogical content knowledge of mathematics. International Journal of Early Childhood, 42(1), 27–41. https://doi.org/10.1007/s13158-010-0003-9.
Lunenberg, M., Korthagen, F., & Swennen, A. (2007). The teacher educator as a role model. Teaching and Teacher Education, 23(5), 586–601. https://doi.org/10.1016/j.tate.2006.11.001.
Lunenberg, M., & Willemse, M. (2006). Research and professional development of teacher educators. European Journal of Teacher Education, 29(1), 81–98. https://doi.org/10.1080/02619760500478621.
McCray, J. S., & Chen, J.-Q. (2012). Pedagogical content knowledge for preschool mathematics: Construct validity of a new teacher interview. Journal of Research in Childhood Education, 26(3), 291–307. https://doi.org/10.1080/02568543.2012.685123.
Meier, D. R., & Stremmel, A. J. (2010). Reflection through narrative: The power of narrative inquiry in early childhood teacher education. Journal of Early Childhood Teacher Education, 31(3), 249–257. https://doi.org/10.1080/10901027.2010.500538.
Mosvold, R., Bjuland, R., Fauskanger, J., & Jakobsen, A. (2011, February 9–13). Similar but different – investigating the use of MKT in a Norwegian kindergarten setting. In M. Pytlak, T. Rowland & E. Swoboda (Eds.), Proceedings from Seventh Congress of the European Society for Research in Mathematics Education, 2011 Rzeszów, Poland (pp. 1802–1811). Rzeszów, Poland: European Society for Research in Mathematics. Available from: http://www.mathematik.uni-dortmund.de/~erme/index.php?slab=proceedings.
Nicol, C. (1997). Learning to teach prospective teachers to teach mathematics (Doctoral dissertation, University of British Columbia).
Nolan, K. (2012). Dispositions in the field: Viewing mathematics teacher education through the lens of Bourdieu’s social field theory. Educational Studies in Mathematics, 80(1), 201–215. https://doi.org/10.1007/s10649-011-9355-9.
Parks, A. N., & Wager, A. A. (2015). What knowledge is shaping teacher preparation in early childhood mathematics? Journal of Early Childhood Teacher Education, 36(2), 124–141. https://doi.org/10.1080/10901027.2015.1030520.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Swennen, A., Jones, K., & Volman, M. (2010). Teacher educators: Their identities, sub-identities and implications for professional development. Professional development in education, 36(1–2), 131–148. https://doi.org/10.1080/19415250903457893.
Vygotsky, L. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
Wager, A., & Whyte, K. (2013). Young children’s mathematics: Whose home practices are privileged. Journal of Urban Mathematics Education, 6(1), 81–95. Available from: http://education.gsu.edu/JUME.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Hauge, I., Kacerja, S., Lange, T., Lie, J., Meaney, T., Severina, E. (2018). Young Children’s Engagement with Mathematics: Expanding Teacher Educators’ Views. In: Benz, C., Steinweg, A., Gasteiger, H., Schöner, P., Vollmuth, H., Zöllner, J. (eds) Mathematics Education in the Early Years. Springer, Cham. https://doi.org/10.1007/978-3-319-78220-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-78220-1_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78219-5
Online ISBN: 978-3-319-78220-1
eBook Packages: EducationEducation (R0)