Abstract
In this paper the authors demonstrate how play can serve as a space for assessing and promoting children’s mathematical thinking. Analyzing data from a larger study of professional development to support culturally and developmentally responsive mathematics teaching in preschool, we found that through Learning Stories, a holistic narrative assessment tool, teachers describe how they explicitly identify the mathematical practices children engage with during play. The structure of Learning Stories provided teachers with a way to think about how they identify and reflect on children’s mathematical practices and, based on that understanding, develop strategies for supporting children’s mathematical understanding. The purpose of this paper is not to argue for play as the only space for teaching and assessing mathematics in preschools but to provide evidence of what is possible when teachers attend to children’s mathematical thinking and mathematize play.
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Anthony, G., & Walshaw, M. (2009). Mathematics education in the early years: Building bridges. Contemporary Issues in Early Childhood, 10(2), 107–121.
Barnett, W.S., Carolan, M.E, Squires, J.H., & Clarke-Brown, K. (2014). State of preschool 2013: First look (NCES 2014-078). U.S. Department of Education. Washington, DC: National Center for Education Statistics. http://nces.ed.gov/pubsearch.
Black, P., & Wiliam, D. (2009). Developing the theory of formative assessment. Educational Assessment, Evaluation, and Accountability, 21(1), 5031.
Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2014). Children’s mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann.
Carpenter, T. P., Fennema, E., Peterson, E., Chiang, C. P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499–531.
Carr, M. (2001). Assessment in early childhood settings: Learning Stories. London, UK: Sage.
Carr, M. (2011). Young children reflecting on their learning: teacher’s conversation strategies. Early Years: An International Research Journal, 31(3), 257–270.
Carr, M., & Claxton, G. (2002). Tracking the development of learning dispositions. Assessment in Education, 9(1), 9–37.
Carr, M., & Lee, W. (2012). Learning Stories: Constructing learner identities in early education. London: Sage.
Carter, M. (2010). Using Learning Stories to strengthen teachers’ relationships with children. Exchange, 32(6), 40–44.
Copple, C., & Bredekamp, S. (Eds.). (2009). Developmentally appropriate practice in early childhood programs serving children from birth through age 8 (3rd ed.). Washington, DC: National Association for the Education of Young Children.
Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P., et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428.
Eberly, J. L., & Golbeck, S. L. (2001). Teachers’ perceptions of children’s block play: How accurate are they? Journal of Early Childhood Teacher Education, 22(2), 63–67.
Edwards, C. P., Gandini, L., & Forman, G. (1998). The hundred languages of children: The Reggio Emilia approach to early childhood education. Norwood, NJ: Ablex Publishing.
Erickson, F. (1986). Qualitative methods in research on teaching. In M. S. Whittrock (Ed.), Handbook of research on teaching (3rd ed., pp. 119–161). New York: Macmillan.
Ginsburg, H. P. (2006). Mathematical Play and playful mathematics: A guide for early education. In D. G. Singer, R. M. Golinkoff, & K. Hirsh-Pasek (Eds.), Play = learning: How play motivates and enhances children’s cognitive and social-emotional growth (pp. 145–165). Oxford: Oxford University Press.
Ginsburg, H. P. (2009). The challenge of formative assessment in mathematics education: Children’s minds, teachers’ minds. Human Development, 52(2), 109–128.
Ginsburg, H. P., & Ertle, B. (2008). Knowing the mathematics in early childhood mathematics. In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives on mathematics in early childhood education (pp. 45–66). Charlotte, NC: Information Age Publishing.
Ginsburg, H. P., & Golbeck, S. (2004). Thoughts on the future of research on mathematics and science learning and education. Early Childhood Research Quarterly, 19(1), 190–200.
Ginsburg, H. P., Jang, S., Preston, M., VanEsselstyn, D., & Appel, A. (2004). Learning to think about early childhood mathematics education: A course. In C. Greenes & J. Tsankova (Eds.), Challenging young children mathematically (pp. 41–56). Boston, MA: Houghton Mifflin.
Graham, T. A., Nash, C., & Paul, K. (1997). Young children’s exposure to mathematics: The child care context. Early Childhood Education Journal, 25(1), 31–38.
Graue, M. E. (1993). Integrating theory and practice through instructional assessment. Educational Assessment, 1, 293–309.
Graue, M. E., & Walsh, D. J. (1998). Studying children in context: Theories, methods, and ethics. Thousand Oaks: Sage.
Graue, M. E., Whyte, K., & Delaney, K. K. (2014). Fostering culturally and developmentally responsive teaching through improvisational practice. Journal of Early Childhood Teacher Education, 35(4), 297–317.
Gunderson, E. A., & Levine, S. C. (2011). Some types of parent number talk count more than others: relations between parents’ input and children’s cardinal-number knowledge. Developmental Science, 14(5), 1021–1032.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.
Jordan, N. C., Kaplan, D., Locuniak, M. N., & Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research & Practice, 22(1), 36–46.
MacDonald, M. (2007). Toward formative assessment: The use of pedagogical documentation in early elementary classrooms. Early Childhood Research Quarterly, 22(2), 232–242.
Mix, K. S., Sandhofer, C. M., Moore, J. A., & Russell, C. (2012). Acquisition of the cardinal word principle: the role of input. Early Childhood Research Quarterly, 27(2), 274–283.
National Research Council. (2009). Mathematics learning in early childhood: Paths toward excellence and equity. Washington, D.C.: National Academy Press.
Parks, A. N. (2015). Exploring mathematics through play in the early childhood classroom. New York, NY: Teachers College Press.
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), 1–18.
Perry, B., & Dockett, S. (2004). Mathematics in early childhood education. In B. Perry, G. Anthony, & C. Diezmann (Eds.), Research in mathematics education in Australasia (pp. 103–125). Flaxton: Post Pressed.
Perry, B., Dockett, S., & Harley, E. (2007). Learning Stories and children’s powerful mathematics. Early childhood research and practice, 9(2).
Piaget, J. (1962). Play, dreams and imitation. New York: Norton.
Piaget, J. (1964). Development and learning. Journal of Research in Science Teaching, 2, 176–186.
Ramani, G. B., Rowe, M. L., Eason, S. H., & Leech, K. A. (2015). Math talk during informal learning activities in Head Start families. Cognitive Development, 35, 15–33.
Reisman, M. (2011). Learning stories: Assessment through play. Exchange, 198, 90–93.
Schack, E. O., Fisher, M. H., Thomas, J. N., Eisenhardt, S., Tassell, J., & Yoder, M. (2013). Prospective elementary school teachers’ professional noticing of children’s early numeracy. Journal of Mathematics Teacher Education, 16(5), 379–397.
Seo, K. H., & Ginsburg, H. P. (2004). What is developmentally appropriate in early childhood mathematics education? Lessons from new research. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 91–104). Hillsdale, NJ: Erlbaum.
Shepard, L. A. (2000). The role of assessment in a learning culture. Educational Researcher, 29(7), 4–14.
Tirosh, D., Tsamir, P., Levenson, E., & Tabach, M. (2011). From preschool teachers’ professional development to children’s knowledge: Comparing sets. Journal of Mathematics Teacher Education, 14(2), 113–131.
Torrance, H., & Pryor, J. (1998). Investigating formative assessment: Teaching, learning and assessment in the classroom. Maidenhead: McGraw-Hill Education.
Tsamir, P., Tirosh, D., Levenson, E., Tabach, M., & Barkai, R. (2014). Developing preschool teachers’ knowledge of students’ number conceptions. Journal of Mathematics Teacher Education, 17(1), 61–83.
van Oers, B. (2010). Emergent mathematical thinking in the context of play. Educational Studies in Mathematics, 74(1), 23–37.
Vygotsky, L. S. (1962). Language and thought. Ontario, Canada: Massachusetts Institute of Technology Press
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
Wager, A. A., Graue, M. E., & Harrigan, K. (2015). Swimming upstream in a torrent of assessment. In R. Perry, A. Gervasoni, & A. MacDonald (Eds.), Mathematics and transition to school: International perspectives (pp. 15–30). Dordrecht: Springer.
Wager, A. A., & Parks, A. N. (2014). Learning mathematics through play. In E. Booker, S. Edwards, & M. Blaise (Eds.), SAGE handbook of play and learning in early childhood (pp. 216–227). London: Sage Publications LTD.
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The writing of this paper was supported in part by Grants from the National Science Foundation (1019431; 1461468) and the Wisconsin Center for Education Research. The opinions expressed in this paper do not necessarily reflect the position, policy, or endorsement of the National Science Foundation or the Wisconsin Center for Education Research.
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Wager, A.A., Parks, A.N. Assessing early number learning in play. ZDM Mathematics Education 48, 991–1002 (2016). https://doi.org/10.1007/s11858-016-0806-8
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DOI: https://doi.org/10.1007/s11858-016-0806-8