Our early math team continues to explore what might be possible for young children in the context of number development and play. We recently designed a linear board game called “Frog Splash” to help preschoolers begin to count the hops of a frog as it nears a swimming hole. After trying this game with children, we’ve already begun to make modifications based on how the children view the game, how they interact with it, and what goals they seem to create as they play.
In his report “Mathematics Education for Young Children: What It is and How to Promote It”, Herbert Ginsburg states: “Yet observation, like any other assessment method, is only as good as the theory on which it is based. If they are to learn anything about children’s mathematical knowledge, teachers need to know what to look for as they observe, for example, children’s block play. We need research on how well teachers observe and interpret children’s behavior, and we need to develop methods to help teachers improve these skills. Yet observation is not enough. As Piaget (1976) pointed out many years ago, ‘… how many inexpressible thoughts must remain unknown so long as we restrict ourselves to observing the child without talking to him?’”
With these recommendations in mind, our practice continues to include talking to children. In some cases, however, we do best by listening. In play situations, deciding how to interact with children during a game is not always an easy decision and requires a particular pedagogical content knowledge. As Millie Almy suggests in her work on Piaget in the classroom, a teacher should have “such knowledge in her head, as part of the frame of reference from which her teaching evolves, so that she can see the child as a being who is at once cognitive, affective, and social. She should be able to respond to him, to ask a question or refrain from asking it, to suggest a new approach or to encourage the one he is using, or to say nothing, in the light of her understanding of both his general cognitive level and where he is that day.”
What we think is possible in a game such as “Frog Splash” does not always align with what children see is possible. We are continuing to learn that attending to children’s thinking requires a flexible stance and an anticipation of views of the world that are different than our own.
For further reading:
Almy, M. (1979). The impact of Piaget on early childhood education. In F. B. Murray (Ed.), The impact of Piagetian theory: On education, philosophy, psychiatry, and psychology (pp. 159–189). Baltimore, MD: University Park Press.
Ginsburg, H. P., Lee, J. S., & Stevenson Boyd, J. (2008). Mathematics Education for Young Children: What It is and How to Promote It. Social Policy Report, 2(1), 3–22.