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A recent article in the New York Times (Spencer, 2011) described a series of well-attended workshops on how to encourage children to play effectively with wooden blocks. At first glance, the idea of teaching children to play seems somewhat absurd. And yet, if we think about learning via play rather than learning to play, it is reasonable to ask how adults can encourage mathematical and verbal complexity in children’s games and activities. By looking closely at what parents and teachers say to children during play sessions, we can perhaps better understand the kind of language that supports intellectual development in the context of child-directed play. In this brief paper, I attempt to show how one teacher uses language to bring together learning and play in a math tutoring session. Specifically, I discuss an instance where the teacher finds a moment in a student’s self-directed game where it would be appropriate to introduce beginning math concepts. In order to better understand and depict the tutor’s talk, I use Conversation Analysis (CA) to study how the interaction unfolds on a moment-by-moment basis. CA’s emphasis on how each turn unfolds — and relates to preceding and following turns — allows me to look closely at the pedagogical implications of seemingly minor choices on the part of the tutor. The data in this paper are from a math tutoring session that took place in a private home. The student in the session (Chloe) is 3 years, 4 months old. The tutor (Pauline) has been teaching for over 40 years; her areas of expertise include one-on-one teaching, and the development of number sense in young children. Throughout the session, the tutor made use of objects such as poker chips, game boards, large plastic dice, and plastic pegs that can fit together. The session was filmed with two video cameras; one on a tripod, and one handheld flip camera. I viewed the video data multiple times, and then transcribed and analyzed key extracts, including the interaction described below. As the extract begins, Chloe and Pauline are playing with multicolored, stackable plastic pegs (see Image 1, below).

You Can Make a Tower : Using Conversation Analysis to Understand a Math Tutoring Session