Preservice elementary teachers' use of mathematical discussion in the implementation of problem-solving tasks
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Engaging in mathematical communication holds promise for student learning, but focusing teaching practice on mathematical discourse is challenging. Teacher education has been shown to have weak impact on practice, and the conservative nature of K-12 schools serves only to perpetuate, rather than reform, existing practice. This study describes preservice elementary teachers’ initial efforts at facilitating mathematics discussions on problem solving activities. Participants were enrolled in a mathematics teaching methods course that included a field experience working with pairs of elementary pupils. Data were collected during cycles of planning, enactment, and reflection and included activity plans, construction of hypothetical student-teacher conversations (task dialogues), video of problem enactments, and reflections. Analysis utilized Stein and Smith’s (1998) construct of cognitive demand and Hufferd-Ackles, Fuson, and Sherin’s (2004) math-talk framework. Findings indicate repeated enactments, collaboration with peers, and analytic reflections helped participants improve the quality of mathematical discussions with pupils. Participants’ visions of leading mathematics discussions generally aligned with enactment, though all participants struggled in hypothesizing pupils’ potential strategies. A modified version of the math-talk framework alongside the cognitive demand framework were useful in making a fine-grained analysis of interactions between participants and pupils. Important links were found between cognitive demand and particular pedagogical moves: Participants who consistently elevated cognitive demand relied on questioning and exploring the pupil’s thinking, whereas participants who lowered cognitive demand replaced pupils’ thinking with their own. Some moves had varied effects on cognitive demand: eliciting explanations and coordinating collaboration between pupils. Repeated enactments of problems provided evidence that 6 of the 8 participants developed varying degrees of pedagogical content knowledge related to implementing their problems and facilitating mathematical discussions. Findings point to areas of focus for preservice teacher education. More concentrated practice is needed on enacting pedagogical moves that elicit high-quality mathematical explanations and coordinate meaningful collaboration among pupils. Targeted work on developing pupil solution strategies and responding to unanticipated solutions may help preservice teachers enact instruction that is more aligned with pupil thinking. Task dialogues may serve as predictive tools for teacher educators and may be useful in helping preservice teachers think about and respond to pupil solutions.