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By V. F. Demianov, Aleksandr Moiseevich Rubinov

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Using representations Discuss and use a range of representations to support explanations. Describe inscriptions used, to explain and justify conceptually as actions on quantities, not manipulation of symbols. Using mathematical language and definitions Use mathematical words to describe actions. Use correct mathematical terms. Ask questions to clarify terms and actions. Communities of Mathematical Inquiry 39 examples to illustrate. Participatory actions Active listening and questioning for more information.

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Fostering productive mathematical discussions in the classroom. Manuscript submitted for publication. , & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge, UK: Cambridge University Press. , & Lehrer, R. (2003). Models and modeling perspectives on the development of students and teachers. Mathematical Thinking and Learning, 5(2 & 3), 109-129. , & Zawojewski, J. (2007). Problem solving and modeling. In F. K. ), Second handbook of research on mathematics teaching and learning (pp.

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