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Award ID contains: 1812887

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  1. ; ; (, Proceedings of the 43rd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education)
    Olanoff, D.; Johnson, K.; & Spitzer, S.M. (Ed.)
    This work seeks to understand the emergent nature of mathematical activity mediated by learners’ engagement with multiple artifacts. We explored the problem solving of two learners as they aimed to make sense of fraction division by coordinating meanings across two artifacts, one being a physical manipulative and the other a written expression of the standard algorithm. In addressing the question, “How do learners make sense of and coordinate meanings across multiple representations of mathematical ideas?” we took an enactivist perspective and used tools of semiotics to analyze the ways they navigated the dissonance that arose as they sought to achieve harmony in meanings across multiple representations of ideas. Our findings reveal the value of such tool-mediated engagement as well as the complexity of problem solving more broadly. Implications for learning mathematics with multiple artifacts are discussed. 
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    Accepted Manuscript Full Text Available
  2. ; ; (, Proceedings of the 41st Annual Conference of the North American Chapter of the International Group for the Psychology of Mathematics Education)
    We describe an experience within mathematics teacher preparation that engages pre-service teachers of mathematics (PMTs) in Making and design practices that we hypothesized would inform their conceptual, curricular, and pedagogical thinking. With a focus on the design of new tools that can generate new possibilities for mathematics teaching and learning, this Learning by Design experience has PMTs exploring at the intersection of content, pedagogy, and Making. We describe the forms of knowledge brought to bear on their experiences through a case study analysis of one pair of PMTs’ Making experience. As the advancement of these forms of knowledge is essential to effective mathematics teaching, these findings suggest the promise of a Making experience within mathematics teacher preparation 
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    Accepted Manuscript Full Text Available