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Browsing Education Faculty by Author "Armstrong, Alayne"

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    A spectrum of possibilities: levels of improvisational behaviour in middle school mathematics.
    (Taylor & Francis, 2021) Armstrong, Alayne
    In this article, we consider the phenomenon of improvisation by small groups of middle years students while engaged in rich mathematical tasks in classroom settings. Working from the premise that improvisation comprises a spectrum of behaviour, we propose that there is a range of improvisational behaviours that may be observed as the students work together. We discuss four levels along the spectrum – interpretation, embellishment, variation, pure improvisation – and draw on vignettes from our research to illustrate each of their characteristics. We argue that improvisation is a valuable way to view students’ mathematical performance as it highlights how students draw on their own experiences and understandings when problem solving, and how students need to be given opportunities to “stay with” mathematical tasks.
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    Beginner’s mind and the middle years mathematics student
    (Taylor & Francis, 2019) Armstrong, Alayne
    Being motivated and on task are not enough in themselves for students to engage in meaningful mathematical learning. The Zen concept of beginner’s mind describes how one’s level of awareness can open one’s mind to growth and possibilities. In this case study, two small groups of middle years students who engage in the same mathematical task, one group demonstrating the characteristics of beginner’s mind and the other demonstrating expert’s mind. While the group with expert’s mind focuses on learning how to follow the steps of one proposed solution, the group with beginner’s mind explores the task more fully, noticing mathematically salient details about the task that the other group overlooks completely and that help lead to a successful solution. My findings suggest that groups of students who demonstrate beginner’s mind are more likely to be absorbed in mathematical tasks, and open to sharing ideas and engaging in meaningful mathematical discussion
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