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Scholarly Works (2 results)

  • Thesis
  • Peer Reviewed
UC Berkeley Electronic Theses and Dissertations (2023)

Welcoming more students to meaningfully participate in knowledge-building practices in mathematics requires that educators make those practices both visible and accessible to them. This goes beyond inviting students to explore problems and build arguments, to include creating the conditions for young learners to experience mathematics as a collaborative and flexible discipline. Collaborative, because collaboration and engagement with one another’s work helps highlight the function and contribution of community and peers to the development and negotiation of practices and structures in a learning environment. And flexible, because flexibility is what makes it possible to reimagine what doing mathematics may really feel and look like for ourselves and others.

In this dissertation, I explored the question: How might mathematics learning environments be organized to achieve greater visibility of diverse and flexible ways of doing mathematics? I employ concept and values coding, discourse analysis, grounded theory, narrative research, and Toulmin’s basic argumentative model to examine secondary students’ experiences and participation in a 6-week online summer course on “Introduction to Geometric Thinking.” I focused on three aspects of their experiences and participation: (i) their views and reflections on tools we used to support collaborative proving activities and how these might have influenced their perceptions of proofs and proving, and themselves as doers and learners of mathematics, (ii) the structure and content of the arguments students created across different tools and modalities during their first collaborative proving activity, and (iii) the values they expressed about mathematical proofs when they provided feedback to their peers’ proofs.

I show that shared workspaces created opportunities for students to participate in mathematical epistemic practices in new ways, including practices that might often remain obscure to students. Further, I share evidence that participation in collaborative and flexible proving activities increased students’ agency of proofs and proving. I also present how the structure and content of students’ arguments changed as they communicated their proofs in different media and modalities, with a subtle shift towards supporting their peers’ comprehension more as they moved from proof exploration and construction to proof communication. Students’ peer feedback on verbally-presented, and previously written proofs focused often on structural characteristics of their peers’ work, whereas students’ peer feedback tended to focus more on the presence or absence of justifications in proofs that were shared only in writing. Finally, students’ comments suggest that a deductive-like organization of a proof, or a presentation of a proof as a step-by-step problem-solving process was perceived as supporting clarity and understanding of a proof.

The collective findings of my study extend prior research on students’ proving practices, values and experiences by showing that learners’ mathematical work can be rather fluid and flexible. The reasoning patterns in which youth engage, as well as what they pay attention to in their own and their peers’ work, depends on various contextual factors including the affordances and constraints of the tools being used and the perceived communicative priorities of different activities.

    • Article
    • Peer Reviewed
    UC Berkeley Previously Published Works (2018)
    Publicly-available datasets, though useful for education, are often constructed for purposes that are quite different from students’ own. To investigate and model phenomena, then, students must learn how to repurpose the data. This paper reports on an emerging line of research that builds on work in data modeling, exploratory data analysis, and storytelling to examine and support students’ data repurposing. We ask: What opportunities emerge for students to reason about the relationship between data, context, and uncertainty when they repurpose public data to explore questions about their local communities? And, How can these opportunities be supported in classroom instruction and activity design? In two exploratory studies, students were asked to pose questions about their communities, use publicly-available data to investigate those questions, and create visual displays and written stories about their findings. Across both enactments, opportunities for reasoning emerged especially when students worked to reconcile (1) their own knowledge and experiences of the context from which data were collected with details of the data provided; and (2) their different emerging stories about the data with one another. We review how these opportunities unfolded within each enactment at the level of group and classroom, with attention to facilitator support.
      Cover page: Middle school students’ reasoning about data and context through storytelling with repurposed local data
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