The main goal of my teaching and research agenda is to democratize access to authentic mathematical activity that honors the diversity of learners’ mathematical thinking, that is both nurturing of and nurtured by intellectual agency, and that is guided by self-directed inquiry, mathematical play, and the having of wonderful ideas.
I think about mathematical things -- and how children think about mathematical things.
My primary research interest is children’s mathematical thinking. I’m also interested in the design of digital and physical tools for learning mathematics; contextually situated, culturally relevant pedagogy; and issues of education and social justice.
I'm currently working on projects focused on better understanding children's topological thinking, conceptualizing critical mathematical inquiry, identifying the benefits of Making experiences within elementary teacher preparation, and designing everyday knowledge-eliciting mathematical tasks.
This project incorporates a novel Making-oriented experience into the preparation of pre-service K-6 teachers of mathematics (PSTs), and documents influences to the PSTs’ knowledge and identities. The experience will enable the PSTs to design and print out new tools, using digital 3-D fabrication technologies, that support mathematics teaching and learning. Research objectives include: (1) describing the forms of knowledge invoked as the PSTs design and make new manipulatives to support mathematics teaching and learning, (2) tracing and elaborating the development of the PSTs’ technological, mathematical, pedagogical, and curricular knowledge as they engage in this work, and (3) documenting what the PSTs’ discourse reveals about the nature of the figured world of the design space and about the identities of those within it.
I've been collaborating with Erin Krupa, also in the Department of Mathematical Sciences, and Jennifer Robinson in the College of Education to develop a new "enhanced" degree program leading to a bachelor of science degree in mathematics with a concentration in K-6 teaching. This program has now been approved and is open to enrollment. It features transformative opportunities to learn mathematics through inquiry-oriented coursework and research experiences so that students will acquire the specialized mathematical knowledge that will prepare them to understand and navigate the challenges, complexities, and diversity of schools and classrooms.
I have been conducting teaching experiments with children ages 6 and 7 in order to model the development of their intuitive and informal topological ideas. I designed a new dynamic geometry environment called Configure (at playwithshapes.com) that I use to elicit these conceptions and further support their development. To date, I have found that these children developed significant and authentic forms of geometric reasoning. It is these newly identified forms of reasoning, which I refer to as "qualitative geometry," that have implications for the teaching and learning of geometry and for research into students' mathematical reasoning.
I am collaborating with faculty at the University of the Virgin Islands to develop a new secondary STEM teacher preparation program called UVITeach by adapting an existing, nationally recognized model. In developing this adaptation, we have found it prudent to consider the social and cultural context in which our future teachers will teach. We conducted interviews and follow-up classroom observations of high school mathematics teachers and other education stakeholders and identified eight features of pedagogy associated with effective teaching. We refer to these features as "Principles of Culturally Responsive Practice." These indicators comprise a model of contextually situated, culturally resonant pedagogy that is informing the design of the new teacher preparation program.
I'm collaborating with faculty at the University of Nebraska at Lincoln to further develop "Distributed Biography," an online application that supports the creation, collection, compilation and display of written narratives by multiple individuals about an individual, event, location, or experience of mutual interest.