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Associate Professor, Mathematics
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.
For more information about our undergraduate and graduate mathematics education programs, including our Teaching Middle Grades Mathematics programs, please see the Links section below.
I like to think about mathematical things -- and how people think about mathematical things.
My research interests are in mathematical experience; people's mathematical thinking; enactive phenomenology; the Making of physical tools for learning mathematics; and issues of education and social justice.
I'm currently working on projects focused on the phenomenology of mathematical experience, cultivating children's creative and qualitative mathematics, and identifying the benefits of a manipulative Making experience within elementary teacher preparation.
- 1:00 pm - 2:00 pm
- ... and also by appointment.
- My website at wonderfulideas.org
- Fractles: Fraction Tasks that Generate Moments of Mathematical Thinking and Reasoning
- Prospective Teachers Making for Mathematical Learning
- The Stretchy Minds Research Project: STEM Creativity for Radical Change
- Configure - A Dynamic Topology Environment for Exploring Equivalence Relations
- Explore my research at Research with Montclair
- Explore my research at Research with New Jersey
- MSU's PhD in Mathematics Education
- MSU's Undergraduate and Graduate Mathematics Education Programs
This research project is addressing the question, "What new worlds arise when children come to understand that qualitative difference is a foundational dimension of learning for creative change?" Taking a design-based approach, we've recently developed a games-based approach to teaching kids about the distinction between differences in kind and degree. The "Stretchy" refers to the kinds of transformations that only exist between two shapes that are topologically equivalent. And the reason we chose this approach is because games offer us "a way to collaborate in the project of developing our agency and autonomy" (C. Thi Nguyen, Games: Agency as Art). Nguyen goes on to propose that our agency in games is much like what the canvas offers the artist: a medium for creativity, playfulness and aesthetic value.
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.
The Educational CAD Model Library, launched in September 2023, is a repository of peer-reviewed educational objects for use in K-12 STEM teaching and learning. I am the curator of the Mathematics Education Collection.
I conducted 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.
Through teaching mathematics for social justice (M4SJ), students can deepen their understanding of mathematics as they come to realize that mathematics is a rich, relevant, analytical tool for understanding and potentially influencing issues that are important to them and their community. But mathematics isn't only a servant of the sciences, it is also its queen (E. T. Bell). As such, mathematics can serve as a venue for critical mathematical inquiry (CMI) in that it entails unique and powerful forms of thinking and reasoning that just might be useful for cultivating critical consciousness. Proceeding from these two perspectives, the focus of this project is to identify, explore, and generate new pathways for praxis at the intersection of mathematical inquiry and education for democracy and social justice.
The Noyce@Montclair Scholarship Program provides exemplary preparation to students for effective elementary mathematics teaching in high-need K-12 schools. Scholars obtain an undergraduate degree in mathematics along with a K-6 elementary teaching certification, and each scholar receives a $13,000 scholarship and a $660 stipend each year for two years with additional funding available for local conference travel. In return for the funds, Scholars agree to work two years in a high-needs school for each year of funding received (i.e., a scholar who receives funds for both years would work four years in a high-need school).
This project operates in collaboration with Joseph DiNapoli, also in the Department of Mathematics, and Jennifer Robinson in the College of Education.
I collaborated 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 (UTeach). In developing this adaptation, we 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 informed the design of the new teacher preparation program.