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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 primary research interest is children’s mathematical thinking. I’m also interested in the digitally mediated Making of 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 understanding and cultivating children's creative and qualitative mathematics, and identifying the benefits of a manipulative Making experience within elementary teacher preparation.
- My website at wonderfulideas.org
- Prospective Teachers Making for Mathematical Learning
- Configure - A Dynamic Topology Environment
- Undergraduate and Graduate Mathematics Education Programs
- PhD in Mathematics Education
- Explore my research at Research with Montclair
- Explore my research at Research with New Jersey
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 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 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.
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.