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Steven Greenstein

Professor, Mathematics, College of Science and Mathematics

Office:: Center for Computing and Information Science 425N1
Email:: greensteins@montclair.edu
Phone:: 973-655-4287
Degrees:: B.S., Georgia State University; M.S., Texas State University, San Marcos; Ph.D., The University of Texas, Austin
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Profile

My interests are in how people learn mathematics and the qualities of their mathematics experiences. Through all the ways I engage in research, teaching, and service, I want my work to support the practices that democratize access to legitimate mathematical experiences that honor the diversity of people’s mathematical thinking and that are guided by agentive intellectual inquiry, mathematical play, and the pursuit of wonder-ful ideas.

Specialization

I like to think about mathematical things -- and how people think about mathematical things... especially when they do so with things.

My scholarly work is playing out in projects envisioned through the Enactive theory of cognition and informed by the philosophy and methodology of Phenomenology. My research attends to the designs of environments, experiments, and material resources that mediate these experiences, approaches to cultivating creativity for radical change, and issues of equity, inclusion, and social justice.

I'm currently working on projects focused on the phenomenology of mathematical experience and the design of educational ecosystems for emergent learning.

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Research Projects

The Enactive and Embodied Choreomathematics of the Polar Coordinate System

This project seeks to make contributions to precalculus education by developing the curricular and pedagogical components of an enactive educational ecosystem that enables the emergence of a graphical understanding of the polar coordinate system (PCS). Along with students in a doctoral-level course in mathematics education, we are wayfaring from inquiries to insights about the qualities and behaviors of polar graphing as we reason through pole-based choreographies of movement and material interactions with conventional and invented graphing tools. Findings from analyses of our wayfaring paths reveal the shape of polar graphing problem solving and suggest configurations of tools, tasks, and practices that enable the emergence of its understanding. These findings have implications for the design of enactive approaches to teaching for emergent learning.

Stretchy Minds

Guided by the question, "What new worlds arise when children come to understand that qualitative difference is a foundational dimension of learning for creative change?" my collaborators and I are taking a design-based approach to developing experiences that teach children "deep creativity" through qualitative geometric games that illuminate distinctions between non-metric differences in kind and metric differences in degree. By providing a medium for creativity, playfulness and aesthetic appreciation (C. Thi Nguyen, Games: Agency as Art), these collaborative games develop children's agency and autonomy as they come to understand these ideas.

Recent Publication: A “Teaching as Emergent Learning” Approach to Teaching Deep Creativity (Greenstein, Kerr, & Olson): https://digitalcommons.montclair.edu/laser-journal/vol2/iss1/3

Making for Mathematical Learning

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.

Educational CAD Library

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.

Children's Topological Thinking

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.

Critical Mathematical Inquiry

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.

Noyce @ Montclair: Preparing the Effective Elementary Mathematics Teacher

The Noyce @ Montclair scholarship program (2017 - 2025) sought to Prepare Effective Elementary Mathematics Teachers. We provided exemplary preparation to students for effective elementary mathematics teaching in high-need K-12 educational settings. Our scholars obtained an undergraduate degree in mathematics along with a K-6 elementary teaching certification. Each Noyce @ Montclair scholar received $15,000 (to cover tuition and fees) and a $10,000 stipend each year for two years with additional money available for local conference travel and digital backpacks. In return for the funds, students agreed to work two years in a high-needs school for each year of funding received.

Developing a Culturally Responsive Pedagogy for the U.S. Virgin Islands

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.