Occasional Paper Series #41

Cultivating a Space for Critical Mathematical Inquiry through Knowledge-Eliciting Mathematical Activity

by Debasmita Basu & Steven Greenstein

As teachers, we know that learning is more effective when instruction connects the mathematics we aim to teach and the home, community, and cultural knowledge students bring with them to school. Indeed, classrooms can only operate as venues for critical mathematical inquiry if instruction draws out and builds on this knowledge. We also realize that the benefits extend beyond making learning more effective. Engaging this knowledge also helps us cultivate the kinds of caring relationships that nurture students’ sense of belonging (Horn, 2017) and contribute to the myriad ways we experience the joys of teaching and learning.

It is one thing to know the benefits of leveraging what Turner and her colleagues refer to as children’s multiple mathematical knowledge bases (MMKB) (Turner et al., 2012)—or “the understandings and experiences that have the potential to shape and support children’s mathematics learning—including children’s mathematical thinking, and children’s cultural, home, and community-based knowledge” (p. 68). It is quite another to undertake the considerable effort required to elicit this knowledge from students. While teachers tend to believe the effort is worthwhile, they often find they lack the time to do it (Gonzalez et al., 1993, p. 1390). Thus, tasks that reveal students’ multiple mathematical knowledge bases can be useful to teachers who wish to leverage their students’ knowledge as resources for more effective instruction. However, such tasks are hard to find and even harder to create.

In this article, we share the findings of a project we undertook, which we titled knowledge-eliciting mathematical activity, or KEMA. Our goal for the project was to develop task design principles that teachers could use to reveal their students’ multiple mathematical knowledge bases. We present some of the tasks we found to be effective along with some of the things we learned, aiming to offer guidance to teachers to develop their own tasks. We believe the principles we used to design these tasks will be useful to teachers who wish to enact a responsive mathematics pedagogy that is deeply connected to their students’ bases of mathematical knowledge.

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About the Authors

Debasmita Basu is a doctoral student in mathematics education at Montclair State University in northern New Jersey. As a high school mathematics teacher in India for four years, she was dismayed that her students tended to consider mathematics as a set of rules and formulas with little to no connection to their lives. Hence, with the greater goal of changing the nature of school mathematics, Debasmita started her doctoral studies in 2014. Her research agenda focuses on designing mathematical activities that aim to cultivate students’ critical consciousness towards various social and environmental justice issues and help them realize the power and value of mathematics.

Steven GreensteinSteven Greenstein is an associate professor in the Department of Mathematical Sciences at Montclair State University. He enjoys thinking about mathematical things—and how people think about mathematical things. Through his work, he aims 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.