Inquiry-Based Learning and the Art of Mathematical Discourse

Abstract

Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate a classroom focused on mathematical discourse. The paper brings this discourse alive through classroom vignettes and explores various teacher moves and their impacts. The mathematical theme of the classroom investigations, Maypole dance patterns, stems from the learning guide “Discovering the Art of Mathematics: Dance.” Both authors are part of the NSF-funded project “Discovering the Art of Mathematics,” which provides IBL materials for mathematics for liberal arts courses, see www.artofmathematics.org.

Keywords:

• Inquiry-based learning
• mathematics for liberal arts
• mathematical discourse
• mathematics and dance
• discovering the art of mathematics
• maypole dancing

ACKNOWLEDGEMENTS

We thank our colleague Judy MacKinnon for sharing her expertise with facilitating classroom conversations in mathematics. None of this work would be possible without the amazing support from our colleagues at Westfield State University, especially Julian Fleron and Phil Hotchkiss.

Notes

¹ If I use these questions only for “incorrect” answers, the students will know that I think their answer is incorrect. However, if I use these questions in general it will not give away my evaluation of their conjecture.

² As it turns out, 2 × 2 diamonds are not possible as a pattern with the regular Maypole dance, no matter how many dancers we have and no matter how we assign black and white ribbons to them. If you follow one dancer’s ribbon as it alternately weaves above and below the other ribbons, its color will show in every other square. However, on a 2 × 2 diamond, these squares show different colors.

Additional information

Notes on contributors

Christine von Renesse

Christine von Renesse uses open inquiry techniques in all of her teaching. Her passion for music and dancing has been woven into her teaching as part of her inquiry-based approach to mathematics for liberal arts classes. Christine has advanced degrees in Elementary Education, Music, and Mathematics from the Technical University Berlin, Germany and a PhD in Computational Algebraic Geometry. She is now at Westfield State University.

Volker Ecke

Volker Ecke loves diving into a mathematical inquiry with his students where they can discover their own power in making sense of mathematics, often for the first time. After undergraduate studies in mathematics and physics in Germany, Volker earned a PhD in Computational Algebraic Geometry and Theoretical Computer Science before joining the faculty of Westfield State University.