Inquiry-Based Learning

The need for more active involvement of mathematics students in the learning process is well documented (e.g. MAA Guide to Evidence-Based Instructional Practices). In the case of Discovering the Art of Mathematics (DAoM), involvement occurs through the use of inquiry-based learning. The DAoM curriculum materials reverse the typical lecture dynamic by being built on guided-discovery investigations.

DAoM materials focus on investigations, tasks, experiments, constructions, data collection and discussion prompts rather than transcribed lectures and worked-out sample problems followed by banks of routine exercises. The transformative impact this has on students in MLA classrooms can be seen clearly in the classroom vignette, student quotes, and videos shown below.

New to Inquiry-Based Learning?

If you are new to Inquiry-Based Learning, come along on a virtual trip into "Our Inquiry-Based Classroom" or visit an IBL classroom in person at Westfield State University. For a first idea about our classroom materials, turn to our blog "Good Activities to Start". To explore how we engage our students in Mathematical Conversations, you may enjoy our blog on "Asking Good Questions". Then follow your interests by diving more deeply into the full listing below.

Inquiry-Based Classroom

What does inquiry-based learning mean to us? How do we teach? Let's walk into Volker Ecke's classroom and listen to his thoughts.


While the focus of this project is on college-level mathematics courses for students in the liberal arts, our experience and expertise with the pedagogy of Inquiry-Based Learning extends far beyond this specific focus. We all routinely teach the full range of college-level mathematics courses using inquiry with strong success: lower-level undergraduate mathematics courses including Calculus I-III, upper-level math major courses focusing on proofs, and content courses for future elementary and secondary teachers. We also work with K-12 teachers in bringing IBL techniques into their classrooms. We currently only have grant support for college-level mathematics for liberal arts. If you are interested in our working with us in other areas (K-12 or non-MLA), please contact us to find out about details and potential costs for such IBL workshops. We do maintain a collection of IBL Resources for courses other than MLA.

Discovering the Art of Teaching and Learning Mathematics Using Inquiry: Table of Contents

This section on the "Classroom" serves as a growing online book about the Art of Teaching using Inquiry-Based Learning. The chapter titles are listed concisely in the side menu for easy access. To find all the section titles for the entire book, please browse through the Table of Contents below. As we're nearing completion of this book please let us know if there's some aspect that you would like to see include.

Getting Started

Mathematics for Liberal Arts

In the Classroom

IBL in other mathematics courses


Mathematical Conversations

Proof as Sense-Making

Assessment Techniques


The Larger World of IBL

Further writing related to inquiry-based learning pedagogy

Student Voices

Book Connections