Faculty Blog

Faculty Blog

Here you will find blog posts by the Discovering the Art of Mathematics authors: Julian Fleron, Phil Hotchkiss, Volker Ecke, & Christine von Renesse.

Often people ask me how to write inquiry activities so there must be some tricks that can be communicated. Together with Prof. Mairead Greene from Rockhurst University, I have been thinking about the questions we ask ourselves before, during and after writing tasks. Our intention is that these questions will help to inspire and guide others in creating good IBL activities in any mathematics course.

multivariable calculus group discussing integration

In my perfect world students would be self-motivated, want to learn, collaborate with other students, ask lots of questions, pursue mathematics outside of class requirements, etc. What then is needed to make this happen? I believe this independent learning I am looking for relies on student curiosity.

As the title of this blog post suggests I believe that inquiry helps tremendously in reaching learners on different levels at the same time - even if they all work on the same investigations. Why? First of all, students can work at their own pace.

Twice now I had the pleasure of teaching a learning community with an English composition class. And each time I was impressed by the peer review process that my colleague Jen DiGrazia used for all student papers. This blog will show you how we adapted the peer review process to improve proof writing.

Students dancing salsa rueda

Our website provides 11 learning guides. Which one(s) should you choose to give this inquiry-based approach a try…? Let me begin by telling you how I make choices about the materials. I like to go for what I love best and I usually mix materials from different books.


Do you think it is possible to teach calculus without ANY lecture? (or any other passive teaching method like watching videos, reading the book etc.) Well, I have been teaching calculus (I, II and III) for the last 7 semesters doing just that. And I love it.


While you lecture you might not see any student mistakes but one of the eye-opening experiences of inquiry-based learning is the huge amount of mistakes you observe.

IBL classroom: Students discussing their board work.

Wouldn't it be amazing to develop a collection of IBL hubs or centers across the US where mathematics faculty could immerse themselves in a broad variety of IBL classroom experiences?


Do your students experience the messiness of doing mathematics, searching for patterns, trying and failing in explaining an idea before they come to a complete argument?

Using name tags to group students

In the first class I ask students to write their name on a notecard and to place it in front of them. At the end of class I collect the name tags and in the beginning of the next class, I will set them up again, likely in different places. I call this strategy one of the “control knobs” of an IBL instructor, because where and with whom the students work has a big influence on the effectiveness of their learning.

Cool thing: Bee dance

Think of the 5 coolest things you know in mathematics. Did you ever think about including them in your MLA course? You can, and perhaps should.
“Cool things” are short “mini presentations or activities” about a mathematical topic that is exciting to us and usually different from the math content that we are currently working on in class.


Group having fun

Phil Hotchkiss describes what is special about the "math for liberal arts" students and shares his tools for addressing this particular audience.


Groups recording on the board

You’re ready to embrace inquiry-based learning (IBL) in your mathematics for liberal arts (MLA), or other general education courses, with the help of Discovering the Art of Mathematics (DAoM) materials. How do you get started?

Inquiry-based learning in a group

Inquiry-Based Learning (IBL) is an approach to teaching and learning in which the classroom environment is characterized by the student being the active participant while the teacher’s role is decentralized.

Graded Student Work

One traditional way of assessment in a College class is in the form of mid-term or final exams. How does this fit in with an Inquiry-Based approach to learning mathematics?

Proud students presenting their ideas on the board

A Learning Contract can make the roles and responsibilities of students and faculty explicit and allow students to make a conscious commitment to learning in this class.

Student journaling

At least once a semester I ask my students to write a journal. My main goal of this assignment is to monitor students’ buy-in into my IBL classroom. How is IBL working for them? What is not working? What could they change to improve their learning? What can I change?

Many of our liberal arts students are, by their nature, very creative. One way of assessing our students that allows them to be creative is by assigning projects.

Notebook Quiz

Julian uses occasional notebook quizzes to complement his more in-depth assessment of student-created solutions.

Student-created solution set

The majority of class time is spent with students actively engaged in process of mathematical inquiry. Written proofs and solutions that describe/document the students' work form a cornerstone of my assessment of their work in this class.

I start every semester with a mathematical autobiography. Each student submits his or her own story describing their history as a learner of mathematics.

Student exploring straight-cut origami

I want my students to learn how to write about their thinking. Therefore, my assignments have to be written in full sentences, explain everything in detail and convey the mathematical concepts. They can also contain the story of how the student discovered the solution, including all struggles and mistakes.

Active student participation

Students are actively engaged in making sense of mathematical investigations, on their own, in their group, and with the entire class. I share some ideas about assessing the students' level of participation in, and contribution to, the work in the class.

Student Poster about Vi Hart

For over a decade, I have been asking MLA students to create biographical posters of mathematicians whose important work occurred after the year 1900.
As a result, students see mathematics as an evolving, human subject – one that is undergoing enormous contemporary growth.

Faculty working in a small group

What do our faculty workshops actually look like? What are some of the pedagogical tools and techniques participants get to explore? In this blog, we describe a few faculty workshop activities.