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.

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.

For the first day especially, we choose investigations that are easy to understand but deep in content, with multiple entry points. The following problems are a few that we have found to be good starter investigations.

Student sliceform: Trophy

I'm getting ready for the first day of class of the semester, excited to meet a new group of students in my mathematics for liberal arts class. As I'm making decision about my goals, and planning my teacher actions in the classroom, I invite you to come along.

The Infinite Study Guide - Original DAoM Student Painting

Our students tell us that they do not like mathematics, it feels disconnected from their lives and they do not have high expectations for themselves in this class. These are among the reasons why IBL is perfect for MLA classes.

Whole Class Discussion: Show of Hands

This semester we are video taping our IBL classes and as I am watching the videos I am reflecting (again) on all the pieces necessary for a productive whole class discussion. My goal for a discussion is to make the “Big Mathematical Ideas” visible by having students construct connections between different solution strategies or attempts.

Dr. Volker Ecke working with students

As I walk around listening to the student groups grappling with making sense of the mathematics on their own, how can I encourage and support their efforts without just giving them "the answers"? How to engage them in mathematical conversations that will make their thinking visible?

Dance symmetry - Student proof 2

We found all positions for two dancers that exhibit both reflectional and 180 degree rotational symmetry. After the students discovered their conjectures, I asked them to prove that their conjectures were correct. This was our first activity of the semester and the students were new to the cycle of exploration - definitions - conjectures - proof.

3a+5b - Student proof 4

Asked to determine all possible values generated by the Diophantine equation $3a+5b$ when $a,b ≥ 0$, students discovered their first proofs involving the infinite. The diversity of entirely different proofs was both a challenge to the teacher and a great affirmation of the importance of inquiry-based learning.