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.

This blog contains a vignette from a “live classroom” or “immersive activity” for faculty during a workshop. We want to give the reader a sense of what it can look like to have faculty be students in a mini classroom experience. Toward the end we explain how we are running the reflection session after the live classroom experience, which ties the student experience to the teacher tools and the 4 pillars of inquiry-based learning.


In this blog, Prof. von Renesse describes how she structured her remote synchronous classes in Fall 2020. There are many great ways to do that, but hopefully there are ideas here that also work for you. She provides different resources like google docs and jamboards, as well as video clips from her classes. While most of the resources in this blog are specific to the Discovering the Art of Mathematics books, Prof. von Renesse used basically the same set-up for her calculus class and her graduate class for teachers.


In this blog, Volker Ecke and Christine von Renesse write about some of the resources and experiences they have had with moving their inquiry-based classes online to a synchronous remote format in Spring 2020.


Faculty collaborating

The purpose of this blog is to engage you in thinking about some aspects of planning events for your IBL community, as well as providing you with the activities the New England region (NE-IBLM) has offered over the last 2 years.

In this blog Faith McNamee, a senior at Westfield State University, describes her learning about teaching with inquiry as a teaching assistant in Pre-Calculus. Faith describes how unreachable the goal of teaching with inquiry seems, even if you are convinced that this is how you want to teach. But being a TA helped her get closer to her goal.

In this blog, Elizabeth Azinheira describes how reading the book "Routines for Reasoning" and implementing the ideas has changed her teaching. In her intervention classroom, Liz carefully designs lessons that allow all her students to work at their learning edges. Liz was supported in making these changes by Dr. Christine von Renesse in a graduate course by special arrangement which included weekly video meetings and several classroom observations. After telling her personal story, Liz provides an overview of the routines and makes some of her lesson plans available for others to use.

In this blog post Professor von Renesse and her students describe their teaching lab class. If we believe that learning happens best in an inquiry-based way then this applies not only to learning mathematics, but also to learning how to teach mathematics. The idea of this lab class is to create a learning environment in which college students can experiment with teaching in a high school setting and learn for themselves what works best and why.

In this blog Drs Phil DeOrsey and Christine von Renesse describe an activity that is especially helpful in getting student buy-in. We let the students explore Islamic Geometry -- they create designs using compass and straight edge, as well as using Geogebra . For their final "achievement" we explain two different ways of exhibiting student artwork.

In this blog, Phil DeOrsey and Christine von Renesse describe ideas behind student resistance and student buy-in. A great resource is Tolman’s book “Why Students resist learning: A practical model for understanding and helping students”. He uses the Integrated Model of Student Resistance to explain how metacognition, cognitive development, negative classroom experiences, and environmental forces (work, family, culture/racism, disabilities) influence student resistance. It is tempting to think that student behavior only results from our facilitation during class but that is rarely the case.

There’s a famous line that many people use when they describe teaching. “Tell me and I’ll forget, show me and I’ll remember, involve me and I’ll understand.” I’ve always loved that quotation. I’ve tried to base my teaching style on it, like most teacher’s I’ve met or worked with have as well. But it wasn’t until recently that I actually knew what that meant. Or how powerful it can be.

Think of your class. What do you see? Do you see lethargic faces, students with their heads down, and only your top 10% answering your questions? Or do you see all students engaged; regardless of level? Do you see students talking about math in a productive argument? I can tell you that in just a few months, I have transformed my classroom from the first classroom example to the second.

Over the last years I have offered a course about inquiry-based learning to graduate students. These students are usually teachers that are working full-time in their own classroom while completing their professional licensure and master’s program. In this blog I will explain how I run the course and, more importantly, you can read about the journey to inquiry of two teachers that worked with me this semester.

This blog shows two different videos, one from Stanford University (CA) and one from Cornell University (NY), in which undergraduate students work on the Pennies and Paperclips task from Discovering the Art of Mathematics.

In this blog we invite the reader to think deeply about professional development opportunities for faculty. The focus of this professional development is to improve teaching by including more inquiry in the mathematics classroom. Our hope is that faculty developing professional development will use some of our ideas to create new opportunities that lead to transformational change and deep conceptual learning about teaching.

In this blog, Julian Fleron describes how he uses mathematical art to make his students think about racism, sexism, etc. Together with his students, he created a powerful piece of art to show that how we view each other depends on where we stand.


There were several things I didn’t like about grading...I didn’t like agonizing about the exact number of points to give, grading homework felt more summative than formative to me and I wasn’t sure if students learned from my written comments. I was also confused about the fact that a “B” could look many different ways. Then I read the book “Specifications Grading” by Linda B. Nilson. While this book doesn’t focus on mathematics it gave me lots of ideas and the goal to change what I am doing...

In this blog, Phil Hotchkiss describes his experience in teaching a "first year only" mathematics for liberal arts course. He explains several components of his course and uses students quotes to show the positive impact on his students.

My goal for this blog post is for you to get a sense of my philosophy and approach to one of the most enjoyable courses I teach; as well as to highlight how an IBL (inquiry-based learning) approach to the course is fundamental for the learning goals that I and my institution have for the course. You can download some of my explorations.

I have seen in the classroom how students’ conceptual understanding grows out of getting lost, feeling confused and making mistakes. Yet at the end, I still tend to “tell” students to not make mistakes anymore or at least not to repeat mistakes. How? By assessing their learning with presentations, tests, written homework, and final exams using rubrics that give the highest score to the work that has no mistakes... So how can I avoid sending mixed messages and create better rubrics and assessments?

Beautiful image of a surface developed for a student project.

In this blog, I reflect on the experiences Chrissi and I had with teaching an advanced mathematics course with a strong focus on students reading and presenting mathematics.

Neurons in the Brain, Image 1

Changing the mindset of our students, helping them understand how our brains work, how we actually learn is incredibly important for any mathematics class, from Kindergarten through graduate school. Since there is a lot of wonderful material, including blogs and videos, already published about this topic, I will use this blog to just present some of the main resources.

In this blog, Brian Katz is connecting beautifully the issues of equity and teaching using inquiry. He also promotes a special edition of PRIMUS which focuses specifically on inquiry-based teaching and learning.

In this blog, guest writer and aspiring teacher Lauryn Zaimes describes her insights into the intricacies of teaching with inquiry gained while videotaping a semester of Calculus. I hope that reading her experience will motivate practitioners like you to ask students to video tape your class sometime. While Lauryn clearly learned a lot from her experience, I learned at least as much!

This Fall (2016) the 13 students in my honors mathematical explorations class embarked on the journey of understanding some mathematical ideas behind maypole dancing. In this blog you can find some videos about maypole dancing, student work proving our conjectures and a beautiful writing project by Sarah Dunn about mathematics, running and maypole dancing.

Students dancing around a maypole in their mathematics class.

Sarah Dunn, student in the Honors Learning Community for "Mathematical Explorations" and "English Composition," reflects on connections between the challenges of running and grappling with the mathematics of maypole dancing. She sees connections in the role played by community support, the thrill of venturing into the unknown, and the passion in pursuing a personal challenge.