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.

Compass Rose

We present the following case study as a way of illustrating the power of inquiry-based learning to transform how we think about what we know and how we know. It challenges us to reconsider the nature of teaching and learning in mathematics. Julian Fleron describes how he and his students explore triangle patterns.
What we know changes several times in the story of Rascals’ triangle. And each time the matter of what we know is inextricably intertwined with how we know it.

Math Explorations showed me how much there was to learn in the world of mathematics. I had been contemplating the idea of pursuing a career as a teacher. Seeing the difference in how math is taught in high school and how it was taught to me in Math Explorations pushed me into thinking about how I could help kids in high school learn and appreciate math. I was convinced that this was the direction for me, so during my next semester I declared a Mathematics major with a certification in Secondary Education.
 

Although I enjoyed and appreciated mathematics, I was not compelled enough by the mathematics of high school to make it my major. This soon changed as I took my first college-level mathematics course, Math Explorations.

Hello, my name is Nicholas Taliceo and I am senior at Westfield State University. I’m a Mathematics major and I love it. I’ve had some amazing experiences – I’ve attended and presented at numerous conferences including the 2015 JMM conference in San Antonio, TX, and had the opportunity to experience undergraduate research, just to name a few. Interestingly, only a few years back, I would have never thought that I would be doing what I’m doing now…

Prime Factor Conjecture

The primary audience of Discovering the Art of Mathematics is mathematics for liberal arts students. The scope of the project’s work continues to expand to include audiences that are more and more diverse. Here we describe the project’s connection to Mathematics majors. What we have found is that Discovering the Art of Mathematics has great value in recruiting mathematics majors AND our view of our Mathematics major has been deeply informed by our work on this project.
 

Dana Ernst Teaching

This blog is part of our guest blog series: Dana Ernst is an assistant professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ. We met him at the IBL workshop a few years ago, where we noticed that besides being a committed cyclist he knows a lot about using IBL in many different classes. Dana is co-author of the wonderful blog Math Ed Matters .

Angie Hodge

We met Angie Hodge at the 4-day IBL workshop run by Stan Yoshinobu 3 years ago. Besides competing in 100 mile long trail runs (yes, really!) she knows a lot about teaching IBL in calculus and in larger classes. Angie teaches at the University of Nebraska, Omaha. She also co-authors a wonderful IBL blog Math Ed Matters with Dana Ernst.

In this blog we tell the story of the different surveys and assessment tools we have used since 1997
to measure the impact of our materials and teaching style. You will find the actual
surveys, the full reports (and summaries) and our current ideas and efforts.
 

Matt Jones is sharing some of his technology ideas for the IBL classroom with us: "A few years ago, I got involved in a professional development project for middle school mathematics teachers where all of us were using iPads. Partially as an outgrowth of that project, I started a blog called The Math Switch . In this post, I am going to detail the workflow that emerged in the first year of the project."

 

Steven Strogatz' wrote a blog post about what it was like to be a beginner at teaching through inquiry. This second part contains his experience of teaching a Mathematics Exploration class at Cornell University using ideas from "Discovering the Art of Mathematics":

Last fall, for the first time in my career, I tried a new way of teaching. Instead of lecturing, I gave my students puzzles and questions to explore together in small groups. What happened over the rest of that semester turned out to be the most astonishing, uplifting experience I’ve ever had as a teacher.


 

Steven Strogatz Teaching

Steven Strogatz writes about what it was like to be a beginner at teaching through inquiry. This blog contains his impressions of the "Discovering the Art of Mathematics" workshop held at Cornell University in summer 2014:
"This experience gave me powerful insight into what it must be like for students in an IBL classroom. It made me realize the importance of providing a safe and nurturing space for the math explorers I was about to start working with in just a few days."
 

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.

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