# 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.

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.

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.

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.

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.

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.

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.

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.

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.

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?

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.

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.

Pennies and Paperclips is a beautiful game whose winning strategies students determine inductively and then work to prove. Proof of the winning strategy for Penny is remarkable for its clarity and simplicity. Proof of the winning strategy for Clip seems to be as straightforward but really offers important lessons in what constitutes proof.

Initial instructions to create 4 congruent right triangles of their choice set students on a path to re-discover the beautiful "proof without words" attributed to Bhaskara.

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.

In 2012 the Discovering the Art of Mathematics team started reaching out to the two-year colleges. At the NEMATYC conference in 2013 we learned that many faculty are interested in support around algebra related courses.

The following video clip was filmed in a Calculus 2 class for math majors. While transcribing the video I noticed that my story of what happened in my interaction with Loghan was different from the actual exchange that you see in the video.

## A Look Into Our Classroom

**What does a day in our Mathematics for Liberal Arts Classroom look like?** It's still five minutes before class starts when I walk into the room. Of the two dozen students already in the classroom, most are already doing mathematics.