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.
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.
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.