## CMESG Day 3

Today at CMESG, we met with our working groups again. My working group on “problem based learning” started to design lesson plans around our problems. I was in the team of people working on upper-division problems. In particular, we wanted to design a lesson around the problem:

Classify the Platonic solids and prove that there are only five.

This turned out to be much larger than we expected, and the problem sort of blew-up in our face. We were not sure where to get started. It was a neat instance of what commonly happens when people approach a new problem; it gets out of hand and they’re not sure how to proceed. We struggled to figure out how much graph theory and group theory to introduce. Where would people take the problem?

If I were to run a problem based learning session, I’d like to go through a three levels of testing before trying the session with my students.

- Try the problem on a non-mathematical friend. Is this interesting?
- Experiment with some math friends. What content might it have?
- Take the problem to a math club as a lesson plan. Where do people take it?

Once I knew that the problem was intrinsically interesting, could have some mathematical content, and wouldn’t go too wonky, I would write it up as a lesson plan to be used in a real class.

## CMESG Day 2

We’re on Day 2 of the CMESG. I attended my first working group, on the theme of Problem Based Learning. This approach to teaching focuses on students’ experience of solving large open-ended tasks. Our working group is going to design a curriculum for “The Problem Based Learning University” which is a theoretical institution with 8000~10000 undergraduates, 500 graduate students, with “standard” service courses and no math program. We’re taking a problem based learning to problem based learning. I love this kind of meta-application of techniques.

We’d be teaching classes to:

- Engineering
- Commerce
- Life Science
- Humanities
- Pre-Health
- Arts
- Education

A good problem should be: “Real”, whatever that means.

Some other criteria that came up for us:

- Comprehensible (Language, culturally, student level)
- Investigative
- Interpretable
- Multiple paths & solutions
- Possibility of no solution
- Opportunity for meaningful failure
- Undirected and require independent thinking
- In class or long term term with research

For me, problem based learning requires bringing students an intrinsically interesting problem. I want to find problems that are engaging on their own. One good criteria for a worthwhile problem is that anyone who is curious would want to know how to solve it. Would my aunt want to solve this question?

How do sundials work? How could we build one?

The topic session that I went to today was: “*Culturally Sustaining Mathematics Education: Connecting Indigenous Knowledge and Western Mathematical Ways of Knowing*” given by Ruth Beatty (Lakehead University) and Colinda Clyne (Upper Grand District School Board).

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