Week 1

Last Saturday was the first math circle meeting. It was great fun to meet all the students, and to see everyone working together. We had a very one- and two-dimensional day. Instructor 1 (let's call this instructor M) used mardi gras beads as a manipulative to help students understand homotopy classes of knots. Instructor 2 (let's call this one D) classified planar Euclidean transformations using a combination of socratic dialogue and small group discussion. Instructor 3 (let's call this one L) built quotient spaces of the plane via discrete isometric actions.



Can you figure out how the mobius band was cut to create this configuration? (Solution)


Some mathematical highlights from the day -- showing that reflections generate all other Euclidean planar transformations, the follow-up observation that "no matter what" is a strong statement after a student's comment that "we need to show that no matter what we do to the knot, it will never be unknotted", quotienting a torus to obtain a mobius band and slicing it along thirds lengthwise.

Orientation meeting

Today, the Math Circle undergraduate team met with the grad student instructors and director. Introductions all around, and then we discussed the following.

• The previously-posted Good Question of Terrell
• Logistics of the Math Circle
• What makes a good teacher? What makes a bad teacher? What skills are involved with teaching?

This post will focus on the third item. All material was generated by the undergraduate team, with little participation from the graduate students.

(A snapshot of the brainstorm on teaching)

What makes a good teacher? (This question took a while to warm up to)

• Organized, well-prepared
• Patient
• Approachable
• Ask lots of questions
• Enthusiastic
• Good lecturer

What makes a bad teacher? (There was immediate feedback on this question)

• Boring
• Droning
• Unorganized
• Incompetent at material
• Talking straight through, really fast
• No board work

What skills are involved with teaching?

• Willing to admit deficiencies, mistakes (*)
• Being comfortable with material(**)
• Pacing material appropriately(**)
• Knowing material, having a plan(**)
• Anticipating questions(*, especially at the beginning)
• Anticipating problem areas
• Knowing what questions to ask(*)(**)
• Keeping people focused(*)
• Leading students as a group
• Get them back on track
• Getting respect from students

We then discussed what skills would be the "most difficult", and what skills are the "most important" in a classroom. Those flagged as most difficult during the brainstorm are marked (*); those flagged as most important are marked (**).