I am currently teaching a math class to prospective teachers. The topics are measurement, geometry and probability. I have no real idea how all three of these topics got placed into one semester course, but I do like the constructivist approach this college class takes in its presentation.

I have taught this class easily 10 times over almost as many years. For the first couple of years I stayed very true to the syllabus that was given to me. I am not a university professor and I did not necessarily feel I had a role in changing the content of the course.

However, with the passage of time, a growth in my professional confidence and the fact that the creators of the course have since retired, I have made some significant alterations to the content. I have rearranged the activities to place measurement of angles before the investigation of polygons and polyhedrons. I have also included a strong dose of Pythagorean theorem so show the students that it is much, much more than a simple collection of letter to the second power. Finally, I have significantly beefed up the probability section to include many different and varied experiments based primarily on materials I got from the NCTM. For the most part, I think I have taken a fine course and made it somewhat more rational.

This course was designed for 15 to 20 students. The homeworks are writing intensive. There is no textbook. Classroom activities were designed for group sharing and discussion. This semester I have 37 students! This is a huge, huge increase and it is due to the fact that the university has had to make some severe cutbacks in course offerings. Since this course is required for several different degrees, it is often oversubscribed. But this year is a crazy one.

The funny thing, though, is that there is a sense of well being in the class. I see happy and above all, grateful students when I walk into the crowded room. There are only two men in the course and nearly everyone there is under 24 years of age. This evening the two men were absent and I got to thinking how this class could have been in some all girls school. Then I was wondering about the positive and potentially negative impacts of this gender segregation on math learning.

Wondering, but no answers. With 37 students, I worry I won't have the time to ever really think about this question again.

This evening's class was about the sum of interior angles of polygons. I defined the terms and then passed out some pre-cut triangles to the group. I then asked them to rip off the corners (the angles) and rearrange them to see that no matter what type of triangle you had, the three angles lined up evenly on a line. This demonstrated that the sum of interior angles = 180 degrees. I know this does not "prove"it in a formal sense, and I said so in class, but for a group of elementary teacher, it is a very simple and powerful demonstration.

We spent the rest of the class making our own tangrams from a blank piece of paper. We followed directions I had found years ago to fold and rip paper to come up the the seven classic tangram pieces. All along, I was having a conversation with them about similarity and congruence; of quadrilaterals and equilaterals; and rectangles vs parallelograms. To the end the evening the students used protractors to measure the angles of the polygons we created, then tried to reassemble the pieces into the original square sheet of paper I had given them.

My ultimate goal is to teach a rigorous math class in fun and intriguing ways. I want to infect these soon to be teachers with a sense that math can be mysterious yet explainable, creative yet powerful, and above all, to set aside their own math-phobic habits (if they have them) and set out to excite a new generation of students.

## 1 comment:

Hi, reading this post, and in particular the last paragraph, with the aim of teaching math in an engaging way reminded me of the style of writing in the books in the series written by IM Gelfand (and others) in the Gelfand School Program. I've always felt that my own high school maths education lacked something, and although I've done first year maths at university level, it didn't fit together. I've learnt a lot of "facts", but don't have a big picture. So I've gone back to basics and am now reading his book on trig. It's way different from a traditional textbook. It's like a professional mathematician explaining something in a respectful way to a younger learner, and it seems like what you are aiming for.

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