At the moment, I’m envisioning that this group will try to read a few pages of Measurement this book every week. This will likely mean we won’t finish the book in the fastest fashion, but that isn’t really the goal of this conversation anyway.

To help guide our conversation, I, along with the help of a few other math teachers (Michael Perhsan, Shawn Cornally, and Paul Solomon), have put together some reading questions which will hopefully serve as good starters for conversations in the comments of this post, but please do not feel constrained by these questions—we would much prefer that you ask your own questions than simply respond to ours.

If our conversations become too complex to be handled by the simple commenting system here, we can always move them to a different forum.

## Introduction: Reality and Imagination

- What does Lockhart mean by mathematical reality? How does he see this world as different from physical reality? Do you buy it? Where do you think the author is going with this distinction?
- Some people say that there are perfect circles, while others say that everything in the world is imperfectly round. Which side do you agree with? Why?
- What do you think of when you hear the term “mathematical reality”? What experiences have you had exploring mathematical reality?

## Developing Mathematical Arguments

- For the problem of proving that connecting the medians
^{1} of a triangle meet at a point—can you draw some sketches with pen and paper to see for yourself that this seems to be the case? If you’re really adventurous, try making a drawing with a computer geometry system like Geogebra.

Here’s a quick video tutorial to show how easy it is to get started with Geogebra:

- How can this problem be tweaked? Is this a narrow version, or part of some larger truth about all shapes?
- Is this true for other shapes? What happens when you draw the diagonals and connect the midpoints of a rectangle—do they meet at a point? Does this hold true for any 4-sided object? Feel free to explore n-sided shapes—pentagons, hexagons, etc.

- Lockhart mentions that the best problems are you own. In that vein, what’s a mathematical problem that you have some interest in?

^{1}A median is a line from the vertex of a triangle to the midpoint of the opposite side.

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Tags: questions, reading