An Open Letter to New Teachers

Two weeks ago, I shared to you about A Mathematician’s Lament, an essay by Paul Lockhart about the mishaps of teaching in K-12 Mathematics. In this post, I’m going to share to you about an open letter to new teachers, a great piece written by Sam Shah in his blog, that discusses teaching tips. I think it’s a must read for new teachers, especially math teachers.


Here is Sam’s letter.

Dear person about to enter the classroom as a full-time teacher,

I love you. Okay, fine, not quite true — maybe respect, like, or lurve is more appropriate — but you have a passion for something and you’re following it. I don’t know if that passion is for the subject you teach, or for working with kids, or the deeply interesting intellectual puzzle of how to get someone to understand something, or for (in the booming Wizard of Oz voice) the Betterment of All Mankind. Regardless, this thing that brings you to the classroom is wonderful, because it puts you in the same ranks as those wonderful teachers that loom large in your past who inspired you and who helped you recognize that what they do has some worth. Continue reading…

A Proof that the Vertex Angle Sum of a Pentagram is 180 degrees

The pentagram is a five-pointed star. It was used by the ancient Greeks as a symbol of faith.  In this post, we exhibit the mathematics of pentagrams — we show that the sum of the angle measures of its vertices equals 180°.

pentagram math

For regular pentagrams, the proof is simple. By the inscribed angle theorem, the measure of an inscribed angle is half the measure of a central angle that intercepts the same arc. The central angles of a regular pentagram as shown above intercept the entire circle. Therefore, its angle measures add up to 360°.

The vertex angles, on the other hand, are inscribed angles as shown in the second image above. Notice that if we add them up, they also intercept the entire circle (Can you see why?).  In effect,  their angle sum is half of 360°,  which equals 180°. » Read more

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