This video lecture from the Princeton Public lecture series features psychologist Stanislas Dehaene and mathematician and author Steven Strogatz discussing math, learning, and teaching.

Dehaene, a leading researcher in how the brain acquires and processes mathematical knowledge, has some interesting things to say about whether mathematics is innate or learned.  He also describes some fascinating research conducted on number sense and geometric understanding in primitive societies.

What I enjoyed most in this lecture, however, are the two stories from Steven Strogatz about his personal experiences learning math.  At around the 23:30 mark, Strogatz tells the story of when he first became “really interested” in math.  Strogatz is a wonderful storyteller, and the tale should resonate with anyone who has discovered, or is discovering, their passion for math or science.

Strogatz’s second story is about his first experience being “weeded out” in an advanced math course in college.  This is a story I wish I had heard as a student, and it’s something I’ll definitely be sharing with my students from now on.

And for more on math and teaching from Professor Strogatz, check out how his book “The Calculus of Friendship” is a great read for advanced math students.

I love spending time with my niece and nephew.  They are inquisitive, thoughtful, energetic, fun, and always up for anything.  As math is often on my mind, mathematical ideas often come up when we’re together.  I love exploring math with them:  we talk about numbers, ponder questions, play with shapes, estimate things.  They usually enjoy it, and if they don’t, they don’t mind telling me so.  Just like the rest of my students.

The last time I was in the neighborhood, I stopped by to see if they were around.  They weren’t home, but a I saw a piece of chalk lying on the ground.  I scribbled a quick note in the driveway letting them know I’d been by.  Before I knew it, a little triangle had appeared under my message.

When I came back later, there were many questions to answer about the mysterious diagram (it’s not the first time such triangles have appeared unexpectedly).  I told them a chilling tale about Waclaw Sierpinski, and then showed them how to make their own Sierpinski Triangle:  draw any triangle; find the midpoints of the sides; connect; repeat!  Soon, we were drawing triangles all over the neighborhood.

 An unprompted pentagon even appeared!

After lots of drawing, lots of questions, and a triangle scavenger hunt, it was time to go.  Another fun afternoon spent with my niece and nephew, and I left impressed, as I usually do.  And hopeful, too, that maybe one day my niece will actually admit that she likes math!