What Do You Notice? What Do You Wonder?

If you want your children to understand and enjoy math, you need to let them play around with beautiful things and encourage them to ask questions.

Here is a simple yet beautiful thing I stumbled across online today, which your children may enjoy:

• Drawing Star

It reminds me of string art designs, but the app makes it easy to vary the pattern and see what happens.

• What do your students notice about the patterns?
• What questions can they ask?

I liked the way the app uses “minutes” as the unit that describes the star you want the program to draw. That makes it easier (for me, at least) to notice and understand the patterns, since minutes are a more familiar and intuitive unit than degrees, let alone radians.

For Teachers or Advanced Students

Noticing and wondering is not just for students:

• What connections can you find between these star patterns and other topics in mathematics?
• For instance, how do the patterns relate to Matt Henderson’s gears: When designing a machine…
• Or can you see what these stars have in common with Euclid’s Game?

There are probably other apps on the web that do similar things, and if anyone wants to recommend them in the comments below, I’ll enjoy playing with those, too.

Addendum

If you are not used to asking questions about mathematics, here is a short paper to give you a kick-start:

• Drawing Stars by Daniel Shapiro

As you spend time thinking about his questions, you will almost certainly wonder about something yourself. Be sure to capture the idea before you forget it!