Here are some good and bad watch hairsprings. The bad one doesn't work.
A helix is a three-dimensional coil that runs along the surface of a cylinder. Spiral is often used (incorrectly) in place of helix, as in spiral binding or spiral staircase. Here are Excel Math Teacher Editions which have coil "spiral" bindings, and an image of a "spiral" staircase.
Math is a language of counting, measurement, shapes and calculation. A language with precise definitions and specialized terms. It's not just numbers. Ok, you might concede, but still ask, Why this focus on spirals?
We have limited attention spans. We can only take so much before we grow tired and look out the window or check our mobile phones. We can only trudge straight up a staircase for so long before we get tired. Look at this subway escalator!
Math can be like that at times, but it doesn't have to be arduous. Variety helps.
A week ago I did a tea post. Yesterday I did another. There were two posts on airplanes. Once I wrote about coins. I'll probably get back to money later. I like tea, and I like money. Math helps me understand both tea and money.
Math is a lot like this blog. The same concepts come up again and again, in different ways. How you learn math depends on the situation, and your teachers.
We can't really teach coins thoroughly without having explored fractions - because coins are fractional parts of a larger unit of currency. We can talk about probability, but we can't express it numerically unless we understand ratios and decimals, such as "1 in 50 chance of a jackpot".
What does all this have to do with this math blog?
Excel Math exposes kids to math in a spiraling fashion. We don't want to bore them but we do want them to learn. And we want it to stick. So they practice. Even mediocre athletes practice, and good ones are always at it! One thing after another, not the same thing all day.
Likewise, we move on to more complex things, then back to prior concepts for a brief refreshing.
If we carefully tweak our spiraling so concepts aren't tangled (like the bad hairspring) or dauntingly linear (like the escalator) we can help kids experience math in an enjoyable way. Math should wind and unwind around and through their world, lifting them to higher planes of understanding, allowing them to integrate math into daily life ...
Oops. Got carried away.
I predict this won't be the last time I write about spiraling, or tea, or watches. Those subjects will come around again. Smoothly.
PS - I went to Helix High School. Really.