One of my students was so inspired by yesterday’s conversation in class, he went home and penned an essay on the topic.  Here’s what he has to say about learning math.

I think that the old way of teaching is not as good as the new way.  My thesis is “Thinking is better  than just memorizing.”   My boxes are “moving up to a higher math,” mindful and mindless, and how new math is better.

Moving up to higher math includes algebra, calculus, and trigonometry.  In some algebra, you need to replace numbers with letters.  In the old way of teaching math, the problem is that a letter can be any number, so there is no memorizing.  I think this is important because you need to be free, not held back by memorization.  In the new way of math, you are more free to think, so it is easier to guess.  With trigonometry and calculus, you need to guess with proofs and calculations.   With calculations, they aren’t on pieces of paper so you need to make them yourself and the old way teaches you just to know equations and that is being mindless.  This leads to my next topic.

Mindful and mindless are two opposites.  Mindful is when you’re thinking and fully awake.  The new way supports mindfulness with showing your work.  This is important because if you memorize a fact and then forget it, you wouldn’t know how to do it.  Mindless is like the old way of doing math, just knowing a fact but never really knowing how it works.  Of course it’s more efficient because you don’t have to think, but in school, you are supposed to think.

Lastly, new math is better.  For example now people are learning harder things in lower grades.  I think this is because people can use more ways to solve problems.  Now new ways are always being made because people are encouraged to think freely and be let out by the chains of the old ways.

My conclusion is that even though the old ways are efficient, you can learn more by being free.  Sometimes mixes of old and new can be both mindful and efficient.

Pretty insightful for a nine year old, wouldn’t you say???