I’m Tom and I hate arithmetic. (“Hi, Tom!”)
Let’s face it. Everybody hates arithmetic. It’s boring, mechanical, unnatural and an unfit occupation for a respectable human. We hate arithmetic so much that we’ve spent the past 40,000 years inventing things to do arithmetic for us.
Consider Stonehenge.

Up to 165 stones, about half of which were 18 feet long and weighed 25 tons.

There is no building stone in the area, so the stones had to be dragged from hundreds of miles away.

The entire construction took 30 million hours (about 1500 years).
All of this work and when it comes right down to it, it’s basically a big calculator. We hate arithmetic so much we will go to ridiculous lengths to avoid doing it. Worse yet, if you openly admit that you hate arithmetic, you’re shamed and ridiculed.
Math is not arithmetic but the way we teach both subjects doesn’t make this clear. Arithmetic is mainly memorization which is expected for something so mechanical.
“Here’s the times table. We’ll quiz you on it later.”
“Here’s the transitive property. Memorize it.”
The basic strategy for surviving arithmetic class is memorize, memorize, memorize. Then we get to math class and NOBODY TELLS THAT THIS ISN’T ARITHMETIC ANY MORE. Instead we’re given more things to memorize without any human context. Math is about creativity, imagination, intuition and seeing the patterns that go on all around us and trying to understand them. There’s none of this in a typical math class, much less a typical math textbook.
Let me put it another way. Let’s say that you like stories. You like to tell them, you like to create your own, you enjoy listening to others tell them to you. So you start school and you’re all excited because you’re finally going to learn how to write these great stories that you’ve been imagining.
You start out and learn about all of the letters. Some of the letters have special names (‘vowels’, ‘consonants’) and you learn them. You learn how the letters go together in words (spelling) and placing words in sentences (grammar). You memorize the structure of a sentence and all of the different parts (‘subject’, ‘verb’, ‘adjective’,’adverb’, ‘gerund’ [yeah, that’s a real thing])
Are we ready to write stories yet?
Nope, still got more stuff to memorize. Subjunctive, declarative, indicative, imperative, the difference between passive and active voice, between first person singular and third person plural, proper use of semicolons, dangling participles, prepositional phrases….
Okay, I’m officially exhausted and we’ve completely given up on our original goal to be able to write our stories to share with others.
A few years back I was teaching a PreAlgebra class for some adult learners and I had one older gentleman who was really struggling with the material. One day I had him come up to the board, work a problem and explain how he solved it. He got the right answer, but he did it in a way that I had never seen before. That’s when I asked him what he did outside of class.
It turned out he was a carpenter. He used math all the time, because you need math to create goodlooking functional pieces. When he was learning carpentry, he picked up the tools and techniques he needed in service to this. He knew what a correctly proportioned bookshelf that wouldn’t fall over should look like and feel like and the tools of math were just things he picked up on the road to that goal.
Math is about exploring the world around us and trying to understand why things are the way they are. Why do certain combinations of notes sound pleasant and others don’t? Why is the sky blue? How do I throw a stone to make sure it goes as far as possible? Numbers, proportions, sequences, patterns are around us all the time. We can see them and we’re compelled by our very nature to try and understand them. This is what math is about.
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