# What is a Variable?

From David Wees: what do we mean by variable?

I see this as one of the huge barriers to high school math as middle schools transition from arithmetic to algebra–see Hung-Hsi Wu with a stellar presentation on these challenges.

Wu’s answer, which I like, is that, in K-5, math is about arithmetic–calculating and manipulating numbers. In 9-12, math is about algebra–learning what is true in general, for all numbers. This is oversimplified, but gets at the main difference. In 6-8, this transition needs to focus on what it means for a variable to represent numbers in general–this goes beyond memorizing what like terms are, or solving one-step equations. It means reasoning, and explaining that reasoning, in a question about generalities–solving a problem for one instance of a variable, then solving it again for a different instance of the variable. This is what algebra is actually use for, at a basic level (it’s why people don’t actually use math in the workplace–someone write a formula or creates a table, and does the math for the worker).

## 3 thoughts on “What is a Variable?”

1. howardat58

1. I have exchanged emails with Wu about basic math, and I like his ideas. (His book for teachers is rather heavy going and labored, however). I asked him “What can I do?” and he wrote back “Whatever you can, best of luck!”.
It seems to me that the CCSS is hell bent on turning arithmetic into algebra, even at grade 1, where they are expected to understand and appreciate the meaning of the equals sign and have to deal with equations.

2. I really like your getting the kids to put their axes where they like. This is real math. More complex problems can become horrible with a bad choice of axes, and the only way to find out is to do it, not to have it done for you.
Next step – transformations of the points, to modify the picture??

2. howardat58

I have exchanged emails with Wu about basic math and the mess it is in, and I like his ideas. (His book for teachers is rather heavy going and labored, however). I asked him “What can I do?” and he wrote back “Whatever you can, best of luck!”.
It seems to me that the CCSS is hell bent on turning arithmetic into algebra, even at grade 1, where they are expected to understand and appreciate the meaning of the equals sign and have to deal with equations.