## A Case of Mistaken Identity: Arithmetic and Mathematics

Years ago, a cartoon in the *Chronicle of Higher Education* jumped out at me. I ended up using it frequently in workshops with teachers for the rest of my career.

Here’s the picture: A traditionally stereotyped matronly female teacher sits at her traditionally stereotyped desk (in the front center of the room), watching a traditionally stereotyped Johnny do some arithmetic problems on the blackboard (Remember those?). She is frustrated and scolds him “Your math skills are horrible! How do you expect to get a job in you can’t add and subtract?” Little Johnny answers brightly, “No sweat! I’m going to be a Congressman!”

Many of us will laugh (and/or cry?) at that cartoon, but, in my opinion, the humor is masking a case of mistaken identity. And it’s one I worry is still prevalent today.

The mistaken identity is this, in six short words: Math and arithmetic are not identical. We’re broached this topic before, but it’s always worth another visit from a new angle. The importance and ramifications of this mistaken identity cannot be understated.

Naturally, of course, *arithmetic* is a part of *mathematics*. But the two subjects are not interchangeable. Any more than punctuation and skillful writing are interchangeable. For countless years, there grew up this impression that mastering six to eight years of paper/pencil arithmetic (that is often timed!) is what mathematics is about. Does this impression still linger?

This wasn’t such a terrible mistake ‘back in the day’, when higher math necessarily required great deals of calculating, and our jobs in the workplace often required extensive shop-keeping skills without the benefit of a calculator. Knowing one’s times-tables was more than handy – it was practically necessary.

Clearly, however the world and the workplace have changed – drastically. And because of that, the classroom – and the mathematics skills taught there – are necessarily changing too. But not always as fast. Do we really want, for example, to spend much – if any – time anymore on learning times-tables and other purely arithmetic procedures? When was the last time those were used in the workplace, especially where time is money? It’s not unlike continuing to spend class time learning to saddle a horse so that one can travel later.

Not only has the world changed, but so have the basic skills needed to survive in it. We need to focus on helping our students learn to tackle and solve problems, using the tools they have at their disposal. This is NOT minimizing the necessity of learning important skills. It is instead to reinforce that nowadays, almost 2 decades into the technologically oriented 21^{st} century, we need to be sure to know what those skills are.

Perhaps I’m out of date to think this mistaken identity still exists. I hope so. But every time I hear the careless phrase “do the math!”, I wonder. Math and arithmetic are related, but one is not the other.

So, let’s return to Johnny, our aspiring Congressman from above. I don’t believe Johnny will be an effective congressman without having a good working knowledge of things like statistics, estimation skills, problem solving, interpreting graphs/spreadsheets, handling data, and even number sense. (How many of our politicians really know the difference between a billion and a trillion?)

But I do believe Johnny can learn and use these skills successfully, whether he remembers (or even learns) his 12-times tables, e.g. And that fact continues to have increasingly pertinent implications for the classrooms of our community and our nation.