*[Feature photo above by Alberto G. (CC-BY-SA-2.0) via flickr.]*

The school experience makes a tremendous difference in a child’s learning. Which of the following students would you rather be?

I continued to do arithmetic with my father, passing proudly through fractions to decimals. I eventually arrived at the point where so many cows ate so much grass, and tanks filled with water in so many hours. I found it quite enthralling.

— Agatha Christie

An Autobiography

…or…

“Can you do Addition?” the White Queen asked. “What’s one and one and one and one and one and one and one and one and one and one?”

“I don’t know,” said Alice. “I lost count.”

“She can’t do Addition,” the Red Queen interrupted. “Can you do Subtraction? Take nine from eight.”

“Nine from eight I can’t, you know,” Alice replied very readily: “but—”

“She can’t do Subtraction,” said the White Queen. “Can you do Division? Divide a loaf by a knife — what’s the answer to that?”

“I suppose—” Alice was beginning, but the Red Queen answered for her. “Bread-and-butter, of course.”

“She can’t do sums a bit!” the Queens said together, with great emphasis.— Lewis Carroll

Through the Looking Glass

…in other words…

If you could lead through testing, the U.S. would lead the world in all education categories. When are people going to understand you don’t fatten your lambs by weighing them?

— Jonathan Kozol

at Westfield State College’s 157th Commencement

### What Good Are Tests?

*[Photo by Renato Ganoza (CC-BY-SA-2.0) via flickr.]*

I don’t know whether standardized tests actually provide much information about individuals, other than whether the student is good at taking standardized tests. Tests can let us accurately compare large groups of similar students — but if that was all the testers wanted, why require the students’ names?

So much depends on:

- reading speed, which varies tremendously from student to student
- whether the student has the sniffles
- or had an argument with Mom and Dad the night before
- or gets easily bored and decides to play “random dots”
- or finds the reading passages interesting or not
- or has indigestion
- or forgot to eat breakfast
- or is taking the test in a familiar or unfamiliar setting
- or is worried about a sick pet
- or…well, so many things.

I’m always grateful if my students do well on the tests, because that can forestall problems with authorities or extended family, and good test scores will eventually help with college admissions. But I’ve never, ever felt the scores gave me any information I didn’t already know from working daily with the student.

### Be Prepared

If you live in a state that requires standardized testing, or if you want to see the test scores to satisfy your own curiosity, please don’t let that affect your attitude toward math education. Keep playing around with math the mathematician’s way — and add test preparation *as a separate area of study*. Work through one or more test prep books in the months before a high-stakes standardized test. There are many factors we can’t control, but at least we can make sure our students are as familiar as possible with the test format and the types of questions they will see.

But if you want to know how well your homeschool math program is working, don’t worry about testing. Pay attention to your children:

- Do they understand that common sense applies to math?
- Can they give logical reasons for their answers?
- Even when they get confused, do they know that math is nothing to fear?

If so, then be assured: your children are already miles ahead of most of their peers. Their foundations are solid, and the details will eventually fall into place as you continue to play with mathematical ideas together.

### Update

Check out this post: How to “Teach to the Test”.

This post is an excerpt from my book * Let’s Play Math: How Families Can Learn Math Together—and Enjoy It,* now available at your favorite online book dealer.

Wow, I can’t believe no one has commented on this right-on-target post yet. Kozol’s imagery impressed me, too, along with your thought that, “Tests can let us accurately compare large groups of similar students — but if that was all the testers wanted, why require the students’ names?” I never thought of that before. GREAT argument.

Brian (a.k.a. Professor Homunculus at MathMojo.com )