After teaching co-op math classes for several years, I’ve become known as the local math maven. Upon meeting one of my children, fellow homeschoolers often say, “Oh, you’re Denise’s son/daughter? You must be really good at math.”
The kids do their best to smile politely — and not to roll their eyes until the other person has turned away.
I hear similar comments after teaching a math workshop: “Wow, your kids must love math!” But my children are individuals, each with his or her own interests. A couple of them enjoy an occasional geometry or logic puzzle, but they never voluntarily sit down to slog through a math workbook page.
In fact, one daughter expressed the depth of her youthful perfectionist angst by scribbling all over the cover of her Miquon math workbook:
- “I hate math! Hate, hate, hate-hate-HATE MATH!!!”
Translation: “If I can’t do it flawlessly the first time, then I don’t want to do it at all.”
Measuring Math Success
I don’t judge my success as a math teacher by whether my students enjoy the subject. Neither do I care much about the traditional measures of mathematical success. I don’t train my children to regurgitate the math facts, and I avoid any sort of timed drill. I’m not interested in how well my children perform in the artificial environment of a standardized test.
How, then, can I tell whether my kids are learning math?
I talk to them.
And I watch them as they live their daily lives, keeping my eyes open for clues:
- Do my children expect math to make sense?
- Can they explain their reasoning?
- Do they panic at multi-step calculations?
- Do word problems scare them?
Thinking like a Mathematician
Students who are learning math the mathematician’s way will struggle with some topics, as all students do, but they possess an overall expectation that math concepts should fit together logically.
While they may occasionally get by with memorizing how to solve a certain type of problem, they recognize the danger of relying solely on memory. Their minds will continue to stew over the ideas — either consciously or at a subconscious level — until they get that “Aha!” feeling when it finally makes sense.
Because they are convinced that math is not arbitrary, these students know that they are capable of figuring things out. When a math problem seems particularly tough, their natural stubbornness kicks in: “No stupid math book is going to get the best of me!”
They may stumble, or make careless errors, or forget what they learned last month — or even last week. But they know that a generous application of common sense will carry them through almost any mathematical encounter.
Preventing Math Phobia
Math anxiety is epidemic in our society. Above all else, my goal as a homeschool math teacher is to inoculate my children against this disease.
Therefore, my number-one yardstick for measuring success is this:
- My children do not fear story problems.
Even if they aren’t sure how to solve a word problem, my children never stare at the math book with a deer-in-the-headlights expression or ask me random questions like “Do I add or multiply?”
After all, they’ve been creating and solving story problems for longer than they can remember. Why should they be afraid?
What About Testing?
As education reformer Jonathan Kozol once said, “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?”
The only thing that a standardized test can tell you about your child is whether that child is good at taking standardized tests. Each student’s test performance 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 questions 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.
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.
Check Your Foundations
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.
Congratulations, and keep up the good work!
This article is an excerpt from my book Let’s Play Math: How Homeschooling Families Can Learn Math Together, and Enjoy It!