Homeschooling Math: Start Where You Are

There’s a well-known quote attributed to tennis champion Arthur Ashe (and to President Theodore Roosevelt, and probably others):

“Start where you are, use what you have, do what you can.”

How does this apply to learning math?

Many homeschoolers fear that their students have fallen behind grade level in math and worry about how to catch up.

We have an educational myth that math is a steady progression of topics arranged by ever-increasing complexity with regular signposts like mile markers that identify what students must learn at each stage along the way.

For example, first-grade students can add one-or two-digit numbers, but three-digit numbers are beyond them. Second-grade students can add three- or four-digit numbers, but never wander off into millions and billions. And so forth.

That is one valid path to learning math.

But it is also true that you can delay teaching formal math, and your children will pick it up quickly when they’re ready. A middle-school student can leap from 3 + 4 = 7 to 3 million plus 4 million = 7 million, and 3 fourths + 4 fourths = 7 fourths, and even 3× + 4x = 7x, all in a matter of minutes.

That is also a valid path to learning math.

Another valid path, one which surprises many people, is that students can begin by playing with algebra and then later mix in numerical calculations. (See the earlier posts on math manipulatives and big ideas.)

This is why I often say math is more like a nature walk than like climbing a ladder rung by rung. You can take off exploring in any direction. As long as you take the time to make sense of each new idea you meet, you are going to make progress in learning math.

Start where you are.

Don’t worry about where you think you should be. There is no “should” to learning math, there is only each person’s journey of reasoning and building mental connections.

As I said last week, a textbook is like a roadmap, showing some of the places you might go on your learning journey. But you are in charge of the adventure, deciding where to visit, how long to stay, and when to branch off on an unexpected side trip.

Use what you have.

Don’t worry about memorizing someone else’s method. “Do what I told you” is the most tedious and boring way to learn any subject.

If you don’t know how to solve a particular math problem, that’s great! That means you have a puzzle to figure out, and figuring out puzzles is fun.

Do what you can.

Take the time to Notice, Wonder, Create:

• Notice the details about the problem, how it is similar to and different from puzzles you have seen before.

• Wonder about the similarities and differences and what patterns they might lead you to discover.

• Create a deeper understanding of the problem as you make connections between the things you noticed and wondered about.

Perhaps you will create a solution to your problem. Perhaps you will create an insight that may help you solve more problems in the future. Or perhaps you will create new questions to ask, a new awareness of the boundaries of your understanding.

Either way, you have done some real mathematics. You have grown as a mathematical thinker.

And that is the best path of all, because it is your own.