# How Can I Teach Math If I Don’t Understand It?

Our childhood struggles with schoolwork gave most of us a warped view of mathematics. We learned to manipulate numbers and symbols according to what seemed like arbitrary rules. We may have understood a bit here and a bit there, but we never saw how the framework fit together. We stumbled from one class to the next, packing more and more information into our strained memory, until the whole structure threatened to collapse. Finally we crashed in a blaze of confusion, some of us in high school algebra, others in college calculus.

## Homeschooling with Math Anxiety

Yet even parents who suffer from math anxiety can learn to enjoy math with their children. All it takes is a bit of self-discipline and the willingness to try.

• If you are afraid of math, watch your tongue: Don’t let a discouraging word pass your lips.
• Pretend like math is the most exciting topic in the world.
• Encourage your children to notice the math all around them — numbers, patterns, shapes, and symmetry.
• Curl up together on the couch to read a math book, or tell math stories at bedtime.

The secret to teaching homeschool math may surprise you: We parents need to learn how to think like a mathematician. Mathematicians avoid busywork as if it were an infectious disease. Mathematicians always ask questions, and most of all, they love to play.

We’ll look at each of these characteristics over the next few blog posts. If homeschool parents cultivate these mathematical ways of thinking, we will help our children to recognize and learn true mathematics.

## Mathematicians Are “Lazy”

Mathematicians are not indolent, but economical with their time and energy. They have too many interesting topics to study and not enough time to learn about them all, so they cannot afford to waste their time on mindless busywork.

Mathematicians are always looking for a simpler way to do things. Skip counting is faster than addition; multiplication is even easier. Algebraic functions are shorthand ways to say things like, “Take any number you like and multiply by five, then subtract four and divide by seven and add one.” Calculus lets engineers solve problems that would be impossible without it.

To list out all the possible solutions to a problem may be impossible, so mathematicians invented special ways to think about counting. Permutations let us count the possibilities for when the order matters: “How many different ways might we award the 1st, 2nd, and 3rd place prizes in a race?” Combinations count the ways to do something when order doesn’t matter: “How many different three-person committees might we choose to plan the party for our homeschool co-op?” Both types of puzzle can be fun for middle school or older students.

Update: Ben Orlin gives a great demonstration of mathematical “laziness” in 1.2 Trillion Ways to Play the Same Sudoku.

## Thinking like a Mathematician

When we look at education through the lens of mathematical laziness, we will be skeptical about the value of repetitive practice problems. If our children keep forgetting how to do certain calculations, perhaps they are not yet developmentally ready to learn them.

One of the biggest problems in math education is how often teachers train students to do “number tricks” the same way we would train a dog to fetch or roll over, by having them repeat the procedure until they can do it without thinking. Children will master the math better if we wait until they have developed a foundation that will help them understand why it works.

In the meantime, there are ever so many interesting ideas we can explore together. Homeschool parents who think like mathematicians will always make time for the fun stuff.

CREDITS: Homework photo (top) by wonderferret, and Game night photo (right) by University of the Fraser Valley, both via flickr (CC BY 2.0). This post is the first of three in my Homeschooling with Math Anxiety Series, which 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.

Want to help your kids learn math? Claim your free 24-page problem-solving booklet, and you’ll be among the first to hear about new books, revisions, and sales or other promotions.

## 8 thoughts on “How Can I Teach Math If I Don’t Understand It?”

1. Love your definition of “thinking Ike a mathematician.” I will share this with my students as well. I already often refer to mathematicians being lazy, hence multiplication instead of repeated addition and exponents instead of repeated multiplication, but there’s lots more to it 🙂

2. Interesting. I’m with you that mathematicians are lazy – or we can say they optimize. Many are lazy that way. I got here off your Devlin link to his Coursera site. I’m interested in finding out how mathematicians think, but I don’t think I could handle that much of Prof Devlin … even a couple of his blog posts wear me down 🙂 I have my own views on how logical people should think, and was going to try to do a series on that myself sometime. Thinking both logically and freely is pretty hard for some people.

3. Jennifer says:

I need to disagree about mathematicians being lazy. Far from it – mathematicians work for many hours, days, and even years attempting to solve a single problem! However, mathematicians do not like to waste time, so they invent symbols and algorithms to avoid mundane tasks. Laziness is a negative trait, and it passes on negative connotations!

4. Yes, Jennifer, you are right. “Lazy” was an attempt at hyperbole to which several readers have objected.

5. I totally agree with you about how teachers should wait and let students find how a math concept works..

6. Too often adults want to give a child the same abstract rules that we remember from our schooling–that is what we think “math” is all about. Thus many people argue against delaying formal arithmetic because they think that waiting until children are developmentally ready means skipping early elementary math entirely, a form of educational neglect. But there are plenty of hands-on, playful investigations of number and shape that children can explore which will build a foundation of knowledge and become a strong support for future understanding.

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