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The Value of Place Value

Value of Place Value

Place value is a marvelous invention in math.

But in America, we don’t seem to take advantage of it.  (The reason I say “in America” will become clear in a moment).

How many digits do we use in math?

You probably never stopped to think about it.  No matter how big a number you deal with, we only use 10 digits…0 through 9.  That’s why it’s called a “decimal” system – it uses only 10 digits.

So we can have a national debt of billions of dollars and still describe it with only 10 digits.  Pretty powerful, don’t you think?

So what’s the big deal?  Why is this important?

It’s important when we teach someone to do the four basic operations – addition, subtraction, multiplication, and division.


The answer is very simple.  When we teach these operations, there are only three things you need to know to do all of them…no matter how big the numbers are:

  • The basic facts for addition and subtraction
  • The basic facts for multiplication and division
  • One basic principle about how place value works

For example, what if you were to add these numbers?  What do you need to know?


First, you need to be able to recall from memory the sum of all the basic facts for single digits (although only some of them are used in the two problems).

Second, you need to understand one concept about place value – when you use all the digits in one place, you add one to the next place to the left (just like the odometer in your car).

And that’s it!!!

Try it.  You’ll see what I mean.

How hard should that be to learn?  In America, we seem to make it harder than it should be.

One reason is that for well over 100 years in America, math educators have argued fiercely about how to accomplish the first requirement – memorizing the basic facts.

Seriously?  100 years?

You’d think after that long cooler heads would have prevailed.  But sadly, that’s not the case.  We continue to fight like crazy over this basic issue.

It’s gotten so bad that in the past 20-30 years, there’s even been a raging debate about whether these facts should be memorized at all!

Who loses when we fight over things like this?  Of course, it’s our kids and grandkids.

The result is many generations of people who now love to proclaim “I hate math.”

So why is this just a problem in America?  Doesn’t everyone have the same requirements?

Yes, they do.  But they handle it differently.

First, they introduce the place value concept earlier than we do in America.

Second, they use different methods to memorize the basic facts.

That’s it.  But it works!

Students in countries like Japan, Korea, China, and others have outperformed students in the U.S. by the end of first grade on many international tests.

That’s why I implied that this is an American problem.  It is.

So why haven’t we looked seriously at how they do it in those countries?

Hard to say.  But some people have looked into this issue, including me.

I’ve come to three conclusions.

First, not enough people are aware of the alternative approaches that are available yet.  It’s still largely ignored.

Second, when we look at things like this, we tend to see what we want to see.  In other words, we interpret the facts differently, depending on what our bias is.

Last, there is a huge opportunity to improve how we teach these topics in America.

My goal is to try to shed more light on this subject.  The more people who know about the issues, the better off we’ll be.

Stay tuned for more.


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Dr. Robert Collins

Bob Collins is a former college professor and research scientist in the Psychology of Learning at Florida State University and Georgia Tech. For the past 30 years, he has been a successful entrepreneur with multiple companies specializing in instruction delivered via the computer and internet. He is the founder and CEO of iLearn, which provides online instruction in math for K-12 schools, parents and students at home, and college developmental math since 1989.

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