## Memorizing Math Facts—is it really necessary?

In today’s society with computers and calculators ready at everyone’s fingertips—is memorizing math facts really that important? To be clear, we are not talking about whether students should spend a lot of time practicing calculation. While one could make a case that a lot of practice getting fast at long division, or even accurate at long columns of addition problems, is no longer valuable, quite the opposite is true for memorization of single digit math facts. Memorizing math facts is probably even more important today than it was 50 years ago.

Using calculators and computers to do complex calculations for us is smart. That’s why a lot of time practicing how to do this by hand may no longer be necessary. Using a calculator saves time and it’s more accurate—except when we make an error in data entry or in the formula we have used to do the calculations. At that point, we must have already done a quick and unconscious mental calculation of the probable answer, so that we see the error. Catching errors in a calculator’s answer requires a ready knowledge of math facts. If you can’t catch your calculator errors then you’ll continue to make more and more of them. Furthermore, if you must use a calculator to compute single digit math facts (because you don’t know them) you will be incredibly inefficient at all math operations. So the ready availability of calculators makes the need for quick mental math facts more important than ever.

Another reason for knowing math facts fluently has to do with fractions. Understanding the manipulations of fractions that should be learned in upper elementary or middle school depends upon automatic recall of multiplication facts. Students who don’t know the multiplication facts fail to see when they should reduce facts like 8/24 or 12/16. They don’t recognize that 6/9 and 16/24 are equivalent fractions, or see why they are when it is pointed out to them. They struggle figuring out the lowest common denominator between thirds and twelfths, let alone between thirds and fifths. Many children are doomed to failure in learning fractions, decimals and percents simply because they lack a fluent knowledge of multiplication facts and the relationships built upon them. That failure makes it nearly impossible for them to succeed in algebra. And we all know that if you can’t “pass” algebra your chances of getting into a four-year college are slim to none.

Instantaneous recall of math facts is also important because it enables students to see patterns in numbers. We know that recognizing patterns is essential in math, but few teachers realize that recognizing patterns in numbers is dependent upon knowing math facts. The pattern 2, 4, 8, 16, 32, 64 is readily obvious to students who know the multiplication facts—but not at all obvious to those who don’t. The pattern of 49, 40, 32, 25, 19, 14, 10, 7, 5, 4 is obvious to students who can mentally subtract, but not to those who can’t.

So there are several reasons that knowing math facts to a level of automaticity is important to future success in higher levels of math. But is it really necessary to embark on an organized process of memorization? Won’t students just naturally become more and more fluent with the facts—once they’ve learned how to figure them out? The answer is no for many children. Because there is less emphasis on calculation in today’s math, students have less opportunity to practice using math facts on arithmetic worksheets than children did 50 years ago. Without practice to build up that immediate recall it becomes more important than ever to have in place a good method of memorizing those facts.