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What About Math Facts?

In this article, best selling author Dr. Ruth Beechick answers several common questions concerning teaching mathematics.


Q.  Do you have an idea how we should teach the times tables?

A.  I think it's important to work by the principle of building understanding, rather than using rote memory only. Within this principle you can operate with any number of activities. Usually they will involve manipulatives, at least for a time.

To illustrate, I'll tell about a class I taught. I gave them all counters, which in our case were colorful, coin-shaped game chips. Then I demonstrated how to figure problems with the counters. For instance, for 2 X 8 the children made two piles of eight and counted them all to obtain the answer 16. After a few such problems they could proceed on their own working problems from their books.

After a time I suggested that they could write some answers on a sheet and refer to the sheet instead of counting repeatedly. So they wrote, for instance 2 X 8 = 16, and looked at their paper each time they needed that answer. They were happy to "cheat" like this and do their problems faster, but of course the sheets soon became a cumbersome jumble. Also, of course, they were memorizing some facts and didn't need either counters or sheets for those.

One day I showed a boy how he could make a row with all the answers for 2 times something. We numbered from 1 to 10 across his paper, put 2 at the left below them and then put each answer under its number. He was excited at the great shortcut, so I said, "You could make a row for 3s under that, and then 4s, and keep going if you want." He ran to his seat and filled out a whole chart of times tables, using his counters when he needed them. Then he bounced around the room excitedly showing other children how it worked.

Soon everyone had made a chart and were not using counters anymore. By then they also had memorized a lot of facts, and we could talk about how it was faster to do problems with the facts in their heads instead of referring to their charts. That's when we began memorizing the facts they still needed to learn.

At this point the job is not overwhelming, because you can have flashcards or practice sheets with just the facts your child needs to learn. Even here, try to avoid simple rote memory. For instance, learn a new fact by relating it to a known fact. If the child knows what five 5s are, then figure from that what six 5s are, and so on. Work on a few facts at a time. Review and practice and review.

I hope this illustrates the principle of building meaning before working on memory. Children using this approach should understand when they are memorizing 6 X 7 = 42 that it would be six piles of 7.

Q.  Is memorization of times tables important? What is a good method to teach them?

A.  There is almost universal agreement among educators (and parents) that children should memorize the times tables and other basic arithmetic facts. The best approach is to first build a good foundation of understanding and visualizing before working on the memory. For one suggested method see the preceding answer.

Q.  We've tried everything to teach our 9-yrear-old son his math facts and they just don't stick? What would you recommend?

A.    This could be because he learned the facts by rote memory without good understanding or inner visualization of what happens with the numbers. I would guess that he has no trouble with 2 plus 2, or with 2 times 5. The difference between those and more difficult facts is that those are easy to visualize. So work at making the others easy, too. Play dominos. Count by twos, by fives, by other numbers. Count money by nickels, by dimes. Observe a dozen eggs. Count them by twos. How many in half the carton? In one-third? Use a number line or hundred chart with the activities suggested with them. Learn the doubles. Then learn the almost doubles: if 6 and 6 make 12, then what are 6 and 7? Learn that adding 9 to a number makes 1 less than adding 10 to the number.

After lots of such activities and visualization, your son won't need to "remember" the facts; he will see them in his head, or be able to figure them out. At that time he can sort out by flashcards or by tests which of the facts he can't answer quickly. Those few, then, he can memorize or think of ways to figure easily.


Q.  I hope you can help me determine whether math speed drills are effective in helping children learn their math facts. My son enjoys working math problems; when he can take his time and count the numbers. I would like for him to be able to memorize his math facts, so I give him a speed drill four or five times a week to practice. Will this repetition help him memorize them? I should mention that he really dislikes speed drills.

A.  I have never quite made up my mind about how much importance to attach to speed drills in math. Sometimes I think we value speed because children will score better on timed achievement tests or because it seems more virtuous than depending on calculators.

But your question is specifically about the effectiveness of speed drills in learning math facts. On this point, I think drills can be a little help at the right time. If your son enjoys counting out the numbers, I would guess that he is in the mental image stage of thinking about the math facts. That is, he needs to see in his head what is happening in the problems. I would not hurry him through this stage, but let him have lots of experience with the visualizing. This way he builds understanding of the facts he will later memorize. Later on, he should appreciate having a faster way to do his problems and may be more willing to do speed drills or games to gain that proficiency.

The repetition itself does not automatically help memorizing much, especially if you have too long a page of problems to do. To learn the times table of 3s, for instance, your son could drill just on that. If you're using flashcards you could put into a separate pile the ones that slow him down. Then he could work on those with his mind, not just with repetition. He could visualize that if five 3s are 15, then six 3s are 3 more, or 18. Or whatever helps the understanding. Then he can do the drill again and see his improvement.

If you can guide him in this kind of learning, which speeds up his time on a drill, you may find the drills become more motivating for him. But if he never likes the speed drills, I don't think it's any great loss. You can, instead, just require the memory of certain facts over the next couple of years and have him demonstrate his mastery at some minimum speed.

Dr. Ruth Beechick is a former teacher, professor, and curriculum developer. Now retired, she writes for homeschoolers whom she sees as the greatest hope for the future of our society.

This article is reprinted with permission of the author, Dr. Ruth Beechick. Excerpted from Dr. Beechick's Homeschool Answer Book, which contains answers on many topics.

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