Specific Teaching Ideas

Times Tables

(From Beechick’s HOMESCHOOL Answer Book)

“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 to 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 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 charty 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.”