QUESTION:

I have been asked to help my grandson memorize the addition tables. If I ask him what is 8 + 5, I watch him doing it in his head. He gets the right answer but takes a long time, which may hurt him later when he is introduced to multiplication. Do you have any suggestions?

MY REPLY:

Great question.

Without knowing your grandson, it’s impossible to know what he is doing when he takes some time to figure out addition facts.

But I’d suggest is that you just ask him — in a happy and curious way — what thought steps he is going through.

You can tell him that you’ve heard that students do mental math in different ways, and that you’d be interested to know how he is doing it. You might also want to reassure him that there is no “wrong” way to do math in your head.

[Be aware: some children have trouble verbalizing what they’re “doing” when they do math mentally. If your grandson has trouble telling you, you might prompt him by asking if he’s using either of the strategies I describe below.]

It may be that your grandson is trying to retrieve a memorized fact, but it’s more likely that he is using some kind of mental operation to arrive at the answer.

For example, it may be that he is “counting up” 5 from 8, to get to the answer. (If so, it would be commendable that he can count up 5 in his head — without using his fingers. Not all students can do this.) It’s also possible that he is taking 5 from the 8, and giving it to the first 5 to make 10, and then tacking on the extra 3, to get to 13 (an advanced strategy).

The main point, though, is that you can’t know till you ask him.

And the other point is that it’s often fascinating to open up a dialogue like this with kids, to find out how they do mental math.

Once you get the dialogue underway, I’d suggest that you just follow wherever it leads. For example, if your grandson is using the second strategy I mentioned (making 10 and adding on), ask him if he can extend the process a bit, and do problems like 18 + 5, 28 + 5,

etc.

If, on the other hand, he is “counting up” 5 from the 8, see if he can use the second method, too.

Essentially, what you have here is a great opportunity to find out how your grandson does addition, and to explore the operation with him. And have fun doing it.

Please feel free to write back if you do open up this kind of dialogue. I’d be curious to know what happens.

And to get to the heart of your question, I would say: Yes, you do want your grandson to develop speed or “fluency,” as teachers like to say. But when he is first learning the facts, it’s critical that he think about the operation, not just memorize facts.

To help him gain speed, I would suggest that you use flash cards or fact worksheets (just google math addition worksheets, and you’ll find loads of them).

And to help him develop a range of good strategies to help him learn the facts with understanding,

I suggest the Facts That Last series by Creative Publications.

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