How NOT to drill addition facts

Some people think "drill is kill", and many people think it's necessary.

And of those that use it, not everyone knows HOW to actually drill math facts effectively.

You know, this is NOT the most effective way:

Shuffle the flash cards and start asking randomly.

Why? Because you are not utilizing techniques that help our brain remember quicker.

For example, it is easier to remember when the mind can tie the fact into something already known.

This is the idea behind silly rhymes such as "five, six, seven, eight - fifty-six is seven times eight."

Besides those, we want to show our children the PATTERNS in math.

So this is how I start drilling math facts (whether addition or multiplication):

I make a list on paper, IN ORDER. For example, lately we've been doing this with my daughter:

8 + 2
8 + 3
8 + 4
8 + 5
8 + 6
8 + 7
8 + 8
8 + 9

We went through the answers and notice how each one is ONE MORE than the next! That's a pattern!

Then I would point to a fact and say the problem so she'd both see and hear it (using two senses). You can additionally MOVE her finger on the chart with yours - so she's using three senses. This should help the auditory, visual, and kinesthetic learners all.

When I'd point to a fact further down the list, automatically she'd know it's more than a fact that is up on the list. It's a visual pattern.

First, I drilled just a few of them, namely 8 + 3, 8 + 5, and 8 + 8 until she remembered those.

After that, I would go first to 8 + 8 which she knew, and immediately after that to 8 + 9, and she was able to deduce it from knowing 8 + 8.

I would gradually add new facts in a similar manner - using the known facts as "stepping stones" so that the new fact was one more or less than a well-known fact.

And so we go "round and round" on this chart.

= > The chart creates an organized context for the addition facts.

Obviously, the child is also associating the position of the fact on the chart with the answer, and so after this is well remembered, it will still take another effort to remember the facts when they're in isolated context, such as in a game, or in a math book, or on flash cards.

But at least it is a very good start, I feel!

What are your thoughts?


Hanley Family said…
Very true...thank you for sharing.

We teach math facts similarly (although my daughter does do a simple worksheet of 25 random problems every day because she just likes that sort of thing!).

I really enjoyed the day she "got" nines. I can't remember what she actually said because it didn't make a lot of sense on its own. But it was apparent that it was dawning on her that 9 plus a number was the same as 10 plus the number minus one.

I don't know that she would have gotten it (especially on her own) if I just drilled without any pattern to the teaching.
It's worth looking into what John Van de Walle has to say about how to teach and reinforce math facts. My take is that you're on the right track. Teaching the doubles would be where I would start, along with the "one more thans" and then the "two more thans" (and one less than and two less than, later, as subtraction is broached). Then, have the child try to "construct" (am I allowed to say that? :) other facts from the ones s/he already knows. Using commutivity reduces the number of facts in addition one needs to memorize almost in half, and you'll be very pleased to realize that the student is doing more than mere rote, but is nonetheless getting tools for quick recall. Then, using what has been effectively memorized will always become the ground upon which to recall any temporarily forgotten facts. It's how I do it and have for 50+ years: if I get "stuck" on something (like 9 x 6) I can use several simple strategies for recalling it correctly rather than having to panic. Lack of panic is a HUGE benefit in most things. :)
HowGreatADebtor said…
I have used "logic patterning" to teach some of my kids the math facts.
Click on "addition" or "multiplication." I love these ideas--they've helped me learn some of the facts I had forgotten through lack of use.

I never heard the "five six seven eight" rhyme. That's a good one! Thanks. :)

In grace,
Colleen M.
David said…
I agree that recognizing patterns is very helpful in memorizing the math facts. However, when I wrote a computer program to teach my kiddos I quickly changed from ordered to random because when the problems were ordered, the kiddos would just count and would not memorize the facts.
Having said that, your post makes a lot of sense and I'm thinking about going back and make it so the user can choose which way they want to see them when learning (ordered or random).
Shameless plug: I had such great results from using my program that I decided to share it with the rest of the world. Check it out!

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