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There is no “Right” way

Is there one right way to harvest all of these tulips?

Should you start from the right? Should you start from the left? Should you collect in groups? Am I asking crazy questions?

Now look at this addition problem:

Is there a “correct” method to solve this problem?

Should you start from the right? Should you start from the left? Should you collect in groups? Am I asking crazy questions?

If you have never had formal or informal instruction about teaching math you might be thinking “‘Yes Jenny! You are asking crazy questions!  Just start from the right!”

That’s what I used to think over ten years ago before I first started learning about teaching math from a Constructivist point of view. Ten years ago I would have taught children to draw a bunch of lines and junk and crank through the traditional algorithm. Yes, they could learn to do that. NO WAY would they ever be able to solve a problem like this quickly and accurately in their head.

It took me almost ten years as an adult to unlock my brain from “the right to left method”.

But kids can learn multiple methods with high accuracy in just a few years, if they have a good teacher who holds off on teaching traditional algorithms until the students actually understands math.

Here is what that type of teaching might look like. If this is new to you, hold onto your seat and prepare for the crazy.

Notice that the problem is written horizontally instead of vertically. If you want your kid to be good at mental math then you have to present problems to them horizontally at least as often as you present them vertically. If you think that the best way to solve problems is by stacking them vertically, then that is your first problem! Maybe the best way is to stack the problem vertically, or maybe not. Strong mathematical thinkers could do the problem either way.

But if horizontal is hanging you up, let’s go vertical:

I’ve seen this method called the “Sum All Totals” way and I think that’s pretty cool. Kids who learn this method really understand that the “4” is really 4,000. That “3” is really 300. etc.

Now let’s go mental:

Start at the left, look to the right, reassess your answer, and keep moving.

If this is new to you, you might need to stare at that last picture a really long time.

Now for the sad part…

Remember how I told you it took me about ten years before I learned to unhook my brain from borrowing and carrying and get good at other methods?

That’s because traditional algorithms are like row-boats. They help you get over really big waters.

It’s super easy to teach a swimmer how to climb into a rowboat. It’s super hard to teach a non-swimmer how to climb out of the rowboat and learn to swim.

No mom would send a non-swimmer into the ocean on a rowboat and say “Look! My kid is water safe!” But lots of people mistakenly think that children who can crank out algorithms “know math”. Maybe they do, maybe they don’t.

I’d like to close with a comment Crimson Wife left on my blog earlier this week that illustrates a lot of what I just said. She’s in the enviable position right now of teaching her super swimmer son how to climb on the rowboat. I’m guessing it’s not going to take Rusty 10 years to learn, like it did me!

Crimson Wife says:

The funny thing is that I’m currently fighting with my almost 7 y.o. to NOT use mental math because he’s working through a section in his Singapore math book where they are having the student practice the traditional algorithm. I finally had to pull a worksheet from my older child’s pre-algebra program where the task was to add three 5 digit numbers. The numbers were so big that my DS couldn’t just use the mental tricks but had to use pencil & paper.

How’s that for inspiration?

Math Boot Camp for Moms, Day 5

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