There’s a lot of talk about making sure kids understand what they are learning — instead of just practicing some arbitrary set of steps. I’m a proponent of this myself.
But how well a child grasps a concept is based on how well he or she connects with it.
The learning style and interests a child has has an impact on if (or how well) he or she will understand a concept. And, as far as I know, there’s no rule on figuring that out.
You keep explaining it in different ways until you see the “aha moment.”
Except there are some times when understanding is too far out of reach. Or the child’s way of learning requires a deeper understanding than what’s available or possible at that point.
So what do you do in those cases?
Do you delay teaching that piece for understanding? Do you go on to something else and skip it altogether? Can you go on to something else?
Before making that decision, consider three points.
1. Nobody understands everything.
The way all the pieces of math work together is amazing. Nobody knows how they all fit — even the most famous of mathematicians. Everyone has something missing. Some of us have much missing.
So if your child is lacking in understanding for a few things — or even many things — that’s okay.
2. There’s more than one way to “understand” something.
Take any math concept and you’ll find that the applications of it are vast. It’s likely that you can use it in business, in fashion, in your yard and kitchen and in the toy box. So you can explain the concept — and inspire understanding — with any of the applications.
You can also explain a concept with metaphors to other math concepts and even metaphors to non-math concepts.
3. But they’ll get it, eventually.
Back in 1998 I photocopied an article from an AMS Notices journal called “Eventually” by Marianne Freundlich. I laminated it and hung it on my office wall.
It’s moved offices a dozen times at least, but has remained an important reminder: “When learning something new, you may not get it now, but eventually you will. Just stick with it.”
The “fake it ’til you make it” principle works in math too. It’s okay for them to practice something that they don’t understand.
But kids need you to know they’re faking it.
Often kids fake their learning. But they’re also trying to fake out the instructor. It turns into a big dirty secret that they keep inside. Like this:
“Mr. Smith, I don’t understand this. I think I can do the problems, though.”
“Well, Joan, let me explain it this way…”
Mr. Smith explains another way. Joan feels uncomfortable because he’s spent so much time on her and she still doesn’t get it.
“Okay, I think I understand now.”
“I’m glad. It’s important for you to understand before we move on.”
Joan thinks she’ll just keep practicing and hope that something clicks before the test. She doesn’t want to ask for more explanation.
Fake it like Fermat!
(That’s supposed to be a play on “Bend It Like Beckham” — I’m not sure it works.)
A well known phrase in math graduate school is, “Okay, I don’t understand that, but I’ll go with it for now.”
Mathematicians fake it all the time. They come back later to see if they can work out the details (and don’t publish or approve of something until they do). But they announce out loud that they’re faking it.
And kids should be allowed this too.
“Mr. Smith, I don’t understand this. I think I can do the problems, though.”
“Okay, Joan, that’s fine. Perhaps after you do it a while, you’ll get it. “
“It’s possible.”
“No problem, if you don’t get it now, you’ll get it eventually. As we move forward, when you come to something like this, just keep doing the steps. That might help you understand, too.”
“That works for me. Thanks, Mr. Smith.”
“Feel free to ask me any questions about it and we’ll continue the conversation until you do get it.”
Not understanding is totally okay — but the child must know it. And, more importantly, they must know that you know it!
So let them fake it!
When understanding is too far out of reach, encourage some rote practicing of the steps. And let them admit, out loud, that understanding isn’t there — even be happy for it.
Anticipate the understanding and be excited that someday it will come.
And if your child wants to move on, do it. They’ll get that other stuff eventually.
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