When the time came for Mr. Scientist to memorize his multiplication math facts, I did what everyone does, what you’re supposed to do> I got out the flash cards and printed off the timed tests. But this is what happened:
And no matter what I did, I couldn’t get him to memorize them. I only managed to make him mad and frustrated. I was at a loss, because he was really good at memorizing anything. Why couldn’t he just memorize the math facts and go one with life? I got mad, too. And we all know that no one learns anything when we’re mad. I decided I must be doing something wrong, even though I was following the formula that my teachers used with me, that everyone else still uses. Why wasn’t it working? I set out to investigate.
What I discovered
And I discovered three things:
1. It’s best to memorize math facts at five or six years of age. (Too late!)
2. I was teaching it wrong, making it WAY more complicated than it needed to be.
3. Memorizing math facts isn’t even math.
It’s better to memorize math facts at five or six years of age
If you follow the Montessori method from age three on, you easily learn the math facts at five or six years old, and that’s it. Miss Braveheart and Mr. Baby won’t have any problems with learning math facts in third grade; they’ll have done it long before. But since I didn’t know about the Montessori method until Mr. Scientist was five, and couldn’t learn it and implement it all right away…well, that’s how we ended up with a nine-year-old who still doesn’t know all of his facts. Miss Adventuress actually knows them better than he does, because she started using Montessori materials at an earlier age.
Why is it that young children can memorize math facts more easily? Because they are in the sensitive period for language, and it turns out that memorizing math facts is actually a language task, not a math task. More on that in a moment. But Maria Montessori recognized that, and designed materials that young children can use, and that they wanted to use, that resulted in memorizing math facts without the effort required from an older child. They learned them naturally, and joyfully. I don’t want to explain that whole process here, because I want to keep talking about what we do with a child who hasn’t memorized the math facts and is already in elementary.
According to the Montessori method, we don’t keep looking back, lamenting what should have been done earlier. We look at the child right now, we observe him to see what he needs, and we follow him, giving him just what he needs from us to be able to achieve his goals. We always follow the child.
I was making it too complicated
To me, the process of learning multiplication facts is super simple. You start with the zeros, and finish that table in about two minutes (or less!), you learn the ones (another two minutes), you continue to the twos, and you take a test to prove you know them. Easy. And for some of us, it really was easy. I never liked those mad minute tests in third grade, but they weren’t hard. For many, though, that is precisely the moment in which they realize they HATE math.
After investigating, I discovered I could hugely simplify the process of teaching math facts. Why would I even teach the zeros? Or the ones? Or the twos? There’s no need to waste time practicing those facts. We don’t need tests with 7 x 1, 9 x 0, 2 x 2. We just need to teach the property of multiplying by zero, and the identity property, and know basic addition facts to cover those three tables.
And then we can teach the commutative property of multiplication. If I know that 3 x 4 is 12, then I also know that 4 x 3 is 12. There is a Montessori presentation with the bead bars that shows this very simply and elegantly. That’s something I’ll share as part of this series. So, we don’t have to teach 10 or 12 facts for each table. Traditionally, we teach 100 or more facts that have to be memorized. But we only need to teach 28. TWENTY-EIGHT! The job already looks much easier, doesn’t it? In another post in this series we’re going to talk more in depth about why this is true, and what those 28 facts are.
Memorizing math facts is not even math.
Understanding what addition IS, how multiplication works, that IS math. But memorizing the three times table? That’s NOT. It’s the same as memorizing a list of presidents. Important, useful information that makes computing large sums and doing long multiplication easier…but it’s not math in and of itself.
I discovered this when I was reading a book about dyslexia, The Learning Brain: Memory and Brain Development in Children by Torkel Klingberg. Klingberg talks about neurological research that has been done that shows us that learning math facts is a language task. The part of your brain that activates during this task is NOT the part that activates when you’re actually doing calculations or when you’re reasoning about mathematical concepts. Instead, it is what neurologists call the letterbox. The same part that activates when you see letters. It’s the red area below labeled “visual word form area” in this diagram.
Image from the NCBI
That letterbox is in the same part of the brain for all humans. It doesn’t matter what language you speak, you use that letterbox to identify and understand the letters and words you see. And that same letterbox is the part of the brain that activates in order to learn and recall math facts. So, if you don’t know your math facts, it doesn’t have anything to do with your math skills or ability. Not even a smidge. Learning the multiplication tables is more like learning the alphabet and letter sounds than it is like learning the process of multipying or dividing.
If you don’t know your math facts, it doesn’t have anything to do with your math skills or ability. Not even a smidge.
I needed to make a change
Having discovered all of this, how could I keep using the same process to teach math facts to Mr. Scientist? The answer is simple: I couldn’t. He despaired of ever learning them and was resistant to my attempts to help, I was tired of fighting him, and we had to make a change. So, we did! I’m not going to claim that the process of learning math facts has turned into one of pure joy; that would be a lie. But it HAS greatly improved, and Mr. Scientist is finally learning his math facts!
We all know how important it is to learn the multiplication and addition math facts by heart. It makes long multiplication, mental math, division, all things arithmetic easier, and a good grasp of basic arithmetic is essential for continuing to more advanced math. Arithmetic is just a tool used to do math, but it is an important tool. So, it is worth stepping back to reevaluate the way we teach math facts, and changing it where necessary. We owe that to our children. I don’t want my son to hate math because I taught it incorrectly, and put too heavy a burden on him.
If you follow the plan I’m going to share for teaching math facts, I can promise the process will be much more enjoyable for your children or students, and for you, than the traditional methods. For example, you won’t have to give all those math fact tests! No more mad minutes! Less stress, more fun, more learning. That’s what I’ll offer you.
In the next post, we’re going to talk about how we’ve been making the task of learning math facts too complicated, and how it’s actually much simpler than you thought. I’m going to share those 28 math facts you need, and explain why those are enough to teach the facts through tens. (Or you can teach through the twelves with only ten more!) And there will be three more posts after that in this series, full of information and ideas. You’ll have what you need to help your children and students to memorize the math facts without tears.
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Want to know more about that letterbox and what neuroscientists are discovering? Here are some resources to get you started:
“Inside the Letterbox: How Literacy Transforms the Human Brain” by Stanlislas Dehaene
The Learning Brain: Memory and Brain Development in Children por Torkel Klingberg
The Number Sense: How the Mind Creates Mathematics by Stanislas Dehaene
Proust and the Squid: The Story and Science of the Reading Brain by Maryanne Wolf
Esta entrada también está disponible en: Spanish