Why Children Must Learn Their Times Tables
All Children Should Know This.
Remember this?
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
I do not remember exactly what age I was when I learned the times tables. Even for my children I do not remember exactly when they learned them. But they did learn them. And I think most of my children's schoolmates also learned them. When I say they "learned" them - I mean they memorized them. Ask me or my kids what is 9 x 7 and we know it is 63 right away.
Kids Today
Ask the kids I see in Ecuador today who are maybe 10 years or older what is 9 x 7 and I can tell what you will very often see: The child will start counting with his or her fingers "9" with one finger, "18" with two fingers, "27" with three fingers...up to 7 fingers. If they do it right they get "63". About half the time they get it wrong.
So what is so terrible about this? We have calculators now and we don't have to do this anymore - right?
WRONG!!!
First Problem - learning long multiplication
Look at this math textbook explaining how to do long multiplication. This is just a two digit problem. A three digit problem is much worse. If this is in the textbook it will probably be on the test! Try doing this problem without using anything from the times tables. Just the first step (9 x 5) takes a full minute (9, 18, 27, 36, 45). A students chances of doing this problem correctly during a test under time pressure is about zero.
Being unable to do something correctly and doing poorly on tests will affect the students confidence - and they will conclude "They don't like math". Compare this to a student who does know the times tables. They still have to be careful and do the steps correctly - but when they do they get exactly the right answer. There is a satisfaction that comes with seeing your answer exactly correct that becomes contagious. Real earned success builds confidence.
Second Problem - learning fractions
For a student knows the times tables well the explanation below of adding fractions will make sense. The student will understand the pattern that 1/3 is the same as 5/15 as both the numerator and denominator is multiplied by 5. But this pattern will basically be a big mystery if you don't know your times tables well. This problem occurs over and over with all textbook explanations of fractions. Adding fractions, multiplying fractions, finding the least common denominator, etc. If your child does not really know the times tables he or she is destined to being in a complete fog when trying to really understand lessons about operations with fractions.
I learned this firsthand recently when I was asked to help tutor a young man in mathematics. I had tutored math several times before for students learning geometry, algebra and calculus. So the students I tutored knew their times tables. But this young man didn't. And trying to teach him these two things (long multiplication and fraction problems) was not possible. I instructed the Mom she should take away all his social media devices until he learned the times tables. I never saw either of them again.
Third Example - Understanding science.
Look at this famous video of Carl Sagan explaining how Eratosthenes determined pretty accurately the circumference of the earth in about 200 BC. Being able to sit and listen to this and completely understand it requires you know that 7 degrees is about 1/50 of the a complete 360 degree circle (approximately). And 800 km times 50 is 40,000 km. You understand lots of things in this world quicker and more completely when you just know your times tables.
Just Learn the Times Tables
Just about any child can memorize the times tables. You can use flash cards. You can give them an ice cream if they learn one row of the table. Ask them questions at dinner time. I always taught my kids there is only one question that is a stupid question. Here it is:
"Why Do I Have To Learn This"?
Kids are literally learning machines. They learn incredibly quickly. They can learn just about anything. So even if you still really agree with everything I have said here - just have your kids learn the times tables. Do it this week.
This might seem unrelated but entertain me for a minute. This morning, I'm making myself some tea, watching some youtube vids of nerdy stuff to start up slowly. A nerd channel I follow (surprise to nobody) has posted a video about installing linux on a watch. I had to click.
The host, the owner of said channel is someone very technical, someone I enjoy watching too, but, I think today I lost so much respect for the guy, I don't know he could win me back.
He sets up the watch, right? All good in the hood as the kids used to say. Then, he finds a feature of watch faces, custom watch faces to be precise. He expresses how he loves the look, that he would use these instead of the numbers being displayed, but he can't tell time on a watch with hands. He says, without shame (that is what is shocking to me) that he can only read digital watches.
This is a grown up in America, mind you, who thought that its perfectly acceptable to be unable to tell time on an analog watch.
I'm sitting there thinking to myself. Who is the idiot here? Am I being an old fart? Is this guy not a functioning adult with a Youtube channel making a living? Do I have a leg to stand on?
So now, I'm divided right in the middle. On the one hand, I feel like the new generations are growing up without proper mental tooling (the soul of your post), but on the other hand, I wonder if it truly matters.
As I wrote that line, I'm already fighting back the notion that its Ok, because no matter how much I want to live and let live, it hurts my brain.
It really does truly matter.
Tell kids today that the time is "quarter to five" and many won't know what that means. You have to say it is 4:45.
And don't get me started on another pet peeve...understanding the magnitude of numbers. The illustrious Dr. Oz recently stated directly to Trump that due to some wonder drug of his Americans would lose 135 billion pounds. I mean this guy clearly has no sense of numbers. Nobody in the Trump MAGA world does.
For a good laugh you can watch this about it.
It's an uphill battle against a downhill trend. @tarazkp (who might find this post interesting) writes about similar topics frequently, how there's a whole generation being lost.
I love that we were taught the nitty gritty when we where young. Yes, we were allowed to use calculators - 10th grade and forward, when the "normal" education was concluded and we went to the heavy stuff, were numbers were obsolete and everything was in letters. We were allowed to use the calculator when it helped our efficiency and speed, but we also knew how to do it without.
LLM/AI poses the same threat. Even before it was hard for so many to express themselves correctly. Learning by correcting mistakes. Now, everything is sent through a chatbot first, corrected without any chance of learning, and done. Educationwise, we're rolling into dark times.
When I was at M.I.T (1974-1978) it was basically the dawn of the era of calculators. My dad got me an HP 35 my freshman year. (You know what reverse polish notation is?). Anyway - while this transition from the slide rule to the calculator was happening a professor at M.I.T. wrote a passionate essay about the benefits of the slide rule. His claim was that when you are faced with a calculation like "7.48 * 3.14159 * 19,700" on a slide rule you must first make some kind of order of magnitude estimate of the answer. The slide rule only gives you the digits of the answer. Something like "463". You have to use your estimate for example the result is between 400,000 and 500,000 to know this means the answer is "463,000".
By comparison many students today will type this calculation exactly as written and report the result as 462932.13604. This is wildly off in terms of the actual accuracy you have in the computation. At most you only have three significant digits in the "7.48" term. So here you should only report the answer as "463,000".
There is one other thing to be said for the slide rule. When you mistype something into a calculator and you have no sense whatever of what the magnitude of the answer should be, you tend to just accept the result. Any mistakes in the typing are not detected.
Which brings me to yet another pet peeve. When I was acting as a grad student at Duke and doing work as a teacher assistant I had to correct many students homework and exams. Many times I saw students turn in answers that could not possibly be correct. Answers off by many orders of magnitude, answers given in units that were wrong. I wish I had done more to really teach those kids to learn to review their own work before they turn it in.
Alas - the slide rule has gone the way of the dinosaur. But nevertheless it is worth remembering it's virtues today.
That's the counter argument - humanity is still here. Calculators didn't destroy it, and the economy is still prospering despite them!
But society isn't. And no, that's not the calculators fault. It's one little thing among the many that make us too comfortable and restrict us from thinking things through. From having that experience, that challenge, that blockade we need to get through. Life as surviving is getting easier and easier, thanks to technology. For some, that is necessary still. But for others, who live in over-developed countries, it's slowly destroying life.