What if every child could love math—and be good at it? Dr. Paul Shoecraft says they can. In his book Arithmetic Counts, he reveals how understanding (not memorizing) helps kids truly own arithmetic—and the confidence that comes with it. Tune in to hear how we can finally fix the way we teach math.
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Welcome to this edition of Newsgram!
The other day I was talking to a friend of mine about my lack of math skills. It’s amazing how often we rely on math in daily life—and how often I wish I’d learned it better. I still remember my grammar school math teacher telling us how important it was. But instead of focusing on the math, I mostly noticed his short fuse and how frustrated he’d get trying to drill concepts into my head like a third-world dictator.
High school wasn’t much better. Algebra was required, and for some reason, my brain just didn’t click with it. But maybe that’s the problem. There’s nothing wrong with my brain. It was the system. No kid is going to win the, it’s you not me argument, but in reality we were right because the way math is taught in this country has been flawed for generations and today, with the help of Paul Shoecraft, author of Arithmetic Counts, I’m going to prove it.
Paul Shoecraft – Arithmetic is a language. It’s a written language for describing numeric events precisely and precisely. Events like paying bills, making out a budget, or buying a car.
That is a glimpse into the solution he’s created but first let’s examine the scope of the problem.
According to the U.S. Department of Education, more than half of American adults lack the basic math skills needed to function effectively in daily life—including things like comparing prices, calculating tips, or understanding basic graphs and like me Paul Shoecraft has had enough. It’s time to fix this problem. And it starts by forgetting about memorization—pun intended.
Paul says we have to look at things differently and stop focusing on memorization.
Paul Shoecraft – Exactly and it’s been that way for over 100 years. I didn’t start school until the first grade but in the first grade, we just added and subtracted small numbers. In the second grade, we did the same thing. In grade three, we also just added and subtracted small numbers. We didn’t get the multiplication and division until grade four and that’s holding children back. Oh my goodness, that’s four years. If you count kindergarten, K1, 2, and 3 are spent on just adding and subtracting small numbers so that children can memorize the addition and subtraction facts. We take four years trying to get children to memorize something that we know they’re going to forget. Not everyone has a good memory for the numbers so we know going in that we’re going to fail with a lot of children. We’ve demonstrated that every year for more than 100 years and yet we’ve done nothing about it.
Here’s another way to look at it. Remember those late nights when you were pumped up on sugar and caffeine?
Paul Shoecraft – Well, you didn’t cram for two weeks before the test, you crammed for the night before because you knew that if you crammed for too far in advance, you would start forgetting what you had tried to memorize or what you memorize
This really hits home for me because I believe in treating the problem not the symptoms. Paul’s system “Move it Math” was designed as an alternative to rote memorization of math facts, his system focuses on understanding concepts and active engagement. His system was piloted in elementary classrooms where they weren’t forced to memorize the number facts and you know what he found?
Paul Shoecraft – Well, they get it and when you know how to figure out the number of facts, when you can count them out and there’s 390 of them, that’s a lot to remember and most people can’t do that but there are some who can. Maybe 10 percent of the population can do that and they’ve become the standard but the rest of us who by definition are normal, no, we forget and we know forgetting is a human condition.
I won’t belabor this point any longer because I think you get it. There is a better way out there but the reason I’m so passionate about this is that struggling with math creates a feeling of failure and that can follow you around for the rest of your life.
Paul Shoecraft – The analogy I use here is checkers and chess. If you know how to play both games, I’ll bet it bothers you more to lose a game of chess than it does a game of checkers. Checkers is a child’s game. Chess, that’s for grown-ups and when you lose that, when you lose a chess, that’s like you’re pitting your intelligence against someone else’s intelligence and it hurts a little. Yeah, absolutely. Yeah. And you take children who are having difficulty in arithmetic because they keep forgetting, say, the number of facts like 2 plus 3 is 5 and 7 times 8 is 56. They just don’t jump into their minds like they’re supposed to if you memorize them. Well, they tend to doubt their ability to do math because they’re being told, hey, you have to know this by now, whatever that is. You have to practice this until you can say it or do it without even thinking. Just like you can say your own name. Well, that’s baloney. That’s baloney.
So why would we create a system that inherently instills a sense of failure in our kids? It’s not intentional. I know plenty of teachers who work very hard to avoid those feelings and to be fair many of them understand Paul’s system and use it in their own way but we are painting with a broad brush here because the majority of instructors do focus on memory and there is just something about math. When we can’t do it, it gets under our skin, at least it did for me.
Paul Shoecraft – I had a terrible time in history, for instance. I couldn’t remember names and dates for the darn. But you know, that never bothered me. I never thought I was stupid because I got seized in history in high school. I thought history was stupid. I don’t think that now. But I didn’t take it personally, doing poorly in history. But when I got confused in algebra in the ninth grade, I took that very personally. That bothered me. Wait a minute. This is about thinking. If I can’t do this well, I’m in trouble.
There’s not much we can do about that. But we can help kids better understand math—and avoid those feelings of hopelessness. It’s really important. I looked into this. Here is a trivia question for you. What professions are populated mostly by people who cannot do math? The answer is none. All work fields within our society require basic numeracy. All of them!
Paul Shoecraft – It’s a big deal. I didn’t realize it was such a big deal, frankly, until I wrote my book.
In 2022 Brian Butterworth published a book called “Can Fish Count?: What Animals Reveal About Our Uniquely Mathematical Minds and in it he says animals like bees and fish have innate math skills and he shows how studying them reveals where our sense of numbers comes from.
Butterworth argues that low numeracy has profound personal and societal costs. While some researchers debate the exact scope of these effects, his work underscores why this matters.
Paul Shoecraft – I’m going to read a quote here of what he said in his book, that a poor understanding of numbers is a serious handicap for individuals. Low numeracy can be a matter of life and death. A large-scale study of adults with colon cancer in the UK and US found that those with low numeracy were less likely to participate in screening, and were more likely to be defensive in getting cancer information, and hence more likely to be untreated or treated too late. In 2009, it was calculated that the cost of the lowest 6% of numeracy in England is about 2.4 billion pounds, or about $3 billion a year, in lost taxes, due to lower earnings, higher rates of unemployment, and increased costs of crime, education, and health. It’s a big deal.
Having said all this, I realize I’m probably talking to someone who struggles with math—and I get that. But if you’re anything like me, you’ll want to at least try to change things. Because there are real consequences to maintaining the status quo. Here’s an example.
Paul Shoecraft – Well, Microsoft, they moved one of their plants to Canada just because there they could hire the people they needed, but they couldn’t in the States because of immigration laws. Our children, they’re not prepared to do good jobs in America that require expertise in the STEM disciplines, science, technology, engineering, and mathematics.
He used the buzz word Immigration so I want to clarify that. In 2007, during the George W. Bush presidency, Microsoft opened a software development center in Vancouver, Canada and the stated reason was that U.S. immigration restrictions made it hard to hire skilled foreign workers in the U.S. so the point is they had no choice. There weren’t enough skilled workers here so they had to hire from somewhere else and it’s not getting any better. Now, while this is just one example it speaks to the importance of this issue. On the flip side, there are also debates about whether the problem is really skills related or mismatch of pay and training so I get that too and we can debate all that another time.
In his book Arithmetic Counts: Why Americans Have Trouble With Math and How to Fix It, Paul Shoecraft says let’s treat arithmetic like a language not just a bunch of numbers and teach it to children just like we do English.
Paul Shoecraft – When children realize that arithmetic is just a written language for describing concisely and precisely what is occurring around them every day, arithmetic becomes real to them. And here’s how you make it real to them.
Here is a crash course for you. Now sit up and pay attention. This is important.
Paul Shoecraft – Take the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. They are the alphabet for this language.
And they’re used to spell numbers. Numbers are nouns because they are the names of things, namely amounts, like the cost of something. And addition, subtraction, multiplication, and division are verbs because they are common, everyday actions that can be performed with numbers or amounts of things. Specifically, addition is a combining action, like putting groceries in a shopping basket, or dinnerware in a dishwasher. Multiplication is also a combining action, but of amounts that are alike, like building a brick wall or putting a handful of nickels in a piggy bank. Subtraction is a separating action, like taking a bite out of an apple or robbing a piggy bank. Division is also a separating action, but into equal amounts, like cutting a pizza into eighths or sharing the cost of a meal with a friend. Now, we talk about four operations, addition, subtraction, multiplication, and division, but it’s true, we only do two things with numbers. We either combine them or we separate them. And then it’s a matter of style. Well, how did you combine it? Did you just combine them or did you have to combine things that were the same?
And since most of us learn by doing here is the homework section
Paul Shoecraft – You say to the children, we want you to go home, we want you to look around the house and write down all of the combining actions you see, and write down all of the separating actions you see, and then break those up into whether you’re just combining anything or combining things that are all the same. Like if you were counting shoes, you know, in your closet, or you could count by twos. You’re combining the same thing, the same amount each time. And then when they come back to class, this would go on for weeks, and then you make a poster, okay? Let’s list this. Addition is, how do we know something is an addition problem? Well, it’s going to look like this, and you have maybe 10, 20, 30, 40, 50 different common everyday combining actions that children are familiar with.
The same for subtraction, multiplication, and division. This makes arithmetic real. They can see it every day. They live with it, and they realize that, and that motivates them to learn it.
If you were able to follow that then the cover of his book will now make a lot more sense to you. Look it up online and you’ll see what I mean.
There is empirical evidence about math performance here in the U.S. that shows decline and improvements at different times throughout history but I think Paul Shoecraft has really hit on something here. We need a better way to make arithmetic real and easy for kids to learn and understand. H is book Arithmetic Counts: Why Americans Have Trouble With Math and How to Fix It is a great resource for doing just that. It is an unapologetic back-to-basics program that teaches understanding instead of repetition and it’s available now at Amazon.com or wherever you like to buy books online.
So whether you’re a parent, a teacher, or someone who still feels haunted by math class, maybe it’s time we tried something different.
Thank you for listening to this edition of news gram from Webtalkradio.com.
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