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# Category: Pedagogy

## Michael Donnelly on Homeschooling and the Law

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## Kevin Currie-Knight on Crisis Schooling Versus Homeschooling

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## Kevin Currie-Knight on Self-Directed Education: Self in Society #9

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## A Great Course for Helping Children Learn Self-Control

“Scientific Secrets for Raising Kids Who Thrive,” a Great Courses offering taught by developmental psychologist Peter Vishton, offers some great advice for helping young children learn basic motor skills and older children learn self-control.

How can parents help their children learn self-control? As a new father, I’m keenly interested to learn. (I’m also interested in improving my own self-control.) I was thrilled, then, to discover the Great Courses offering, “Scientific Secrets for Raising Kids Who Thrive” (currently on sale), taught by developmental psychologist Peter Vishton.

The course features twenty-four half-hour lectures, the first of which (on which I’ll focus) covers helping young children learn basic motor skills and older children learn self-control. Other lectures cover topics such as getting kids to eat their vegetables and the pros and cons of video games.

Vishton discusses the importance of “tummy time,” placing a supervised infant on his tummy so he can build muscles and coordination and, eventually, crawl. In this segment, I was especially interested in Vishton’s cross-cultural comparisons of swaddling practices and efforts to help infants develop.

To me, far more interesting was Vishton’s discussion of impulse control. Among other things, Vishton discusses the famous “marshmallow experiment,” in which children could eat a small treat immediately or wait for a larger treat. I had heard about this before, but Vishton fills in many fascinating details. For example, he describes how, at age three, most children were bad at delaying gratification, while, by age seven, most children were pretty good at it. He discusses a follow-up study finding that children who were good at controlling their impulses tended to be more successful later in life by a variety of measures.

So how can parents help? Vishton discussed a study of children taking Taekwondo, a type of martial art. Classes that emphasized self-control, the study found, helped children be more self-controlled generally. Another study that Vishton mentioned found similar results for yoga classes.

In all, the lecture surpassed my expectations. The production quality is fantastic, with good lighting and sets and an excellent lecturer. The video streaming was good overall, with just one glitch that resolved when we went back a minute.

This was the first set of video I’ve purchased from Great Courses. I’d purchased audio before, long ago, and decided to invest in some video courses on history, music, math, and science. I’m glad I added Vishton’s course to the mix.

I have just one complaint about the first lecture. Vishton discusses Taekwondo as an activity a parent might choose for a child. But what about what the child wants? As Craig Biddle writes in his recent article on parenting, “because our children’s use of their faculty of choice is what enables them to live proper human lives, we should enable them to choose their own values within the range of reasonable, life-serving, developmentally appropriate alternatives.” I would have enjoyed hearing Vishton’s thoughts on allowing a child to choose which activities to pursue and on whether and in what ways a parent should encourage a child to pursue activities that foster self-control. Without such a discussion, some parents might confuse fostering self-control with fostering mindless obedience. I’ll be interested to hear if Vishton addresses such matters in subsequent lectures in the series.

That minor complaint aside, I’m thrilled with the course, and look forward to watching more of the lectures from this and other courses. And, now that I’ve finished this brief review, I think indulging in a piece of chocolate is entirely appropriate.

**Related:**

## The “Common Core” Subtraction Technique Caleb Bonham Criticizes is Actually Useful

I’m a fan of Caleb Bonham’s work. However, in his recent video on Common Core, he gets a little off-track. The subject is a technique for subtracting one number from another. Bonham claims the technique in question was imposed by a Common Core curriculum and that it is overly complicated. In fact, the technique is very old and very useful. The fact that a Common Core program happens to use it is no cause to damn it.

As Bonham explains, the traditional solution to the problem, thirty-two minus twelve, is to first subtract “two minus two” in the “ones” column, then subtract “three minus one” in the “tens” column, for the correct answer of twenty.

The approach used by Common Core, by contrast, asks a student to see the following:

32 – 12 = ?

12 + 3 = 15

15 + 5 = 20

20 + 10 = 30

30 + 2 = 32

The sum of the 3, 5, 10, and 2 is 20.

Bonham thinks this approach is overly complicated, and, in some situations, he’s right. But the approach indicated is, in fact, how I often do subtraction problems in my head (except that in this case I’d jump straight from twelve to twenty, and so get eight plus ten plus two), and it’s a perfectly legitimate approach. It is also an approach that helps students reach a conceptual-level understanding of addition and subtraction, rather than merely learn rules of subtraction by rote.

Of course, in this case, because we’re dealing with two, two-digit numbers that end in the same digit, adults and more-advanced students can easily see that the difference between the numbers is some increment of ten (in this case twenty). But what to do in other cases?

To illustrate the advantage of the approach given, consider the problem thirty-one minus twelve. In this case, the rule-based approach requires that a student “borrow” from the three. It’s much easier to solve the problem in your head by saying, “eight plus ten plus one equals nineteen.”

Or consider the problem seventy-three minus twenty-eight. A good way to do this problem in your head is to think, “To go from twenty-eight to thirty I need to add two; to go from thirty to seventy I need to add forty; to go from seventy to seventy-three I need to add three. The total is forty-five.” There are other good ways to find the answer, of course, but, for me, the way I described is the easiest way to do it in your head.

The broader lesson here is that, just because something is associated with Common Core, doesn’t mean its bad.

Update: I’ve also written about a vague, nonsensical problem from a Common Core-approved test.

## Beating the Monty Hall Problem

A couple friends of mine described the so-called “Monty Hall Problem” to me a few weeks ago. (I’d probably heard about this long ago, but if so I’d forgotten about it.) The problem, named after “Let’s Make a Deal” host Monty Hall (pictured here), is a puzzle of logic and statistics.

Here’s the problem (in my own terms): Imagine a game show where you’re trying to win a car. The game works as follows. There are three doors on stage. Behind one door is the car. Behind the other two doors are goats. (Or you can imagine whatever other prize and booby prize you like.) You get to make an initial selection of one of the doors, but you can’t see what’s behind it. Then the host shows you which of the other two doors opens to the goat. Then you get to stay with your initial choice or switch to the other unopened door. What should you do?

When my friends suggested to me that the correct move is to always change your selection to the other door, I thought they were nuts. I thought they had fallen for a logical trick. After all, once we know that one of the doors opens to a goat, we’re left with only two choices: our original choice or the other unopened door. There’s a fifty-fifty chance of guessing correctly.

I couldn’t quite put my finger on the error that I thought was behind the advice to always switch, but I thought it had something do to with confusing the two time sequences (the initial versus the final choice of doors).

But then I was reading through Sam Harris’s *The Moral Landscape*, and he uses the Monty Hall Problem to illustrate the dangers of always going with our “gut” reaction. How, I wondered, could an intelligent neuroscientist fall for this same trick?

So I decided that, by God, I was going to figure out what was wrong with the standard Monty Hall analysis. What better way to do that, I thought, than by running my own trials? (The Wikipedia entry on the matter suggests that others have run simulations and even let pigeons have a go. Apparently the pigeons tend to switch to the third door.)

I rolled a die to determine which door hid the car and which door I initially selected. Then it’s easy to figure out if, by switching, you get the car or the goat. By always switching, I ended up selecting the car 17 times out of 30 trials, which was not very helpful given it’s about halfway between 15 (fifty-fifty odds) and 20 (two-thirds odds).

But running the trial quickly gave me the idea of what’s going on. In my first trial, I selected Door 1, while the car was behind Door 2. That means that “Monty” reveals a goat behind Door 3. By switching from Door 1 to Door 2, I get the car.

In my third trial, I selected Door 1, and the car was behind Door 1 as well. Thus, when “Monty” reveals a goat behind Door 2 (or Door 3), I switch to the other door and end up with the other goat.

Here’s the general idea. Every time you initially select the door that happens to hide the car, you switch to another door and get a goat. Every time you initially select a door that hides a goat, you switch to the door that reveals the car.

Or, in other words, by switching, one-third of the time you’ll end up with a goat, and two-thirds of the time you’ll end up with the car. (If this is not now obvious to you, I suggest you run your own trials to get the hang of how it works. In rolling the die, I assigned sides 1 and 2 to Door 1, sides 3 and 4 to Door 2, and sides 5 and 6 to Door 3. Or you could set up actual doors if you want to get fancier and more concrete.)

So what’s going on here? When “Monty” reveals one of the remaining doors to contain a goat, he is introducing new information into the process.

To make this more obvious, we can imagine a game with more doors. (Wikipedia suggests this.) What you’re really doing in making your initial selection is forcing “Monty” to reveal additional information about the remaining doors. So let’s say there are more doors, and “Monty” has to reveal the rest of the doors except for one.

Let’s say there are six doors, and you initially select Door 1. Let’s say “Monty” reveals goats behind Doors 2 through 5. The car, then, is behind either Door 1 or Door 6. What do you do?

Your three basic choices are these. Always stick with your initial selection, which, in this case, gives you a one-in-six chance of getting the car. Or you can choose randomly between the remaining two doors, which gives you a fifty-fifty chance of getting the car. Or you can always switch to the remaining door, which is the prudent move.

I actually ran a new trial with six doors (using a six-sided die to determine the door with the car and the initial selection). Out of 18 trials, I got the car 17 times by always switching (which is even better than the statistical prediction). (I didn’t really need to run the trials at this point, but I figured I’d follow through with it.)

Or you can imagine 100 doors. If you want to run trials for this, you might use the real random number generator. The outcome follows the same pattern. If you always stick with your initial selection, you’ll end up with the car about one out of a hundred times. If you always pick randomly between the final two doors, you’ll increase your odds to fifty-fifty. If you always switch to the other door, you’ll increase your odds to 99-in-100. The only time you’ll lose out is if by luck you happen to pick the door with the car in your initial selection, then switch.

Realizing that you can increase your odds by moving away from the strategy of always sticking with your initial selection, to picking randomly between the final two doors, to always switching, should disrupt your initial “intuition” (if you had it) that the odds are always fifty-fifty.

Of course, I’m pretty sure the game shows have figured this sort of thing out by now.