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Unfortunately, learning by textbook osmosis didn't make the learning strategies list. (Image courtesy of flickr user indi.ca, cc license)

Taking notes during class? Topic-focused study? A consistent learning environment? All are exactly opposite the best strategies for learning. Really, I recently had the good fortune to interview Robert Bjork, director of the UCLA Learning and Forgetting Lab, distinguished professor of psychology, and massively renowned expert on packing things in your brain in a way that keeps them from leaking out. And it turns out that everything I thought I knew about learning is wrong.

Here’s what he said.

First, think about how you attack a pile of study material. “People tend to try to learn in blocks,” says Bjork, “mastering one thing before moving on to the next.” But instead he recommends interleaving, a strategy in which, for example,instead of spending an hour working on your tennis serve, you mix in a range of skills like backhands, volleys, overhead smashes, and footwork. “This creates a sense of difficulty,” says Bjork, “and people tend not to notice the immediate effects of learning.”

Instead of making an appreciable leap forward with yourserving ability after a session of focused practice, interleaving forces you tomake nearly imperceptible steps forward with many skills. But over time, the sum of these small steps is much greater than the sum of the leaps you wouldhave taken if you’d spent the same amount of time mastering each skill in its turn

Bjork explains that successful interleaving allows you to “seat”each skill among the others: “If information is studied so that it can beinterpreted in relation to other things in memory, learning is much more powerful,” he says.

There’s one caveat: Make sure the mini skills you interleave are related in some higher-order way. If you’re trying to learn tennis, you’d want to interleave serves, backhands, volleys, smashes, and footwork—not serves, synchronized swimming, European capitals, and programming in Java.

Similarly, studying in only one location is great as long as you’ll only be required to recall the information in the same location. If you want information to be accessible outside your dorm room, or office, or nook on the second floor of the library, Bjork recommends varying your study location.

And again, these tips generalize. Interleaving and varying your study location will help whether you’re mastering math skills, learning French, or trying to become a better ballroom dancer.

So too will a somewhat related phenomenon, the spacing effect, first described by Hermann Ebbinghaus in 1885. “If you study and then you wait, tests show that the longer you wait, the more you will have forgotten,” says Bjork. That’s obvious—over time, you forget. But here’s thecool part: If you study, wait, and then study again, the longer the wait, the more you’ll have learned after this second study session.

Bjork explains it thisway: “When we access things from our memory, we do more than reveal it’s there. It’s not like a playback. What we retrieve becomes more retrievable in the future. Provided the retrieval succeeds, the more difficult and involved the retrieval, the more beneficial it is.”

Note that there’s a trick implied by “provided the retrieval succeeds”: You should space your study sessions so that the information you learned in the first session remains just barely retrievable. Then, the more you have to work to pull it from the soup of your mind, the more this second study session will reinforce your learning. If you study again too soon, it’s too easy.

Along these lines, Bjork also recommends taking notes just after class, rather than during—forcing yourself to recall a lecture’s information ismore effective than simply copying it from a blackboard. “Get out of court stenographer mode,” says Bjork. You have to work for it.

The more you work, the more you learn, and the more you learn, the more awesome you can become.

“Forget about forgetting,” says Robert Bjork. “People tend to think that learning is building up something in your memory and that forgetting is losing the things you built. But in some respects the opposite is true.” See, once you learn something, you never actually forget it. Do you remember your childhood best friend’s phone number? No? Well, Dr. Bjork showed that if you were reminded, you would retain it much more quickly and strongly than if you were asked to memorize a fresh seven-digit number. So this oldphone number is not forgotten—it lives somewhere in you—only, recall can be a bit tricky.

And while we count forgetting as the sworn enemy of learning, in some ways that’s wrong, too. Bjork showed that the two live in a kind of symbiosis in which forgettingactually aids recall. “Because humans have unlimited storage capacity, having total recall would be a mess,” says Bjork. “Imagine you remembered all the phone numbers of all the houses you had ever lived in. When someone asks you your current phone number, you would have to sort it from this long list.” Instead, we forget the old phone numbers, or at least bury them far beneath theease of recall we gift to our current number. What you thought were sworn enemies are more like distant collaborators.

I hope you didn’t see my first-to-worst performance in last night’s hotties vs. nerds edition of ABC’s WIPEOUT. If you did, you know what happened: after winning the round of 24 by almost a minute and then winning the round of 12 by the equivalent of a furlong, I got stuck in the round of six trying one element over and over — the wrong way — as people I had beaten in the first two rounds passed and eventually eliminated me.

Nuts–’twas a very good shot at $50k that my family of four surviving on my writer’s salary could’ve used.

Anyway, while it just aired last night, it’s been a bit since the filming and I find I’m having kind of a hard time letting it go. Why oh why couldn’t I see that if I’d just dangled my legs off the spinning bar, it would’ve draped me across the target platform? Instead, I hopped on top of the bar, rolled off it, and hit the landing platform with a momentum that carried me off the slick edge and 20 feet into the water…over, and over, and over. There’s a clip online and it’s painful to watch. At least it is for me. You’re probably laughing. And for that you’re going to hell. But I digress.

In this game in which contestants seem to have a median IQ of about 74, I lost not on athleticism, but on poor problem solving. But the thing is, I’m actually a halfway decent problem solver: I’ve contributed puzzles to the New York Times and am a puzzlemaster at the GeekDad blog.

What happened?

Don’t blame the stress. Despite recently having my head taken off by a hydraulic panel in a mock driver’s ed course, being shaken from a 30-ft sailboat’s mast, bouncing the wrong way off the idiomatic big balls, and being scraped off a platform en masse with my competitors by egg-beating rings, at the start of the round of six I was feeling pretty hunky dory. I’d done fine under pressure in the first two rounds by artificially whipping myself into a froth of invincibility. I’m good enough, I’m smart enough, and doggone it people like me, I told myself over and over and over until I started to believe it. Thus prepped, I imagined myself with an S on my chest, supremely confident and ready for anything.

This overconfidence isn’t my normal state, but I use it sometimes when climbing rocks or speaking to groups, and it served me well in the first two rounds of Wipeout. On the show, it allowed me to think that if an element was hard for me, it MUST be hard for everyone else. When I got pummeled by driver’s ed, I quickly wiped the cold, gravelly mud out of my eyes and jumped right back on the course, imagining that I was still very much in the game.

Massively egotistical? Yes. But it works. A little overconfidence can land a presentation at work, a date in a bar, or, in my case, the assertion to my three and five year olds that certainly it’s bedtime.
I brought this same artificial overconfidence to the round of 12, where 100% effort (and long chicken legs…) actually was the secret to success.

Now to the round of six. It was hot and before we started instead of standing around chatting with the other contestants, I stretched, did a couple sprints, and poured many a free bottle of water down my black life jacket. In short, I acted like an overconfident tool, which is what I had become at that point. And I expected that as an overconfident tool, I was bound for the glory I have seen so many overconfident tools claim over time.

Finally, the day of the geek had dawned.

I was first off the swings, first to stick the exit from the spinning platform, first onto the rotating helicopter blade, and first to attempt the exit from the spinning bar onto the pig-mud-slick platform. Of course, I fell the first time. No worries. If it was hard for me, it MUST be hard for everyone. I put my head down and kept trying. 100% effort.

But the key was this: I put my head down. Actually, I’m kind of prone to this strategy I’ll call suffice and execute. And usually it works out–usually my “suffice” is within the ballpark and a little extra effort is better than spending two minutes to find the most efficient way that saves 30 seconds. Having quick, good-enough solutions is part of what allows me to froth into overconfidence when I think it’s needed.

I do things like slogging through slide alder to the base of a climb instead of wandering around to find the streambed that leads directly to the rock face. In chess, I let my pawns become cannon fodder while I set up a knight/queen attack against my preternaturally talented five year old who, nonetheless, can’t bear to lose a pawn. I steamroll off message in radio interviews, confident that we’ll find humor and (maybe even sometimes) insight off-the-cuff.

Again, “suffice and execute” serves me well.

That is, until it doesn’t.

It seems the strategy of suffice and execute is prone to frequent success punctuated by infrequent bouts of catastrophic failure. By now you’ve seen the tape. Need I say more? (By the way, when the windmill crushed my C2, yes that actually does hurt.)

It’s the strategy that led Hannibal to march his troops over the Alps, led the scientific community to believe in the hoax of Piltdown Man for 40 years, led Lord Kelvin to say in 1895 that heavier than air flying machines were impossible, and can lead a country headlong into an intractable war. In short, it’s a major reason why smart people do stupid things.

In my life, and I think elsewhere, overconfidence creates blinkers and it took watching myself act like a robot idiot on Wipeout for me to see it.

So what will I do next time I get a big chance?

It seems to me the step that’s missing is revision. Suffice and execute may still be the answer 90% of the time, but I need to install in myself a circuit breaker that recognizes when things aren’t working and flips the switch back to the strategy generation portion of the ol’ suffice and execute. In the moment, I need to know when to go back to the blackboard. And maybe I need to dial down the artificial overconfident froth, allowing me to admit a strategy is flawed.

Confidence and follow-through with a strategy is great. It can land a mediocre approach. But after rolling off the top of a spinning bar and sliding into the water for the fourth of fourteenth time, maybe it’s time for me (and maybe for you?) to take a look at the strategy that got me there?

Twitter: @garthsundem

Garth’s brain science and geek humor books at Amazon

Believe it or not, I’m rarely accused of being a romantic. I know, I know — baffling! And this even after I brought home Thai food for our anniversary. Okay, I forgot the anniversary. But a couple days later when I brought home Thai food, boy was my wife surprised! Okay, okay, I didn’t actually *bring home* Thai food, because, you know, I was walking home from the park with the kids in the double stroller and by the time I got home it would’ve been cold…yadda, yadda, yadda. The point is this: it’s the thought that counts, even if that thought is two days late, and not, in fact, acted upon. Just imagine how nice it would’ve been to have surprise Thai food for our anniversary! See: THAT’S romance.

And to make sure it never happens again, I decided to write optimal romantic performance in the language of math so that I’m not saddled with any future romantic questions that I’ll almost certainly screw up. Simply, I let the app do it for me. Questions include (but are not limited to) “How much should I spend on Valentine’s Day gifts?” and “Should I apologize?” and “Which Valentine’s Day date offer should I accept?” Anything’s better than leaving these questions to my romantically-challenged brain. Now I don’t have to.

Paleontologists recently unearthed bones, likely in Montana or Wyoming, of a new dinosaur species dubbed Stochastisaurus. “Based on surrounding species and the fossils themselves, there’s an approximately 88% chance that Stochastisaurus was an herbivore,” says the lead researcher. The new species of dinosaur more likely than not had something interesting about its head, perhaps heavy bone plating like Pachycephalosaurus, a frill like Styracosaurus, a crest like Corythosaurus, or a hollow series of tubes like Parasaurolophus. This interesting head feature is almost exactly equally likely to have been used for defense, reproductive competition, or as an instrument of communication with other Stochastisauri.

Debate continues regarding how Stochastisaurus walked—did it move on four legs like a Diplodocus or on two like an Iguanodon? “There are, in fact, twice the number of four-legged dinosaur species compared with the number of two-legged, two-armed species,” says the lead researcher, giving Stochastisaurus a 2-to-1 chance of walking quadripedally.

Though other researchers have questioned the finding, suggesting the fossilized bones are, in fact, an intrusion of hardened mud that proponents of Stochastisaurus have simply super glued into the shape of a hypothetical ancient creature, the species’ finder points out that, “the puzzle of dinosaur recreation frequently requires construction based on the most likely configuration of small pieces. For example, it’s almost certain Stochastisaurus had a tail, body, head, and legs, and our recreation faithfully constructs these body features.”

Similarly, researchers point out the infinitesimally small chance that Stochastisaurus had tentacles, two heads, or a cockpit where a human controller could sit, reminiscent of Kiryu. And sure enough, researchers’ model has none of these.

“This has a very good chance of being an exciting discovery,” says the lead researcher.

First, I’m afraid I fell victim to one of the classic blunders—the most famous of which is never get in involved in a land war in Asia, but only slightly less well known is this: probability is not additive (as a couple astute Times readers have now pointed out). For example, if you have a 4-sided die, there’s a 1/4 chance of rolling a specific number first try. If you roll again, is there a 2/4 chance, and after five rolls a 5/4 chance? Nope. Instead the math goes like this:

• one roll of a d4: (4^1-3^1)/4^1=1/4=0.25
• two rolls of a d4: (4^2-3^2)/4^2=7/16=0.44
• three rolls of a d4: (4^3-3^3)/4^3=37/64=0.58
• four rolls of a d4: (4^4-3^4)/4^4=175/256=0.68
• twenty rolls of a d4: (4^20-3^20)/4^20=1096024843375/1099511627776=0.97

APPROACHING BUT NEVER EQUALING 1/1 OR 1.0 OR 100%. (There’s never a sure bet…)

And so my approach, stated word-for-word in the puzzle Frankie the Fixer, of “adding 1% to each roll’s chance of being boxcars” is extremely misdirecting—in fact, I misdirected myself—it isn’t as simple as summing 1% across the number of rolls and adding the result. That’s exactly the same as adding 0.25 every time you roll a d4, which leads to the erroneous probability of 5/4 after five rolls.

Instead—as a couple readers pointed out—the trick is making the 1% additions ALONG WITH EACH 2xd6 ROLL’S 1/36 CHANCE, thus looking at each roll as a 0.028+0.01=0.038 probability of success. The gist of this rambling (but I hope definitive) explanation is that—yes—it takes 18 rather than my stated 16 throws for Frankie the Fixer to break the magic 0.50 probability.

Here are answers to yesterday’s fiendish puzzles:

1. The trick is to convert everything into runners on base per out. In this case, Rivers’ cutter earns .168 on-base/out, and his fastball earns .252 on-base/out. The slugger is trickier. A .345 ob% for cutters means that each at-bat he has a .655 chance of being out, and so .527 on-base/out. Facing fastballs he earns .453 on-base/out. The total on-base/out of a cutter is the average of pitcher and hitter—0.348 on-base/out. The total on-base/out of a fastball is 0.353 on-base/out. So Rivers’ best pitch remains his best pitch, the cutter.

2. This is a twist on Martin Gardner’s famous gender problem. First, combining birth order with gender means with two kids you could have BB, BG, GG, or GB. Now, Imagine the number of distinct possibilities with the calendar:

•  If you FIRST have a boy-on-a-day-containing-a-1, you could have a boy or a girl second, on any of the 31 days, for a total of 62 possibilities, 31 of which are two boys. Cool.

•  And the same is true if you SECOND have a boy-on-a-1: 62 possibilities of which half are boys. Only, 13 of these “new” possibilities aren’t distinct. You already included boy-boy on every day containing a one. So instead of adding 62 more, distinct possibilities, this adds only 49 new possibilities, of which only 18 are two boys.

•  So add up all the possibilities for two boys: 31+18=49. And add up all possibilities: 62+49=111. There’s a 50/111=0.45 probability that both kids will be boys.

Did you get here after quickly vanquishing my puzzles in this morning’s New York Times Science section? (12.7.2010) If so, you’re likely ready for a challenge. Below are the puzzles the Times cut—perhaps because they’re too darn tricky or maybe ’cause the first gently pokes fun at the sacred cow that is Mariano Rivera. But they’re certainly not too tricky for you, gentle reader. No, no, if you’ve made it this far, they’re right up your alley.

The Lost Puzzles:

1. Imagine a pitcher—we’ll call him Marion Rivers—who has only two pitches, a fastball and a cutter. Overall, he’s got a 1.93 ERA with the cutter and a 2.89 ERA with the fastball. Now imagine a slugger who has an on-base percentage of .345 averaged across cutters and an OB% of .312 when facing fastballs. If it takes an average of 2.35 hitters reaching base to score a run and all myriad else is equal, what pitch should Rivers throw this batter?

2. If I tell you that I have two children, both born in October, and at least one a boy born on a day whose date contains at least one “1″, then what is the probability that both my children are boys?

Thanks to Stanford prof and NPR “Math Guy” Keith Devlin for a conversation a couple weeks ago that put probability back on my front burner. He’s got a great post at his Devlin’s Angle column about a puzzle similar to my October birthday problem (and deep puzzlers will notice the similarity to Martin Gardner’s original).

I’ll post answers tomorrow. But for now, suffer you suckers! Ha, ha, ha, ha, haaaaaaa…(evil laugh).

Still reading? Gee, you are a glutton for puzzle punishment. If your fix isn’t yet fixed check out the smattering of goodies in my newest book, Brain Candy: Science, Puzzles, Paradoxes, Logic, and Illogic to Nourish Your Neurons.

Want a real Halloween nightmare? Imagine filling your child’s too-small bucket in the first three houses and going home with only a small slice of your kid’s potential rake. But if you allow your little monster (or in my case, blue whale with pink and purple barnacles), to carry a big bag, you should be prepared to spend the hours and hours (and hours) needed to fill it. Bad news: there are nightmares on both ends of the bag guesstimation spectrum.

So instead of playing the equivalent of Russian roulette with your child’s Halloween bag size, use the equation below to calculate—with the power of absolute mathematical certainty (wink, wink)—the bag size that’s best for you and yours.

•  T= Total time in hours you plan to spend trick-or-treating

•  A= Trick-or-treater’s age. If over 20 (or below zero…), shame on you. You’re stealing my kid’s goodies.

•  Hc= Hours spent on costume. If store-bought translate into hours at $20/hr.

•  Pd= Population density in trick-or-treat neighborhood. Enter 1 for “rural”, 2 for “open suburban”, 3 for “tight suburban”, or 4 for “Apt or dorm”

•  Ma= Estimated median age in neighborhood. For comparison, median age in the Gaza Strip is about 15 and in Japan about 41.

•  X= Your child’s ineffable, illogical, but very real lust for candy. Enter 1-10 with 10 being “has strategized since last Halloween”

Interpretation Key:

If Bckt is less than 1, your pockets are more than enough

If 1<7, use small-size, plastic jack-’o-lantern bucket

If 7<Bckt<15, use the standard trick-or-treating bucket

If 15<Bckt<25, use a grocery bag

If 25<Bckt, use a trash bag

.

If you’d like the live version, I’m Skyping into Good Day Sacramento on Saturday morning at 6:40am PST to explain this revolutionary scientific breakthrough in person. (I’m sure they’ll post vid online.)

–Notice the outstanding Halloween colors of Brain Candy: Science, Puzzles, Paradoxes, Logic and Illogic to Nourish Your Neurons

–garthsundem.com

–Twitter: @garthsundem

Yesterday I posted how Game Theory solves the date-night dilemma: opera or the football game. Actually, I posted the problem but not the solution. For all of you who scratched your heads on Saturday night, here’s the answer:

Mathematically, the cleanest solution is for them to use a commonly observed randomizing device: they flip a coin. Heads it’s football and tails it’s opera. And once the coin lands, there’s no incentive for one player to switch, as it would only result in the loving husband and wife going separate ways for the evening and the loss of all preference points.

Actually, there’s another option. One person can get mad. Imagine that through her anger, she’s able to remove two of her total preference points—she threatens that if they fight over the decision, she won’t have as much fun no matter what they end up doing. Now the grid looks like this, with the original preference points on top and the points if she gets mad below them:

The outcome: it’s best for both if the guy gives in and goes to the opera before she gets mad. Thus they are guaranteed five preference points (but the poor dude never gets to the football game).

And the decision comes down to this: the person who is understood to be naturally capable of burning the most preference points and most likely to burn them (i.e. can and will get the maddest) will earn their top-choice activity, every time.

Sorry dude.

Can’t decide between the opera and a football game? (If needed, replace these bland stereotypes with specifics from your own relationship). Game Theory’s got your back.

Imagine the possible outcomes: football together, football alone, opera together, and opera alone. We can show this with the following grid (imagine the guy choosing a column and the lady choosing a row—they accept the outcome that gets two marks):

Now imagine each person has five “preference points” they can distribute among the four outcomes (again: football together, football alone, opera together, opera alone). And imagine if you will, that they strongly prefer to go somewhere together. Imagine she really wants to go to the opera (four to one) while he’s only somewhat more attached to football (three versus two). The grid would look like this:

The decision is obvious: if they both vote opera, they earn six total preference points (as opposed to four for football, and none if they split). But what if the guy feels as strongly about football as she does about opera:

Now they’re up the creek. It’s griiiidlock! Even with the opportunity to collude (argue) they can’t reach consensus and they don’t want to risk choosing opposites, which would result in no preference points for anyone. What should our “hypothetical” couple do?

Stay tuned. I’ll post the answer tomorrow.

Here’s another interesting dilemma: To buy my new book Brain Candy or to let your brain gently slip into disrepair, eventually resulting in settling forever onto your couch like a barnacle to watch an ever-repeating version of the movie Beverley Hills Chihuahua. Really, the choice is yours.