From the Sunday, March 23, 2008 Foxtrot comic by Bill Amend

So many people have asked about a sequel for “Numbers [...]]]> Update: The project described below is on hold. At the moment I’m trying to finish some other courses that will be even more comprehensive and effective. More news soon.

From the Sunday, March 23, 2008 Foxtrot comic by Bill Amend

So many people have asked about a sequel for “Numbers Juggling – Times without the Tables,” that it’s time I got moving on it.

As you probably know by now, “Numbers Juggling – Times Without the Tables” is a way to get anybody to learn and understand basic multiplication in a short time, with the least frustration. It’s a booklet 7-lesson e-course, and it’s helped thousands of kids and adults get a handle on multiplication without rote memory or gimmicks – just good math that anyone can understand.

So now you’ve read it and have taught your child the multiplications from 1-15, and you’ve learned the theories behind why the methods work. What now?

“Numbers Juggling – Multiplying Large Numbers”, of course!
But it’s not written yet. Oh, no!

But that’s good! If you had to wait until it was done, you’d have to wait until May. Because it’s still “in the works,” I’d like to give you a chance to get in on it while it’s being written. That means starting today.

And because you’d be getting it this way, it’s going to be less than half the price of the (already cheap) finished course.

So, for a measly $4 you can get “Numbers Juggling – Multiplying Large Numbers” delivered to you, a short chapter each day, by e-mail, starting right now.

What you’ll learn:

• 7 secrets to checking your answers without division. And they’re all faster than using a calculator!
• The Instant method for multiplying up to 20, without the tables, and without rote memorization.
• Multiplication games that aren’t childish, but any child (or adult) can practice and learn from.
• “Secret” learning strategies that kids will actually use, and not resist.
• How to multiply any whole number by any digit, (like 345*8) easily and accurately.
• How to use that knowledge to multiply any huge whole number by any large whole number.
• The spectacularly easy way to estimate products of large numbers with amazing accuracy. By just looking at 17,343*682 you’ll be able to say, “It’s about 12,000,000.” (It’s really 11,827,926 – that’s soooo close! It’s only off by about 1%.)
• Why most “tricks” are counterproductive, and which ones aren’t. (This will save you from wasting a lot of time with “fluffy” math and trendy fads.)
• Of course, all the “math behind the math” will be explained for those who want to learn a little number-theory (although we won’t get too technical, I promise!)

If you don’t know the great stuff in the first “Numbers Juggling” booklet and e-course, you should. If you order it with this special sequel offer, you can get the first “Numbers Juggling” for a deal, as well. Normally, it’s $9.95, but if your order it with this sequel, you can start learning these multiplication secrets for $6. That’s both courses for a total of $10.00, instead of $18.90. You don’t have to be a genius to do the math on that one. It’s a great deal.

I love helping people discover how fun and easy arithmetic can be, and I love writing these courses. Everything in them is designed to make sense to anyone, and bring them along to a deeper understanding of things that used to confuse them. If they don’t help you right away, just write to me for a full refund.

I stand behind Math Mojo 100%, because I know it works. It turned me from a self-conscious mathaphobe into a guy who loves math and uses it every day to enjoy life more fully. I know it can help you, or anyone you are teaching, as well.

Fair enough, but I think he may have misunderstood my methods.

That could, of course, be due to the way I communicate them (or miscommunicate them). First let me [...]]]> Today a concerned reader took issue with what he understands my methods to be. (See comment #4 at Augends, Addends and the Commutative Law of Addition.)

Fair enough, but I think he may have misunderstood my methods.

That could, of course, be due to the way I communicate them (or miscommunicate them). First let me say that none of the algorithms (ways of solving math problems) I teach are “mine.” “Math Mojo” is the name of my attitude, not the methods. The methods have been either gleaned from better sources than me (and most are hundreds, if not thousands, of years older), or I have “re-invented” them. That is typical for most people’s alternative methods.

Now to the issue; the reader stated:

After all these years (30) of struggling to teach children math, I finally realize why it is so difficult. A brief perusal of some of the mathematical girations you go through to multiply two numbers together explains a lot of why kids are poor at math. Commutative and associative properties are more easily understood when you have the basic tools to work with without adding zeros then subtracting the number from your cousins name on your mother’s side of the family. Teach the basics by rote then progress to the more abstract. Simple to complex seems to work.

Professor Homunculus’ reply:

I’m sorry you’ve come to that conclusion. If you’ve been teaching math for 30 years, you surely have some insights. But I can’t see see how you’d say, “simple to complex” seems to work. May I ask where it seems to work? And if it does, why is it a struggle for you, and why is it so difficult? Have you been teaching with the “girations” (sic) you say I use to make it so frustrating?

I’m not quite sure I understand the logic of your position.

(Caveat – I feel very strongly about this issue. Please don’t take it personally. It’s a sickness.)

I teach hundreds of kids each year, in person, and I don’t know how many on the internet. The overwhelming reactions on both sides (theirs and mine) seem to be satisfaction and light bulbs going off left and right. Many children and their parents have actually cried in front of me in relief from “the basics” (times “tables”, multiplication “facts” and such.) Not everybody likes the methods I use (I wouldn’t expect them to) but so far, you are the first to blame me for the failure of your school system.

“Math Reform”

Please don’t get me wrong. I’m not representing some idiotic, airy-fairy “math reform” (as you call it). I probably want to throttle those people more than you do. Math Mojo is about discovering solid, meaningful relationships between numbers, not being a some new-age (rhymes with sewage) dunce. But neither is it about being a drone to a system that never really worked.

By the way, what is “math reform?” Is it the movement that resists the “tradition,” or is that movement that resists that? I’m never sure about that. (I resist both.)

As I’ve said in the Introduction to These Chronicles:

“Never accept ‘alternative’ as better until you have tested it. By the same reasoning, never accept the ‘accepted way’ until you have tested it, either.”

It also pays to pay attention to the results of that testing.

Come on, look at all people who actually excel at anything. Think Shakespeare was enthralled with writing book reports in which he’d get points taken off for bad grammar (“To who, my lord?” King Lear l.iv.24, V.iii. 249) ? Think Gauss liked adding up long columns and having to “show his work?” “Hey, Mozart, stop with that nonsense and go practice your scales!”

What? Not all students are exceptional? Gee, I wonder why anyone would think that. In one way or another, all of them are. That is not the common contradiction you might think it is. Read it again.

Simple Complexity? Complex Simplicity?

I don’t think there is anything more complex about the methods I teach than there is about what some people call “the basics.” I talk a lot about the theories behind them, but that’s only in order to explain it to those who are interested. You may be assuming otherwise, which is understandable, because sometimes I get so into it that I can’t shut the hell up. My bad.

Really, the only “dogma” I may subscribe to is that there is no one best way. And if there was, it certainly wouldn’t be the times tables.

“…and Let your Backbone Slip….”

If I can get most kids to know multiplication of one-digit numbers in less than five minutes with what you seem to think are “gyrations”, why on Earth would you devalue that in comparison to whatever “the basics” might be?

Here’s something that I’ve been wondering about. Maybe some interested reader has some thoughts on it:

If I gave a ten-year old child a car, and said, “Here are the keys. You put your foot on this pedal to make it go, and this one to make it stop. Turn the wheel to steer. Now you know how to drive. Be home by ten,” would that make any sense? I mean, yes, the kid would know, “the basics” but they’d be less than meaningless to him – they’d be frustrating. And they’d be dangerous to him and us.

How is that all that much different from giving a kid the “basics” (“Just shut up and learn them, or you’ll fail!”) of multiplication? He’s had no fun learning them, cannot relate the “facts” to anything else, and generally learns that this is exactly the point where you start hating school. Oh, boy!

Most children have no problem learning multiplication by 10. Imagine then saying to such a child, “Hey, did you ever notice that multiplication by nine is the same as multiplying by ten, then subtracting the number?”

Of course the child has. What kid hasn’t? Hmmmm, there is something they’ve noticed themselves. And now they are recognized as having seen that for themselves. Even if they hadn’t, they will see it now, and it will be interesting to them. (Imagine that!)

Now, with no difficulty, you’ve engaged the kid. You could treat the whole thing as a “math trick for nines”, and then go on pummeling them with the tables. Or you could have them try multiplying all the digits by nine that way to if it worked. Then try it with nine times a two-digit number. Did it work?

It did! Hotcha! It took them less than three minutes to learn the nines “tables,” and have a relationship with the number nine. Is that too complex?

Let me go out on a limb and try to put in clear terms what the heart of the problem is for most children learning multiplication: We have a calcified system, which for some reason(s) finds it necessary to defend itself as ” the one best system”. So if the students don’t learn, it’s because they just won’t accept learning with “the one best system.”

Seems to me that if the kids aren’t learning with it, then the “one best system” isn’t working. Should we then blame it on a method that almost nobody in the public schools is teaching?

That doesn’t mean that we should Teach Extremely Rotten Crap instead. It means that we should search for ways that seem to work, which can rationally be shown to be meaningful, and try them. If they don’t work, try something else. Or is that too complex?

Progress can be complex. Yes, it’s simpler to keep failing, but I guess that just doesn’t float my boat. Most students and parents aren’t big fans of failure, either. And I’m betting that most teachers would say that they feel the same if they weren’t afraid of hearing the sound of NCLB (“No Child Left Behind”) jackboots in the stairwell.

Look, I’m frustrated with the crazy Ideas floating around, passing themselves off as “education,” especially when it comes to math, as you obviously are, too. I just think you are picking on the wrong target. Maybe much of my writing does not convey the absolute simplicity and elegance of the methods I endorse. Face it, I’m a hack, run-on-sentence kind of guy. ADD does that to you. (But I like it, heh, heh, heh…)

But if you experienced how quickly, and with what joy and relief most kids and adults learn from someone who really “gets” this stuff, I think you’d add some of it to your repertoire. Really, “just memorize it” only goes so far (and it doesn’t go anywhere that’s interesting).

Actually, let me say it now – Rote rots. It is a miserable and counterproductive method of inculcation disguised as teaching. It may work is some rare cases of children who have some mental handicaps, but it’s not the way to bet, even in those cases.

Almost every single person who has learned by rote could have learned more effectively by some other method. The only reason some people haven’t noticed this is because they have never tried anything else for any meaningful amount of time. It’s the “better- to-curse-the-darkness-than-light-a-single-candle” syndrome, and it is endemic to public schools.

Addendum:

Today someone sent in a comment about this post anonymously. I’m sorry, but I don’t accept anonymous comments. The commenter misunderstood almost everything I said, but he did bring up some valid points. Unfortunately, he erroneously assumed that I was against the points he was making. Maybe I should clear it up.

I do not think that the only thing teachers do is teach by rote. I can’t believe that anyone would be silly enough to think that’s what I was saying, but apparently the commenter did.

He assumed that I believed that “the traditional way” was devoid of teaching concepts. Of course the “traditional” way teaches concepts (albeit pedestrian ones). I’m just pointing out that rote memorization sucks, not everything about the “traditional” system sucks. Jeez.

Who’s Tradition is it Anyway?

By the way, it was the writer that kept using the term “traditional.” I don’t really like using that term broadly. I mean, what system? Who’s system? I, for one, am not ethnocentric enough to think that what’s taught in the schools in my (or any other) country is “the traditional system.”

The main premiss of the comment was, “The traditional method of teaching mathematics works.” Sure, and the Surge is working, and the check is in the mail, and Paul McCartney is dead.

Knowing by Heart

Aside from there being nothing offered to back up that dubious premiss, the commenter seemed to think that I was not for learning by heart.

Let me disabuse anyone of that idea. I am for knowing basic multiplication by heart. I an actually for learning basic math stone cold in your bones. Everyone should know up to 20 by 20 without having to think. 19 * 14 =266 for instance, should be as apparent as C-A-T spells cat. You shouldn’t have to think about it.

Here’s the big difference in our thinking, though: I know, that when you teach in person, it shouldn’t take more than a few weeks to get a child to have that stuff down so they can do it in their sleep, and none of it entails staring at meaningless “tables.”

Knowing by Heart vs. Learning by Rote

Rote is a method of learning (generally by brute, primitive memorization, without a system for memorizing). It is drudgery. On the other hand, “by heart” is a way of knowing. Let’s see if this can be made clear:

You know the names of your family members, sports stars, celebrities, teachers, colleagues, game rules, and myriad other things “by heart,” but you didn’t have to sit in front of a “table” and bore yourself to tears while the evil “Dr. Textbook” insisted that that was the only way to learn them, did you? Of course not. You learned them because you had a relationship with them that meant something to you. There was no resistance to learning them, either. Not only was it natural, but it was effective, and immediate. I’m here to tell you that you can do the same thing with numbers.

“Memories…”

In the next post, I think we should talk about memorization. One of the tools that many magicians use is mnemonics. Even a trivial ability with mnemonics beats the poop out of rote memorization. Here’s the catch, though – people who don’t use nor understand mnemonics have a really poor opinion of them. I can understand that. Being a magician, I’m also aware that a lot of people have really poor image of magicians as wise-guys seeking attention.

Digression:
Q: Why did God create mimes?
A: To give magicians someone they can look down on.

Ok, I’m back. It’s unfortunate that people will then generalize that magicians are jerks just because their weird Uncle Earnie used to force them to pick card after card for no reason. That’s not magic. Real magicians (Ricky Jay, Rene Levand, Cardini) have reached levels of art that Weird Earnie and trendy “street magicians” can not even dream of.

The same goes for mnemonics. If you want to experience an amazing example of math and mnemonics in action, google “Arthur Benjamin,” among others.

I have been using and teaching mnemonics for years, and have found that as soon as a skeptic tries it and learns it from a competent teacher (Harry Lorayne’s books being the best for laymen, I believe) those skeptics become evangelists for mnemonics. But don’t take my word for it.

More in the next post. (Don’t forget to check back!)

Calculators

Somewhere our commenter seemed to think that I was for calculators in elementary school classrooms. Odd, considering that one of my mantras is “Calculators were invented by vampires to suck your brains out.”

I was also accused of doing some kind of disgraceful disservice of generations of teachers. Get real. I’m trying to defend teachers (real ones, anyway) against the lock-step of NCLB, ill-conceived curriculums that don’t let teachers actually teach, standardized tests that take up teachers’ and students’ valuable time and only reward the testing services that lobby for them, and the tyranny of endless, meaningless paperwork teachers face every semester.

Don’t take my Word for it. (Tell ‘em, Albert!”)

According to this entry in Wickipedia,

“In his early teens, Albert attended the new and progressive Luitpold Gymnasium. His father intended for him to pursue electrical engineering, but Albert clashed with authorities and resented the school regimen. He later wrote that the spirit of learning and creative thought were lost in strict rote learning.”

This point is also frequently and erroneously ascribed to Math Mojo methods:

The commenter seems to think the methods I use are somehow part of the “improved math methods” that are screwing up math ed. I’m with the commenter on this one for part of his point. I do think that much of the know-nothing, feel-good crap that passes for education today is making math ed. even more miserable than it was when I was a kid (jurassic period when “tradition” reigned unquestioned).

The problem arises when one assumes that anything that isn’t traditional is part of that crap. It’s kind of pitiful to have people generalize that everything that isn’t their “one best method” is to be put in the same pile.

Here’s the poop:

The airy-fairy newage trash that some schools are falling for is awful. It is worse than awful – it’s tragic. They don’t actually engage the student’s minds in meaningful ways. Sure, their press kits say they do, and maybe some of them actually could, in the hands of a competent practitioner. But the schools never give their teachers enough training, or even time to learn the stuff, before they send them out to use it. Face it, most elementary teachers are so overworked as it is, they barely have to cover the minimum curriculum.

It’s sort of like saying, “Grasshopper, the best way to be is “Enlightened.” Now go out and show your students how to be enlightened,” without giving “Grasshopper” the time to learn and have that learning mature into a great love of Enlightement, which he can then first begin to share in a meaningful way.

That is why I write so much about Math Mojo methods. Although they mostly take minutes to learn, they are meaningless without learning some of the deeper concepts behind them. And by deeper, I don’t simply mean the algebra, or some algorithm. Learn the Math Mojo nuts and bolts, and think about the methods, and you can come up with many deeper thoughts that relate to numbers and patterns, as well as to life in general.

It beats the hell out of “just shut up and learn it, because I said it’s the best method, and I’ll fail you if you don’t, and it will all be your fault.”

Or not?

’nuff said,

Dr. Gregory House
Professor Homunculus

I’ve just been perusing a very interesting blog (and a great resource for teachers in public schools). It’s called MathNotations.

This post intrigued and annoyed me, though. (Hey, maybe that’s a sign that it is a good blog!) It’s a poll about which method should be used to teach multidigit multiplication, like 48*73, for [...]]]>

I’ve just been perusing a very interesting blog (and a great resource for teachers in public schools). It’s called MathNotations.

This post intrigued and annoyed me, though. (Hey, maybe that’s a sign that it is a good blog!) It’s a poll about which method should be used to teach multidigit multiplication, like 48*73, for example. (If you do go to the link, make sure you scroll down and read the comment on Jan 30th by Michael Paul Goldenberg. It is excellent.)

Unfortunately, this poll is guilty of the same myopia as the American school system in general. It’s about creating a “standard.” Standard is just another word for limitation for people who really don’t know how to excel.

In the case of this poll, it is about choosing (out of an artificially limited group of choices – which is the logical fallacy of “false dichotomies”) how multidigit multiplication should be taught.

The wording of the poll is:

“Here are your options regarding your preference for how multidigit multiplication should be taught in Grades 3-5:”

Um, here are my options? I think not.

One of the great problems in (at least) American education today is that we’re firmly locked, sealed, and vacuum-packed into the box of pedagogical dogma.

Standard algorithm, partial products, lattice method, indeed! The myth of the “one best method” is still so rampant in our “developed” nation.

Education is not about inculcation of any algorithm. It is about students gaining insight, knowledge and lasting value. You can’t do that with “just shut up and learn this method,” just as you can’t do it with, “I’ll shut up and let you teach yourself.” Those are the ultimate false dichotomy in education of our time.

If teachers don’t know at least ten methods of how to multiply, they shouldn’t be teaching multiplication to more than nine students. It’s easy and important to understand multiplication in depth if you are entrusted to teach it to young minds. Go to the library, get “Calculator’s Cunning” by Karl Menninger, and get some chops.

And that doesn’t mean “tricks.” God, how I hate tricks. They trivialize anything they are attached to. How can I say this? I can because I am a professional magician. We (at least the good ones) hate “tricks”. One thing magicians know, is that as soon as you teach the “trick,” the magic is gone. It takes all the appreciation out of the effect.

You never show anyone how to do anything until they are ready to appreciate the thought and effort behind it. You would only teach a trick to another magician, or serious student of magic. You wouldn’t even teach it to one of them unless they’ve demonstrated that they are ready for it, and have a firm basis in the other magical concepts and skills that they need to pursue the trick you are teaching.

One of the dangers of teaching “tricks” is that you, as the teacher, might actually think that you are seeing a light bulb go off when the child says, “Oh, I get it!” But that is the same false light bulb that we magicians see every time a person says “Oh, I see how he did it now!” when someone tells him how a particular magic effect is done. They only know the most superficial part of the method. They can’t actually do the effect to any worthwhile degree, they only “know how it’s done!”

It’s like the hip jazz musician who meets the suburban musicologist, and says about him, “Yeah man, that cat knows where it’s at, too bad he doesn’t know what it is.”

The same goes for teaching multiplication. You must teach the reasons that the method works. If the child isn’t ready to understand the reason, s/he is not ready to use the “trick.” In other words, it shouldn’t be a trivial trick, it should be a meaningful method. And that meaningful method should be based on the distributive property.

How do you do this?

You have to get to know the child, and where s/he is with math so far. What so many pedagogues forget, is that education is about the student, not about the material. If the child struggles with addition, take a step back and cover that until the child understands it in his bones.

It doesn’t matter that you have to cover curriculum. It doesn’t matter that you are on the multiplication unit in school at this point. Clearly the pupil is not. You are a teacher, you know this. The administrators don’t, I know, I know. This is a problem. You can please them, or you can teach math. You can’t do both. If you can’t fight a bad system that you’re in, you are the system.

So you figure out if the child is ready to learn what you plan to teach them. If they struggle with “the tables,” and you are about to teach them the standard algorithm, you must get get them up to speed until the real light bulb goes off in their head – until they understand that “times” (with whole numbers) means “groups of”.

Then you must make sure they understand the distributive property in order for them to learn what they are multiplying when they multiply multidigit numbers. Have you explained that to them well enough? Do you understand it yourself?

It doesn’t matter which of the typical methods are taught in schools if they are going to be taught as “tricks” or taught as “show-and-tell” of “how to do it.” None of them will have any meaning.

And by meaning, I don’t mean, “grades went up.” You can get great grades with “tricks.” It makes teacher’s work easier. But it doesn’t teach anything valuable in the long run. If you teach for understanding, you get lasting value. If you teach with tricks and games, you are teaching that math is only good if it is not about the math. Great lesson, huh?

Education is not about inculcation of any algorithm. It is about students gaining insight, knowledge and lasting value. You can’t do that with “just shut up and learn this method,” just as you can’t do it with, “I’ll shut up and let you teach yourself.” Those are the ultimate false dichotomy in education of our time.

As usual, please take my views cum grano salis (with a grain of salt.) I’d love your comments, input, thoughts, rebuttals, etc. Math Mojo improves more from your input than from mine.

a) help you (or your child) with life in general and the education that counts, or b) just help you (or your child) pass the next math test?

If your answer was b, you just saved yourself some time and effort for [...]]]> Do you want to understand and be able to multiply in order to:

a) help you (or your child) with life in general and the education that counts, or
b) just help you (or your child) pass the next math test?

If your answer was b, you just saved yourself some time and effort for the next few minutes. You don’t have to read any further. But you’d be costing yourself (or your child) years of frustration. Passing a little (or big, standardized) test is just jumping through an artificial, meaningless, hoop. You don’t have to be a slave to the school system.

If you really need to beat the system, you need to game it. You need to learn math much, much better than they teach it to you in public schools. Then their tests will be a joke, and you will blow them away without being intimidated. But if you just want to learn enough to get through the next test, brother, you are digging your own educational grave.

It doesn’t make sense to accept their dogma, and then blame them for feeding it to you. Do something about it, now. Pick a subject you feel you’re lacking in, and then find alternative ways to supercharge yourself at it. “Ah speet on yo’ steenkin’ test from a high altitude!”

This is going to sound like heresy, but here it is – If you have a test that you don’t really have a good chance of passing because you don’t understand the material, don’t just cram and hope you’ll pass – Forget about the test, totally! Plan to fail it, but use that time to find a better way to learn. Go to the library, scour the internet, ask a friend, or check a bookstore for in formation related to the subject, and don’t stop looking and learning about it until you understand it better than anyone else in your class. Being “good enough” will never make you good enough. Make sure you can “speet on the steenkin’ test.”

Then, instead of just failing the test that you would have failed anyway, you fail the test, but actually learn the material so you will not fail any more tests on the subject, and you’ll be on your way to real knowledge.

Imagine this scenario:

Little Smike is faced with a test of basic multiplication, which his schoolmaster, Mr. Wackford Squeers, is going to give on Friday. Now, Mr. Squeers knows nothing about multiplication except for “the multiplication tables” (a posters of which he has hanging in various places on the walls of his classroom). And all he knows about how to teach or learn them is to “just shut up and memorize them!,” although he’s never even taught his class anything about methods of memorization.

Smike has tried and tried. He has shut up, he has stared at “worksheets,” he’s spent time with flash cards, and has even suffered through silly songs and rhymes, but he just doesn’t get it. Is Smike stupid, or does Smike just need a way to understand multiplication, instead of just learning how to parrot back meaningless information? Isn’t it often the smartest people who have the hardest time learning, because the methods of teaching are so insipid?

Mr. Squeers laments the fact that, though he is working so hard, his students just don’t seem to learn. What could be wrong with the little urchins? Why don’t they learn, despite his best pedagogical intentions?

Being from a family of administrators, Mr. Squeers subscribes to the time-honored platitude of, “You can lead a horse to water, but you can’t make him drink,” in order to excuse his ineffectiveness. He has certainly taught the little tykes well. Why don’t they just learn? (Perhaps he’ll have to thrash them.)

Poor Mr. Squeers. What he doesn’t realize, is that if they haven’t learned, he hasn’t taught. He can inculcate, threaten, or test them to the high heavens, but that’s not teaching. Perhaps if he made the water taste better. Perhaps if he offered the horse some milk, some lemonade?

You can make a horse drink, you just don’t always have to use water. You can teach multiplication. You just don’t need to use the times-tables.

Luckily for Smike, there is a new assistant in the class, a Mr. Nickleby. Mr. Nickelby knows an interesting

method of multiplication, which he learned from a magician while touring with a traveling stage company.

The method requires the use of basic addition and subtraction, rather than “multiplication tables.” It is counter-intuitive, but much more effective than the tables.

Unfortunately, Smike hasn’t been taught addition or subtraction adequately, because the class had to rush to “cover material” in because of the “No Child Left Unstressed” Act. But Mr. Nickleby has a plan – What if Smike spent the time between now and Friday actually learning simple addition and subtraction? That he could manage, it’s much easier than memorizing meaningless “multiplication facts” from a chart.

To make it even easier, Mr. Nickleby shows Smike a simpler way to add than is taught in most of the better schools. He uses a tool called an abax. And he teaches Smike how to subtract from left to right, instead of the old, less effective method. This builds Smike’s confidence, even though Smike hasn’t learn anything that will help him on Friday’s “multiplication facts” test.

On Friday, Mr. Squeers snickers as Smike fails the test miserably.
“Nickelby, old boy, it seems like your ‘star pupil’ is a miserable failure,” he chortles in his schadenfreude*.

“Yes, Sir. Failure there is for sure, Mr. Squeers.”

By the following Monday, though, Smike is the only child in the class that has a through understanding of basic addition and subtraction. He can perform these operations from left to right, without paper, quicker than than even Mr. Squeers can do it with pen and paper.

With that, Nickleby helps Smike parlay that knowledge into learning the basic multiplications up to ten-times-ten, in about five minutes. Smike will never forget what eight times seven is again. He will never struggle or be insecure about “multiplication facts,” whereas most of the other students had forgotten them by the weekend.

The moral of the story? Schools may suck, but education doesn’t have to.

The next few posts at the Chronicles will be about a Roadmap to Multiplication. I’ll be outlining the skills anyone would need to get a deep understanding of multiplication, and how to get those skills.

*Schadenfreude – “taking joy in the suffering and misfortunes of others.”