The Math Mojo Chronicles » multiplication

Geek-Speak

Brian — Mon, 05 Jul 2010 20:55:24 +0000

The cartoon below is similar to a small part of the method I teach in “Numbers Juggling – Times without the Tables” e-book and course (see http://learn2multiply.com)

You can see a video of the method I teach here:

http://www.learn2multiply.com/video-quickstart/

You’ll need a password for it. You can get the password by requesting it below

(After you fill out the form, hit the “back” button on your browser to return to this page)

What’s interesting about the comic is that the method works the same way, (using slightly different fingers for each number) and for the same reasons, but it comes to a very discouraging and misleading conclusion at the end. The “Numbers Juggling – Times without the Tables” e-book and course clear up the problem the cartoon describes.

Although the comic is funny and makes an ironic point at the end, I find disturbing and not entirely true. Read it for yourself, and then check out my notes at the end.

In the cartoon, the point is that the answer is “totally unsatisfying – this is the worst thing about being human.” It is ironic and funny, but I think it is the wrong message, and an incomplete and wrong conclusion.

Here’s the deal :

Because some people speak geek and some don’t, there is a huge communication gap. Geeks understand the “reason” that it works is because x = y. But their language is algebra, which lots of geeks don’t understand. So geeks end up saying things like, “Now that you’ve seen the proof, you know fully why it works.” Yeah, some people do, and some don’t.

What geeks don’t understand, though, is that algebra is more or less just a language. It is not the reason, really, it’s just the language they use to explain the reason. Plain english can explain the reason as well, it just takes longer. Algebra is pretty much just shorthand. Because geeks “get” this shorthand, they’ve forgotten that other people don’t, and they don’t see the reason to expend the effort to rethink it so they can explain it in plain english.

You know the syndrome – it’s like the computer geek who is going to “help” you with something. He’s going to go into the unix shell and explain all the coding to you, but you just want to cut and paste the thing.

That’s the dilemma that Math Mojo aims to solve. I’m not a geek, but I “get” geeks, and I’m not a “dummy” anymore, but I “get” dummies.

So, in the ”Numbers Juggling – Times without the Tables” book and course I teach “secret” ways of multiplying (the main one is without the fingers, but it works similarly). Each step is explained in plain english, then (in the e-mail course) it’s translated into algebra, so that the reader can seamlessly follow along and understand the value of each “language.”

One of my aims is to subtly get the readers to see that they can understand the algebra if it is made plain to them in their own language first. Then they slowly have their “lightbulbs go on” and realize that algebra is not some intimidating “geek-speak”, it is simply a shorthand for what we already understand. It doesn’t necessarily explain things, but it always describes things.

What geeks don’t get is that if someone doesn’t “speak” algebra, they can’t understand the description, so it doesn’t explain anything to them. It’s like when Robinson Crusoe tries to communicate to Friday in English, and Friday doesn’t get it. So what does Crusoe do? He speaks louder. That’s what geeks more or less do. How smart can they really be, then?

It’s the human geeks like Carl Sagan, de Grasse Tyson, Isaac Asimov, and the king of them all, Martin Gardner, who know how to talk to both worlds, who are really going to save us, if we can be saved at all, I think.

My message is exactly the opposite of the conclusion of the comic. I appreciate the irony and the humor of the comic, but you can take the irony further. The more you know (geek), sometimes the less you understand (about relating it to others). That is what is unsatisfying.

The real message is that it can be extremely satisfying to understand deeper things, as well as understand that although you are unique, the ability to understand is not. (Almost) anyone can understand things if you understand the human relationship to understanding knowledge as well.

If you are learning something, and sometimes you don’t understand the explanations even though you are truly trying, don’t beat yourself up about it.

I spent the weekend trying to build a garden shed from “professional instructions.” They left out a lot of important steps because they made so many assumptions about the reader’s skill level, even though the plans were ostensibly for beginners. Made me want to choke someone.

Then I realized that it wasn’t me. It was exactly the “geek-speak” dilemma. I then sat down with the plans, took it slow, and tried to figure out what the writers were trying to say. I even ended up figuring out something things that will help me with my building skills in the future.

It’s good not to have blind faith. It’s good to use your brain.

Remember, there is a higher percentage of teaching-disabled teachers than learning-disabled students. Don’t blame yourself. Don’t blame anyone. Just see if you can identify the problem, and find a way to deal with it in your language, or find a way to learn the language that is more compatible with the problem you are dealing with.

Math is something that you are going to have to deal with, like it or not, for the rest of your life. So you might as well learn as much as you can about it. The more you dig in, the more you’ll find things to like about it.

Eduction (Edux)

A professor friend of mine, Dr. Kent Lawson, taught his own theories about something like what I’m trying to express here. He taught at RPI, and at SUCO(State University College at Oneonta, NY). He was a decorated professor of Theoretical Physics. I had the privilege of taking one of his physics for non-physics majors courses, as well as one of his Eduction (Edux) courses.

Dr. Lawson passed away last year, and his family left all of his materials to me, which I consider a great honor. I am going through about 40 boxes of class notes, audio tapes, old reel-to-reel tapes as well as a few video tapes. It is slow going, as he wrote much of it in his own handwriting, and he had “essential tremors” (something like Parkinsons disease – the great senator, Robert Byrd, had the same affliction. Maybe you’ve seen him on TV) so it is almost impossible to read.

Dr. Lawson was very concerned about the de-humanization he saw all around him. A lot of it was pernicious and some of it was less malicious (like academia). He was a great translator of physics, but even more, his Eduction (Edux) theories contained (among many other things) a system of exercises to help humans see the kind of thought-traps we fall into. It offered ways to identify and deal with them.

The comic above is a classic example of such a thought trap. Math Mojo is my way to deal with it.

I hope some of this made sense. Thanks for taking the time to read it.

Hoskeebo!

Brian (a.k.a. Professor Homunculus)

P.S. You will probably be hearing a lot more about Edux from me in the future. The culmination of Math Mojo will be to eventually offer entire online courses of Edux, in the spirit that Dr. Lawson presented it, and in his words.

P.P.S. I still like the comic. It’s very well done, and there are many other good ones on the site where it came from. Click on it to take you there.

The Next “Numbers Juggling” Multiplication Course

Brian — Thu, 16 Jul 2009 07:00:24 +0000

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.

How To Practice Multiplying by Two with Playing Cards

Brian — Wed, 11 Feb 2009 18:06:19 +0000

Click on the image to learn how to multiply without the tables

Here’s the first of the new videos for MathMojo.com’s biggest selling booklet, “Numbers Juggling – Times Without the Tables.” It is a great way for children or adults to be able to multiply any two digits instantly. But it does it without any boring, rote memorization.

The book has just just gotten an upgrade. It’s in its third edition, and I’ve added over a dozen videos, for all the digits (they don’t all work like multiplying by two). They’ll be available to anyone who has bought the booklet, for a small upgrade fee. I’ll be sending out a notification of how to access them in a few days.

If you learn the methods (they take only a few minutes), you will know all your basic multiplications, without ever having to stare at tables, etc. Unless you practice them, though, you will not be particularly fast at them. But we don’t want to be doing any boring worksheets, etc.

For that, I’ve come up with a fun, easy, nothing-to-buy (as long as you have a deck of cards laying around the house) method to practice.

If you want to get a copy of the booklet, the e-course and the videos that come with it, just click on the image.

Enough talk. If you’ve learned the ”Numbers Juggling – Times Without the Tables” method, get out a deck of cards and watch the video.

Have fun!

You can order the booklet, the resources, and access to the videos here:

or you can get more information at Learn2Multiply.com

In the next week or so I’ll be making a video series of how to multiply by larger numbers. It will be very inexpensive, easy to learn, and much more fun than worksheets, rubrics, “standards,” testing, curriculum, NCLB and all those inessential institutional inventions.

Math Skills versus Math Concepts (Pt. 1)

Brian — Fri, 23 May 2008 14:41:05 +0000

There seems to be a big “fight” about “which should you teach first, math skills or math concepts.” A popular example is the “multiplication tables” versus the concept of multiplication (as repeated addition, for example).

It’s a pretty good bet to say that when memorizing things it’s easier if you can relate the objects. Like if you went shopping and had to get toothpaste, a toothbrush and dental floss, that would be easier to remember than if you had to get shoe polish, armadillo meat and an f-string for a lute (do lutes even have f-strings?)

So if you can have the items related to each other, it’s easier to remember them. It’s certainly easier to make sense out of them.

Now, when you consider the following numbers from the point of view of a child learning them:

9, 18, 27, 36, 45, 54, 63

they seem to have nothing in common, except that they are on a chart of “the multiplication tables” that the child is told to “shut up and memorize!”

On the other hand, if you show the child groups of objects, which have nine in each group, and you put them next to each other, they can readily see how nine grows into 18 if you add two groups, then into 27 if you add another group, and so on.

This increases the child’s appreciation for what he is learning, and decreases resistance to that learning. So showing the concept definitely helps learn the skill.

The school of thought that says, “Teach the skill and the concept will be easier for the child to understand later” is based on what we want the child to learn, not how it’s best for the child to learn it. This is utterly misguided.

It’s the “authoritarian” way. It’s the same school of thought that says, “You will do as I say whether you like it or not, because I know what’s best for you.” That is the most counterproductive way that was ever thought of. It is the default, brain-stem, neanderthal way. And it doesn’t work to produce intelligent children.

It may produce obedient drones if that’s your goal. But I’m pretty sure that if you read this blog, that’s not exactly what you’re after.

Actually, the “authoritarian” way doesn’t even create obedience. But it’s a great way to produce anti-social rebels who will revolt against the thing you are trying to teach them. I don’t mean that they’ll become the creative-rebellious types who produce great things for society, I mean they’ll become the destructive little shits who only complain, and then grow up to be exactly the kind of disappointed authoritarian types as the dunces who tried to inculcate them with “facts” and “skills” that became neither to them.

A Theory of Relativity…

Imagine giving your child a list of names, like: Mark, Simone, Leonora, Derrick, Romulus and Matthilde. Now tell them what each looks like and acts like, and that Mark and Simone are married, and Mark is their father’s brother, and Leonora and Derrick are their children, and Romulus and Matthilde are Derricks friends from school. You can even make a chart of all their relationships and characteristics.

Or, you an invite them all over for a barbeque and letting the child play with them and get to know them. They gradually learn how each is related to whom, and they get a personal relationship with each. Those people become meaningful to the child (imagine that!)

Which do you think will stick with the child more? Which would he rather do, sit and stare at a list and a chart while you grade him on his progress, or play and interact?

I hope this little analogy, imperfect as it is, nailed the difference between understanding and drilling for you.

Respect your Mind

When we teach concepts first, and skills later, we are reinforcing the Idea of respecting the minds of the children we teach. It may take a while, but when you do that, the child slowly gets the Idea that it’s okay to trust your brain. They’ll see that when you don’t expect them to memorize something and then use it quick (because, say, you have to “cover material”, and it’s in this “module” of the “curriculum”, and that “it will be on the test soon”), that they can actually grasp it, and understand it more deeply. That way, everyone gets more satisfaction from the teaching/learning endeavor.

Tomorrow I’d like to mention a kind of caveat to all of this, concerning a bit of Zen philosophy.

Apropos of nothing:

I’ve recently gotten into the “Twitter” thing. Not sure if I like it, or what it will bring, but it is new, interesting, and a great distraction from work. I’m supposed to be using it as an organizational and motivational tool. We’ll see.

Recently I read a “tweet” from http://twitter.com/bcubbison. He asked, “What kind of people would name their planet after dirt?” It made me wonder what the people who named their planet “Uranus” are like.

BTW, do you use Twitter? If you do, check me out at twitter.com/Prof_homunculus, and follow me.

Addendum

On Thursday, July 31, 2008 I read an interesting blog post at The Amazing Mind blog, entitled Learning Mastery 5 – Back to the Basics. You might want to check it out. The blog is very interesting in general as well. He bring up many topics and points about them that everyone should ponder now and then. Have fun.

Practicing and Checking Multiplication With Playing Cards (1)

Brian — Mon, 28 Apr 2008 03:34:03 +0000

Math Mojo has got some surprises for you. New lessons on how to improve your basic math skills, and videos! Professor Homunculus is getting his Video Mojo workin’ to bring you some great new stuff.

The first set of videos will be about how to practice multiplication using playing cards. So grab a deck of cards and let’s get going!

First, take out all the Spade cards from the deck – we’ll only be using those. Then, remove the court cards (the Jacks, Queens and Kings) from those cards. Consider the Ten to be a zero and the Ace to be a one.

Now you’ve got 10 cards, which represent the digits zero through nine.

Shuffle the cards. Now decide, in your mind, which digit you’d like to multiply by.

Deal the cards, face up, on the table so that you can see the faces of all the cards.

Get out a piece of paper and a pencil.

Depending on how advanced you are at multiplication, start at either the right (if you multiply the “school” way) or the left (if you know Math Mojo) of the spread deck, and start multiplying, writing only the answer (not the carries – never write the carries!)

In the video, we’ll be multiplying all the digits from 0 to 9, by 3. It’s simple to start with 3.

After you learn how to do it, try multiplying the cards by the other digits.

We’ll multiply by some higher digits in future videos.

You may have noticed that I don’t know my left from my right in this video. My bad!

Tomorrow we’ll practice checking, using this same example.

If you liked this post, you’ll love:
Free Instant
Access to
The MATHMOJO MONTHLY
("Comes out Quarterly, Mostly!")
NEWSLETTER
Tons of no-nonsense, easy-to-use tips that will
help your child understand math
in a fun, friendly way.
It’s FREE and it’s FUN!

Learning Multiplication by Rote is a Disease

Brian — Sun, 30 Mar 2008 04:15:10 +0000

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:

ess than meaningless

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?

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).

Rote rots. It is a miserable and counterproductive method of inculcation disguised as teaching.

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.

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

Multiplication, ADD, Wildaboutmath

Brian — Sat, 08 Mar 2008 23:07:43 +0000

Recently I got an request to review my booklet, “Numbers Juggling – Times without the Tables.” Request came from Sol Lederman, who runs the “Wildaboutmath” blog.

I’d heard that name before, but really couldn’t remember much about Sol, so I checked out his blog to see how serious it was.

Wow, it’s a great blog, full of lots of valuable information about math, how to learn and teach math, and the joy of math. You should definitely check it out.

Sol reviewed the booklet, and you can read his review here.

The review was generally positive, but Sol had a very valid and important criticism. Since the greatest value of the booklet is really in the seven follow-up e-mails in the e-mail course, it should be marketed as a course, rather than a booklet.

That got me thinking (as every good book-review should do). So now I am developing real, in-depth, home-study courses for each of the basic operations of arithmetic.

Each will be about thirty modules long. The modules will walk you through the basics to absolutely turbo-charged speed-math methods.

I’ll be telling you more about it as it develops. If you are interested drop me an e-mail. (Use the contact box near the upper right corner of this page).

Now on to the ADD part of this post. Many people who have problems with math have problems with attention, focus, concentration, etc. I am one of them. I have suffered with ADD for as long as I can remember. It was only “officially” diagnosed a few years ago.

As it happens, Sol suffers from it as well. Or suffered. He has a blog dedicated to journaling his recent “cure.” I have not met Sol, and cannot vouch for anything, but he seems very dedicated to describing his experiences honestly.

Let me say that I am a skeptic, down to my bones, and hope you take everything with a grain of salt. But I would investigate what he has to say. I have subscribed to the RSS feed to his site, and intend to look into the methods he as used. You might want to take a look as well.

Augends, Addends and Commutative Property of Addition

Brian — Fri, 29 Feb 2008 18:12:41 +0000

original photo from Richard Masoner Edited by Brian

Not sure what got me thinking about this today, but I was musing about the commutative property, and how it applies to addition and multiplication. (Yeah, it was a pretty boring morning.)

Specifically, I was thinking about the word, “augend”. The augend of an addition problem is the first of the series of addends. It’s not a word that is usually taught, and I was wondering why not.

You should be aware that addition and multiplication have the commutative property, and subtraction and division don’t. That just means 4+6 is the same as 6+4, and 3*7 is the same as 7*3, but 8-2 and 2-8 are not the same, nor are 9/3 and 3/9.

So it doesn’t really matter which of the numbers is placed where in addition, so you don’t need to specify which is the augend, and which is not. You can call them all addends. Same with multiplication – you can call them all multiplicands. (Not so with minuends, subtrahends, dividends and divisors, though – they don’t commute.)

But I think we should teach about augends. There are several good reasons why, and you can read about them at a lesson I just put up at Names of the numbers in basic arithmetic operations. That lesson is all about why we give the different parts of arithmetic problems their names, (like dividend, divisor, and quotient) and why it makes sense to learn them.

Now that I feel like I’ve cleared this all up for you and me, I’ve got something that I’m not so clear on. Maybe some kind reader has some insight about it she or he’d like to share. It’s this:

Since you must differentiate the names of the parts of subtraction or division problems, what happens if a problem has more than two terms, like 8-3-2? Is there a name for the third term? What if there are fourth or fifth terms?

I assume that they are called, “the second (secondary?) subtrahend, the third (tertiary?) subtrahend, and so on, but I’m not sure.

Anybody got any insights?

You may want to check Names of the numbers in basic arithmetic operations first, though.

By the way, if anybody can write me and tell me why I chose the image that I used for this post, I’ll send them a free Math Mojo e-booklet. (Use the contact me near the top right navigation bar on this page.)

Update: You don’t have to write about that anymore – we have a winner! Mark (see below) got the booklet.

To clarify: The big dog in the picture is “Doggy Daddy,” and the little dog at the door of the train is “Auggie Doggy.” (They are Hannah-Barbera cartoon figures.) They are about to enter a commuter train. Get it? Augend/Auggie, commutative property/commuter train? (Groan.)

Multiplication, Algorithms, Tricks, and “The One Best Method”

Brian — Wed, 30 Jan 2008 13:49:16 +0000

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?

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.

Hints for Learning Simple Multiplication

Brian — Mon, 28 Jan 2008 10:34:37 +0000

A girl recently asked:

“I need help learning multiplication. Can you help me learn to multiply?”

Professor Homunculus replied:

I have lots of questions to ask you, but first, here is something you can do right away to help you learn multiplication by 2, 3 and 4:

Get out a deck of cards. Make sure they are all (52) there. Now count them by twos. If you end up saying “fifty-two,” and have no cards left, you got it right.

Now try by threes. If you end up saying “Fifty-one”, and have one left over at the end, you got it right again.

Now try by fours. If you end up at “fifty-two” and have none left over, you’re right again.

Now do that over and over. Always count by twos, threes, and fours, no matter what you are counting from now on.

If you get a group of coins, like pennies, as change, count them by threes.

If you have to count the amount of kids in a class, count by threes or twos.

And so on.

Actually counting things in groups is a lot better than looking at tables, and parroting them back.

If you really want a great way to learn to multiply very fast and easily, consider getting a copy of “Numbers Juggling – Times without the Tables.”

You can find a link to it on the right-hand side of each page of these Math Mojo Chronicles.

Also, have you checked out MathMojo.com? Go there and click on the link for “speed multiplication by 11 and 12″. (It’s down the page a bit).

Then, check out:
http://www.squidoo.com/multiplication/
It will teach a cool multiplication trick, but you’ll only be able to do it if you first learn (and practice) what you learn at the “speed multiplication by 11 and 12″ link, above.

You are actually in luck. Recently a new book came out, and I have to say, it is a great book for girls to learn math from.
It’s called “Math Doesn’t Suck,” and it was written by an actress who is also (of all things) a mathematician. It’s a pretty awesome book.

Now for my questions:

How are you at addition? How are you at your other subjects in school? How are you with sports? Do you practice anything regularly (a sport, musical instrument, game?)

When you wrote the comment, were you aware of your misspellings and grammar mistakes? I’m not asking to judge you, just for info for how to help you.

Any answers to those questions will help me figure out how to help you better.

Name
Email