The reason for this post is that Angela (Mother Crone) left a very interesting comment on yesterday’s post concerning how mental math has helped her daughter, who is dyslexic.

How many screwbulbs does it [...]]]> Nice title, eh? Let me preface this with the admission that I know just about nothing about dyslexia. Clinically, I mean.

The reason for this post is that Angela (Mother Crone) left a very interesting comment on yesterday’s post concerning how mental math has helped her daughter, who is dyslexic.

How many screwbulbs does it take to light in a dyslexic?

(Yes, that was unbelievably cheap.) Although I have no insights into clinical dyslexia, I have fought my whole life against certain dyslexic-like symptoms. I also suspect that any person who is at least mildly aware of his or her thought-processes struggles with similar symptoms.

For example: when I do a crossword puzzle – when I write in an answer that had been partially complete, I often transpose some letters. Say the answer to 32 across is four letters long, and I’ve already filled in the first two from “down” clues. They are O-D. Now when I come to the clue for 32 across, it’s, “What are the … ?” So I know that the answer is O-D-D-S. When I go to fill in the D-S, I will often write S-D. I won’t even notice it unless my wife is there to point it out to me (which is usually the case). Or, if I’m doing the puzzle alone, I won’t figure it out until I have beaten my head against the wall trying to get the right answer to one of the “down” clues that crosses the D or the S. Because they are transposed, they will “block” any correct answer I come up with until I finally see what I have done.

It’s interesting that I almost never transpose letters when I am writing in a whole word or phrase. If none of the letters of the answer for O-D-D-S was already present, I’d simply write the word “odds,” but if any letters are missing from a complete word, I have a good chance of transposing them.

It happens so often, that over the years I’ve had to train myself to occasionally step back during the puzzle and stop searching for clues, and just “sift” through the answers I have so far and look for discrepancies. (Actually, I’m glad I’ve had to do this. It’s a great habit to get into when trying to solve almost any type of problem.)

The reason I don’t play Bingo

Also, I often transpose the digits of the number of a clue when I go to write it into puzzle. For example, I see clue 47 down is “Plant of rock and metal.” (For the answer, see below) I immediately think, “Got it! Now where is 74 down?” And I’ll search for 74 down, and either notice that there is no 74 down, or it has the wrong number of letters for my answer. After a few seconds of confusion, I’ll have to look back at the clue and notice the correct number.

My wife isn’t as aware of my problem with this as she is of the “transposed letters” problem. There is almost no chance for an observer to notice me doing this, as I don’t fill in anything incorrectly. The whole phenomenon takes place in my head, and I don’t write anything down before I notice what I’ve done.

And this is exactly one of the points I want to address. Many people (not dyslexic themselves) see dyslexia as simply a social problem. “Oh, how embarrassing that he made such a goof in front of people! It must be hell to live with the shame.” (Or something like that.)

Public goof-ups are just the tip of the iceberg. When you have a cognitive problem (Dyslexia, ADD, depression, etc.) it’s not really about your public ego. It’s something you deal with when your on your own, as well. The frustration of not being able to solve a problem that you understand is sometimes unbearable. I can speak from personal experience with ADD (still struggle with it) and depression (have pretty much overcome it).

People just don’t see that you are struggling with the issue using very different thought patterns than they are. Sometimes while I know they are thinking, “Why doesn’t he just…” I’ll be thinking, “Why doesn’t that ignorant bastard solve his own problems before giving misguided advice to me?”

While some people are embarrassed for the dyslexic person, some of us are more embarrassed that the others don’t have the depth and breadth of thoughts that some dyslexics, or others have.

I am fortunate enough to see that there are some people who can appreciate the “different” thought patterns of dyslexics, ADD “sufferers”, depressives, etc. My wife is not only a special education teacher (which explains her patience with me!) but she has a non-judgmental persona. She can notice things and remark on them without jumping to a conclusion.

Lots of people can do that, but a lot of people can’t. Unfortunately, many of them that can’t hold positions of “power” in the education system. They are the people who make the “standards” and “curriculum.”

…and those who can’t teach, administer.

They are the people who have successfully ruined what once gave me hope that the American school system could someday be excellent. They are the people who are trying to take curiosity and learning, and “otherness-thinking” away from the younger generation.

They are the ones that make life hell for talented, dedicated teachers. They’re the ones that want to put your thinking right back in the box, and hermetically seal that box.

So are you just going to rant, or are you going to give us something we can use?

Hmmm, maybe. Angela mentioned that her dyslexic daughter is “stoked” about doing math mentally. I know how she feels. When I write answers I tend to transpose digits, but I almost never do what when I do math mentally. Other people have written to me that other Math Mojo methods have helped their dyslexic children or students. Although I can make no claims for it’s clinical efficacy, if you struggle with cognitive problems, you might want to give mental math a try.

One thing that has gotten a lot of positive comments from people helping dyslexic children is the Abax. I’ve even gotten testimonials from special education teachers about it.

If you would like to know more about this fascinating manipulative, and how to use Math Mojo methods with it, check out Introducing the Abax, at MathMojo.com

Take a number…

I’d like to address the use of mnemonic devices for memorizing numbers. When I use mnemonic devices, once a number has been “translated” into a device, I never transpose any digits. The system helps prevent it.

I would like to know if anyone out that has any experience with full-blown dyslexia and high-powered mnemonic systems. If you do, please leave a comment about them. I don’t mean the “Most Very Educated MathMojoers Judiciously Serve Under No Public-school-system” stuff (hey, I just made that up! Someone stop me before I pun again…) I mean the phonetic system for memorizing gigantic numbers.

Anyone else, please feel free share your experiences and thoughts about dyslexia and math in a comment, below.

By the way, there is a word for “dyslexia with numbers.” It is called discalculia. Please don’t self-diagnose yourself as discalculic just because you have problems with math. Discalculia is rare, and needs an in-depth diagnosis. It is a lot more severe than the symptoms I have mentioned.

Which leads me to my final point:
I am very grateful to Angela for letting us know about her daughter’s progress. People with dyslexia, ADD, etc. can be the luckiest people in the world. When you see a problem as a challenge, not as a handicap, you have an advantage over people who will go along in life never imagining what it is like to make a great improvement over terrible odds.

It is the “motivational dissatisfaction” with your situation that can lead you to take steps that the hoi-polloi only dream of. It is a kind of “sublimation.” Sublimation is a kind of coping mechanism (or defense mechanism). I recently read that it is considered the only defense mechanism that positive.

An example of sublimation would be the famous Charles Atlas, who was the original “ninety-eight pound weakling” who used to get sand kicked in his face at the beach regularly. Instead of not going to the beach anymore, he started lifting weights, became one of the fittest men in the world, and marketed the “Charles Atlas Fitness Program,” which made him rich and famous to boot.

So here’s to all you mental Charles Atlases out there!

Hey, Hey, Mama…

Answer to 47 down (damn, I really almost wrote 74 - true!): Plant of rock and metal = Robert. (Why, what did you think?) For you young ‘uns, Robert Plant is the lead singer for Led Zeppelin (By the way, I just made that clue up. I better make a note of it…)

Here is an except from that comment:

We’re going to use what I call “numbers crunching” to check. That is the same as using the nines-remainders. You do know how to get the nines-remainder of a number, don’t you? It’s very simple, but it takes a bit of explaining.

It also [...]]]> To check multiplication of single digits by longer numbers with playing cards:

We’re going to use what I call “numbers crunching” to check. That is the same as using the nines-remainders. You do know how to get the nines-remainder of a number, don’t you? It’s very simple, but it takes a bit of explaining.

It also pays to know why checking with nines-remainders works. Both of those things are beyond the scope of this article, but I’m working on a booklet and a video about how to check your answers for all of the basic operations of math using “number crunching”. There are lots of tips and shortcuts that make this method absolutely simple and effective. Let me know if you’re interested by using the “Contact” box near the upper right hand corner of this page.

(This video will be re-edited and uploaded by the end of Wednesday, April 30)

If you know about crunching, you’ll be interested to know that practicing with cards like this is perfect for checking with crunching. It turns out that if you crunch all the digits from zero to nine, you get a crunch number of 0.

Since we’ll always use sets of cards to represent the digits from zero to ten, we’ll always get a crunch number of 0.

So take whatever digit you were multiplying by, you’d have to multiply it by 0 to get your final check number. As you know, anything times zero is zero, so whenever you practice with cards like this, your check number will always be zero!

So if the crunch number of your answer is anything but zero, you have made a mistake somewhere.

Starting with ten cards is pretty easy. It turns out that as long as you use complete sets of all ten digits from 0 to 10, you will always have a check number of 0, no matter how many sets you use. So you can use ace to ten of as many suits as you like (as long as you remember that the tens count as zeros, and aces as ones).

That makes sense, doesn’t it? Because if a single set of zero to nine crunches to 0, then two sets must also crunch to 0, because 0 + 0 still equals 0.

In a very few days you should be able to work yourself up to multiplying any single digit number by a full set of forty cards (four sets of ace to ten, with all suits) within a few minutes. And then another minute or so to check them.

One of the benefits of doing it like this is that you are going to have to do all the additions and subtractions to get the nines-remainder of a forty or forty-one digit number in order to check it. That’s great practice in those two operations.

This is a fantastic morning exercise for children or adults. When you do something like this before breakfast, your mind becomes much more awake than it would have been.

Watch the video, then try it.

By the way, you may have noticed that at some point in video, I say, “The number has to crunch to nine,” where you may have thought I meant to say, “zero.” But remember, in Mod 9 (nines-remaindering, or “crunching”) zero is nine.

Did you know that technically, you can use any digit-remainder to crunch with, not just the nines-remainder? Most of the shortcuts (ask me about them) don’t work with nines-remainders other than nines, though, so that’s why we use nines, mostly.

Elevens-remainders are good to use as well. They have some shortcuts, just not as many as the nines, though. If you need to be absolutely sure of your answer, it’s best to check with the nines, and the elevens. I’ll have more posts up soon about each of them, and they’ll be thoroughly covered in the booklet that will be out soon.

Remember, a little bit of knowledge can be dangerous; so when you use numbers-crunching, be aware that it is “just a trick” until you understand it more deeply.

The first set of videos will be about how to practice multiplication using playing cards. So grab a deck of cards and [...]]]> 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.

One of the drawbacks to using the “crunch” method, which I described, is that it is not 100% accurate.

Often, people who need to defend the status [...]]]> A few posts ago, I offered some tips about how to check large division problems without having to multiply huge divisors and quotients to get even huger dividends.

One of the drawbacks to using the “crunch” method, which I described, is that it is not 100% accurate.

Often, people who need to defend the status quo (you know who they are, they work in the principal’s office) insist that checking by crunching is not acceptable, because it is not foolproof.

Let me give an example:

You could divide 1206 by 18 and get 64

It looks like it works. But it doesn’t. The real answer is 67.

Sometimes you can transpose digits, or make a mistake, the crunch of which will work out to the crunch of the real answer. After all, there are only 10 digits which all integers can crunch to.

It is very seldom, though, that you will crunch mistaken digits and do the multiplication, and have the answer come out to a crunch number that still has the same crunch number as the real answer.

The reason that mistakes are so seldom, is that it is easy to add numbers like 1+8 and 6+4 and multiply the results.

Although mistakes still can be made, much less mistakes are made with this method than with the cumbersome method you probably learned in school. Consider this: What is easier to do,

(1+8)*(6+4)
=9*1
=0, (all of which you can do in your head, with no training, in seconds)
or
18*64? (Do you really want to multiply that mentally if you don’t have to?)

There are many small-minded people in education, who insist that methods other than theirs must be foolproof, when their own methods are even less foolproof.

The mission of MathMojo is not only to teach easier, more effective methods, but also to make math more meaningful to you. And one way to do that is to sharpen your critical thinking skills.

Here is a perfect opportunity to do just that. Can you see the flaw in the small-minded person’s argument? They set up conditions that new things must fulfill in order for them to consider using them. But they don’t put their own things under the same conditions.

That phenomenon is one of the most prevalent flaws of society. Catch it when you see it, and call them on it.

Hotcha!

Want to try another one? How about

962/52 ?

Well, they’re both even, so that’s going to [...]]]> We’ve been talking about using factors to make long-division problems easier, sometimes being able to turn them into a manageable sequence of short-division problems, in which no paper and pencil (and certainly no calculators!) are needed.

Want to try another one? How about

962/52 ?

Well, they’re both even, so that’s going to be a piece of cake to start. Divide both by 2 and turn the problem into:

481/26

Can you factor them further? You can tell that 2 won’t be a factor. And a quick look at 26 tells you that 3,4,5,6,7,8,9 and 10 won’t factor into it. It’s only factor, other than itself and 1 is 13. When you factor 13 into 21, you get 2.

Now all you have to do is test if 481 is divisible by 13. If you know the trick to test for divisibility by 13, you could try that, but let’s just assume you don’t, and go ahead and divide it in our heads.

13 goes into 48 three times, with 9 left over. Carry the 9 to the front of the 1 in 481, and get 91. Divide that by 13, and whaddyaknow, it goes in exactly seven times. That gives us 37.

We have reduced the problem from

without much trouble, and no writing. I think you can handle 37/2 on your own from here.

Right, it’s 18, r. 1.

Remember, that’ the answer to 37/2. But if you want to check it as the answer to 962/52, you’re going to have to re-factor in the 13 and the 2 to the remainder. When you multiply the remainder (1) by the factors (2 and 13) you get 1 x 2 x 13, which is 26.

Checking 962/52 = 18, r. 26

962/52 = 18 r. 26

So the crunch to the problem is 0, remainder 26.

So the crunch to the answer is 0, remainder 26.

The crunch to the problem matches the crunch to the answer, so the answer is very probably right.

What if the problem had been 927/18? Both numbers are not even this time, so it is not readily apparent if they have common factors.

If you know how to factor (if you [...]]]> In the last post we looked at the problem of 926/18, and we simplified it to 463/9, so we could make it a short division problem.

What if the problem had been 927/18?
Both numbers are not even this time, so it is not readily apparent if they have common factors.

If you know how to factor (if you don’t, you can get a lesson at The Pretty Good Guide to Prime Factorization at MathMojo.com.) then you factor both of these numbers by 9.

Here’s a hint: If a number can be crunched to 9 or 0, then nine is a factor of that number. If you want to know more about crunching, I refer you to “The See-Say-Write Method of Speed Addition“.

There are also many hints you can find about how to determine if numbers are divisible by other numbers. MathMojo will eventually cover this in depth, but I’m sure you can find info if you google “divisibility rules.”

Ok, so let’s factor 927/18.

Using short division by 9, we get 103/2. How easy is the problem now? Just cut 103 in half in your mind and get 51 remainder 1. But remember, like in the last post,
If you factor a division problem before you solve it, you must multiply the remainder by that factor after you are done.

So the answer to 927/18 is 51 remainder 9, (not 1).

Go ahead and check it. Remember how? If not, check out this post.

Check out the third and final post on this subject about Long Division Shortcuts. 

Imagine you have to do this division:

926/18

How would you do it? Would you rewrite it with that funny division symbol (“division bracket,” or “right parenthesis followed by a vinculum over the dividend”)? Would you use a calculator? (Please say “no” to that!)

After you rewrote it, would you start by trying to [...]]]> (Is that title an oxymoron?)

Imagine you have to do this division:

926/18

How would you do it? Would you rewrite it with that funny division symbol (“division bracket,” or “right parenthesis followed by a vinculum over the dividend”)? Would you use a calculator? (Please say “no” to that!)

After you rewrote it, would you start by trying to figure out how many times 18 would go into 92? If you did, you would be doing it the way most people learned in school, and you would be wasting a lot of time and effort.

Look at it again. Your school probably spent a lot of time trying to teach you about factors when you were young. But it probably didn’t take too well, because they probably didn’t teach you at all – they just did mathematical show-and-tell over and over, and called it “teaching.”

Have no fear, your brain is capable of much, much more. Let’s start…

You’ll probably immediately notice that both numerator and denominator are even numbers.

Using factors, we can see that 2 goes into both numbers. Now we’re turning the problem into short division. Without rewriting anything, we can simply cut 926 in half, from left to right, getting 463. Do the same with 18 and get 9.

You’ve successfully turned the problem into 463/9. PLEASE don’t write it down. You can keep a number in your head like that if you practice. Start practicing now. You will be happy you did.

Next we do short division again. 9 goes into 46 five times, with a remainder of 1. The remainder goes in front of the 3 (of the 463) giving us 13. 9 goes into 13 one time, with a remainder of 4. It would seem that the answer is fifty-one, remainder 4.

There is just one other thing to remember. Since you reduced the original problem by a factor of 2, even though you kept the proportion of the improper fraction (that means that the improper fraction 926/18 is the same thing as 462/9) the remainder is not the same. You must factor the 2 back into remainder. 2 x 4 = 8, so your real answer would be fifty-one, remainder 8.

Make sure you remember this:
If you factor a division problem before you solve it, you must multiply the remainder by that factor after you are done.

Had you not kept the remainder, and instead, continued to divide the problem until you either reached a finite decimal number, or a repeating decimal, then you wouldn’t have to worry about “unfactorizing” the remainder.

What? You’d want to check it? Well, you could multiply 51 by 18, add the remainder of 8 and get 926, or you could multiply 51 by 9, add the remainder of 4 and get 463. Or you could even do the original long division.

But, you, you clever custard you, you read the previous post, right? And you know about checking by crunching. Or didn’t you? Well, it’s never too late…

In the next post about long division shortcuts, we’ll talk a little more about factoring division problems.

M.J. had two good premises, but her conclusion does not [...]]]> This post is a continuation of the other posts about the video on YouTube entitled “An Inconvenient Truth” with M.J McDermott (not to be confused with Al Gore’s film) which concerns the dismal state of American basic math education in public schools. You can view it here.

M.J. had two good premises, but her conclusion does not jibe. “Their methods suck.” (True.) “My method is better.” (True.) “Therefore mine is the one everyone should use.” (Nahhhhh.)

Why don’t you experiment a lot and discover what works best for you, and keep refining it? It can be so much more fun and rewarding to do that. Respect your mind, not the opinions and emotional responses that were put there by others in the past. Try this stuff out, then decide.

It’s important to mention that people who think it’s OK not to learn the basic arithmetical operations because “you can do it with a calculator” are just plain damn dumb. That’s like saying, “Hey, this ‘walking’ stuff sucks. It takes effort! Why do we need to learn to walk? That takes years! Let’s just give everyone a wheelchair!’

Not having the basics down cold, and being asked to educe basic mathematical algorithms for yourself, is like not knowing how to read, and having to derive the sense out of every word you read as you go along, without knowing what the letters mean. It would be amazingly cool, and I’m sure some autists have done something like it, but expecting every school child to do that is nothing short of educational child abuse. And then subjecting them to standardized testing? Well, that’s just medieval.

Learning the basic operations can be much easier than the ways generally taught in school. Learning them only takes years if you have ignorant educators, or good educators limited by ignorant administrators and politicians. The “No-Child-Left-Unstressed” act only exacerbates the situation. It’s great for teachers – bad teachers who don’t know how to teach and need someone looking over their shoulders to make sure they are “on track”. If a person can’t be trusted enough to do the job s/he was hired to do, why should s/he be doing it?

On the other hand, that law, born of ignorance and arrogance, limits and straight-jackets good teachers into using only the “standard” methods of doing things. “Standards” are nice and quaint. They are “minimums.” They do not inspire – and no valuable learning comes without inspiration. Inspired teachers are punished in today’s schools. Inspired kids drop out, hate school, and usually are more intelligent than the drones that the “No-Child-Left-Untested” law creates. Thank you, standards!

My point is, this way to multiply is better than the “standard” in probably every way, yet people keep clamoring for the “standard.”

Why is it that people see a change for the worse, and say “We need to change back to what wasn’t worse” instead of raising standards and look forward to a change for the better, which is easily at hand?

I’m afraid the “new” math suffers from lack of willingness to do work, and “old school” math suffers from lack of imagination.

How about using both effort and imagination?

If Newton and Euler stayed “old school” we wouldn’t have calculus.

An algorithm is more like a recipe than a law. It’s only a word; don’t be intimidated by it. An algorithm is basically a set of well-defined instructions.

First of all, it’s silly to think that there is one best algorithm for all multiplication problems. There are lots of algorithms, and lots of problems. You don’t use the same kind of hammer for every kind of nail, do you?

Karl Menninger, in “Calculator’s Cunning” (a brilliant book, by the way) has dozens and dozens of ways to do multiplication. He suggests that people who can reckon really well need to have a lot of arrows in their quivers. That was in 1931, and the situation has changed a bit. Dozens of methods might be a bit much now, but we should all certainly have more than one tool for each operation.

Each time you learn a new method, it helps you understand other methods, as long as you learn a bit about why each method works.

Think of music. There are plenty of ways to play a song, but it’s the same song. Some of the “standards” are pretty hokey. Some of them are absolutely great. But if we insisted that we stick with what we did before, a lot of the music that you love would never have been made. (If you like Steve Miller, that might be a good thing.)

This article concerns M.J. McDermott’s youTube video about the sad state of basic math education in America. You can visit the video here, or you can simply scroll down to the next entry here in the Math Mojo Chronicles, where it is embedded.

It [...]]]> (If you use a little imagination you can guess the title of this article.)

This article concerns M.J. McDermott’s youTube video about the sad state of basic math education in America. You can visit the video here, or you can simply scroll down to the next entry here in the Math Mojo Chronicles, where it is embedded.

It seems like M.J. McDermott has unleashed a firestorm that need to be unleashed. She’s gotten almost 60,000 hits in one week on youTube for a video about math! Imagine that! Good work, M.J.!

I’ve commented on that video several times, mentioning that there is at least one much better algorithm than what is called the “standard.”

Not one of the hundreds of other people who commented on the video seems to be aware of this, which is strange, because most of the comments to M.J.s video were posted by obviously thoughtful people. And one man who is obviously a lot better at mathematics than I am even made a video-reply to M.J.s video – but still stuck in standard mode.

Here is a synopsis of my part of the discussion so far:

I’ve just waded through 180 comments and was floored to see that NOT ONE PERSON mentioned that the “standard (for whom?) algorithm” – though better then that other ones presented – is NOT the most efficient, nor the easiest to learn, nor the one that teaches place value the best. There is at least one much better one.

(What? You want the method handed to you? – Go investigate!)

That is also what’s wrong with the system – everyone has the “one best method.”

Happy calculating!

Someone posted later:

One thing that occurs to me, and that I have not seen anyone else mention is that the standard forms are easily expanded from double digit to any larger size number ( 3, 4, 10or even 20 digit numbers are easily multiplied) once the standard form is known. These other methods will become unreasonable cumbersome very soon. Algorithms like the lattice method belong in a subcatagory like “having fun with numbers” , fun to play with once you master the traditional method.

And I replied to it:

Actually, the algorithm I alluded to is infinitely expandable and much more practicable in every way. It constantly amazes me that people want to cling to the unsupportable idea that the “standard” algorithm must be the best, just because it’s better than the crap in some feel-good, know-nothing books. It’s time to look higher for better things instead of patting ourselves on the backs for being “standard.”

’nuff said!

brandon8888 then commented:

I looked at many algorithms for over an hour, but found none that fit your description. Time to put up!

My next post was :

I’ll put up good explanation for the “mystery algorithm” soon. In the meantime:

Doing something as simple as 26 x 31 only requires that you multiply 26 by 3 in your head and stick a 0 at the end. That’s 780. Mentally add 26 to that and you’ve got 806. Why on earth would you want to do it any other way?
It’s fine to learn the “standard algorithm,” but if you don’t explore other (better) ways, you’re stuck with it. An algorithm is a recipe, not a law.

Someone posited the Idea that, “…you’d better learn the traditional system …” because algebraic division can only be done with that method. Au contraire:

My comment to this was:

Your comment is certainly well meant, but for the fourth or so time, it is not true that the “standard” is the only way. “Traditional” is usually a euphemism for “closed-minded.” There are other algorithms that can be even more helpful for algebraic division than what has been called the “standard” algorithm.

I’m sure you will realize that to understand anything it helps to come to it from more than one direction. Keep an open mind, but, as M.J. points out, not open to just any b.s. that comes along!

Then I posted this to a conservative blog:

I know we are all so brilliant, and we all know what’s “wrong” with the state of education, blah, blah, blah…
I’m not happy about it either, but I doubt that anyone reading this, and who has watched the youTube video in question, knows a really good algorithm for multiplication. No, it is not the “standard” one.

It is amazing that everyone wants to hoist their flag and complain, but no one really wants to admit that their way isn’t “the best.”

I’m sure I don’t know the best way, either. But one I do know is faster, easier, and more fun that the “standard” one. (Jeez, since when does “standard” mean “best”?)
And you do it in your head. No paper and pencil, and sure as hell no calculator.

Please go investigate.

Happy calculating!

---

What I wanted to write (but youTube only allows comments of a maximum of 500 characters:

You seem like a nice woman and your heart is definitely in the right place. The problem is certainly as you describe it, and it is heartbreaking to see the absolutely absurd methods people use to accomplish simple operations.

But may I say that your solution to the problem has several discrepancies. “Standard” algorithm is a more subjective term than you’d like to believe. Standard for whom? Certainly not to the people who can do basic operations quickly, accurately, and enjoyably.

You may find it hard to believe, but many mental math methods can be much easier than your “standard” algorithm. And there are countries and some schools who teach it. And kids who learn it enjoy math, and blow the doors off your “standard” students.

It is ludicrous for anyone past fourth grade to need pencil and paper to do a simple two-digit by two-digit multiplication problem.

If you like, I can teach you how to do 21 x 36 in your head, without paper or pencil. If you want I can teach it to you over the phone in less than two minutes.

I don’t try to make “little math geniuses” out of kids, but I’ve yet to meet the child who’s curiosity about math I can’t awaken. (And I’ve met a lot of kids!)

I’ll give you this: Calculators are the bane of any math class. They were invented by vampires to suck kids’ brains out.

This has been a very long post. There’s more, but I think I’ll save it for tomorrow.

Do you ever dream of numbers?

Hoskeebo!