M.J. had two good premises, but her conclusion [...]]]> 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 [...]]]> (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!

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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!

The title of this post is a little strong, but I want to make an important point.

No, I’m not going to rag on Al Gore.

This post [...]]]> First a tip of the hat to thethinkingmother blog, an interesting homeschool blog, where I found out about the video that is the subject of this post.

The title of this post is a little strong, but I want to make an important point.

No, I’m not going to rag on Al Gore.

This post is about an interesting and provocative post on youTube, by M.J. McDermott. Ms. McDermott is a meteorologist on a Seattle news station, and she is concerned about the miserable state of math education in this country.

Click here to view the embedded video.

Me, too.

But it is all too easy to shake our little fists in the air and want to “get back to the good old ways” of doing things. The good old way in this case is what Ms. McDermott calls “The Standard Algorithm.” And there lies the rub.

As a “guerrilla math” advocate, I take like to at least look critically at what we call “standard.” Standard for whom? How high is this standard? What goes above and beyond the standard, and how do we get there?

Face it, standard is, well – standard. It’s “good enough.” And that is true in this case. The “normal” way we multiply large numbers, with pencil and paper, carrying the ones to the tens, dutifully writing one row of partial-products under the next, remembering to put enough zeros behind each new row… – well, it works.

It is not particularly inspiring, nor creative. But it works. Bully.

If you’ve been poking around on this blog, and on mathmojo.com, you’ll know that I think mental math blows the doors out of the “way we are taught in school.” And by that I mean the good old ways as well as the more wussified pap that Ms. McDermott has done such a good and heartfelt job of exposing.

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

The truism refered to in the title is the notion that “the good old way” is somehow the best way. Or that there even is a best way. Or that, if there is one, it’s the one you think is best. Where ever you stopped thinking is where you tend to think the end is.

It occurs to me that the people that other people like to label “liberal” tend to like the “new age” (rhymes with “sewage”) approach to education. That causes the people some like to label “conservative” to backlash, and want to get back to “the good old ways of the good old days.”

But the conservatives forget that the “new age” is a backlash against the fact that the “good old ways” weren’t always so great. I’ll admit that the “standard algorigh” (I’m beginning to hate that term) is better than a lot of the fuzzy “I love you – you love me” feel-good horsefeathers that is sometimes taught. But that old time “drill and kill” stuff just beat the creativity and inquisitiveness out of too may students.

That smug, conservative way of bullying people with “the right way” is as assinine as the liberal “feel-good” B.S. It’s bad enough to bully, but when your “right way” is mearly one step better than “doesn’t suck”, it’s really hard to be inpired by you.

I wish that both sides would chill out and instead of telling us what is right and what is wrong, would go out and do a creative and critical thinking. One without the other is counterproductive.

Mathmojo is a labor of love for me, but I intend to work at it full-time now, until I have written at least one book and made a series of podcasts about each of the four operations, from the basics to turbo-charged streamlined ways to do massive problems.

It’s been slow going, because web-design and programming just aren’t in my blood. I’m getting a handle on the beast now, and I hope to get one good lesson up per day here or on mathmojo.com.

We’re only up to the beginning of intermediate multiplication on “Eating Math for Breakfast”, but when we’re finished with those lessons, I will begin pages, podcasts, flash animations and videocasts of a wonderful and intellectually gratifying way to do huge multiplications mentally, quicker than others can do them with the “standard algorithm” and pencil and paper. Stay tuned and send in your encouraging thoughts. That’s what keeps me going.

An observation: The way most intelligent people consider how using a calculator to solve basic multiplication problems is absurd, is the same way people who do mental math think of using pencil and paper.

The thing is, the better you get at the basics, the more you enjoy them, and the more brain power you are building to use for other things. So why not get really good? Why just be standard? Why just “not suck?”

Touting how great “standard” anything is compared to things that truly suck, is like saying, “Hey, lookey there at that durn fool still riding that mule. He ought to get hisse’f one of these newfangled Model Ts! That’s the fashion!”

While his neighbor in the Ferrari whizzes by dusting both of them, dreaming of the day we’ll all have jet-packs.

Hotcha!