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Unfortunately for me, they are not my financial insights. If I had any financial savvy I wouldn’t be a math blogger. But recently I was googling “math mojo” and I came upon the Reading the Markets blog. In this post, the author says, “I think we profit enormously from looking at alternative approaches to a problem.” She mentions this MathMojo blog as an example thereof.
I was impressed, not just for the ego stroke, but by the fact that the author “gets it.” It turns out that she is a Yale-trained philosopher, so I imagine that she gets it more than I do. But I was glad that my message is getting through. MathMojo isn’t simply about math and arithmetic. It’s about approaching things differently, and training and trusting your brain.
The “Reading the Markets” blog is about “Insights from Financial Literature’” a subject that is Greek to me (sorry about the pun, Brenda). But if it were a subject of interest for me, I know I’d make a bee-line for that blog. Insights always trump information.
If you learn no math from MathMojo, but learn that the “standard algorithm” (or the standard way to do anything) is only one way to skin a cat, and not necessarily the best way, then you’ve “gotten it.”
Getting out of “but the teacher said we have to do it this way” way of thinking is about the best thing you can do for your mental development. Yeah, maybe you have to do it that way in school, to get a grade, but please realize that grading is a way for schools to keep you obedient, not make you enlightened.
Go ahead and give the teachers what they want, but make sure you pursue anything you like to a much higher degree than those minimums they call “standards.”
Be an uncommon denominator.
Hotcha!
Brian (a.k.a. Professor Homunculus )
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Sky and Telescope.com has an interesting article this month. In “A Rogue Star Going Wild?” (no, it’s not about her) it discusses the Homunculus Nebula.
It’s not exactly a math article, but Professor Homunculus likes it anyway. Check it out.
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I’m almost finished putting up the first week of the new “Quick and Dirty Multiplication” Math Mojo course.
In the meantime, a few people have asked me to get to work on a “Quick and Dirty Addition” Math Mojo course.
I won’t be able to get to that for a few weeks, but if you need immediate help, I’ve put together a few resources that I’ve created over the last year or so.
The goal would be to take anyone who can already say, 3+ 6, and knows the difference between the ones column and the tens column, and be able to add huge columns and rows of whole numbers in a short time, accurately, and easily.
Check out the videos below for an example of what anyone should be able to do in less than a month of practice.
Speed Addition Demonstration Video
The video you are about to watch is simply a demonstration of how fast a huge addition can be done with Math Mojo methods. It does not explain anything. All the things you’ll need to be able to do addition like this will be explained in the resource page (see below).
Speed Addition Demonstration
Speed-Checking your Addition
Same goes for this video. It is simply a demonstration of how fast checking huge additions can be done. This checking method is taught in full detail in The See-Say-Write Method of Addition Mojo. (If you order your copy from the resource page that you can get to by filling in the form below, you will get a free practice booklet of over 100 pages bundled with it.)
Speed Checking Addition Mentally
One of the resources I’ve gotten together for this post are an audio file that you can listen to here. It’s about 12 minutes long, and will explain the basic Idea of speed addition. It talks about the reason we count and add the way we do. It explains it so that a child can understand it.
I’ll also be sending you to another Math Mojo page about Learning Addition from the Ground Up, that has a very comprehensive video about basic speed-addition.
After that, I’ll recommend the only thing that requires any payment (and it is only $9.95). It’s my e-booklet, “The See-Say-Write Method of Addition Mojo.” It teaches only two things, but they are amazingly powerful, and are hardly ever mentioned in schools. The first thing it teaches is how to add two 2-digit numbers (like 76+89) in your head, without having to think about it consciously. You’ll be able to do it easier than most people can add 7+9 in their heads.
The second thing it teaches is how to check your answers. Don’t underestimate this! It is one of the best kept secrets in all of arithmetic. It’s almost never mentioned in schools, and when it is, it is glossed over, and not really taught. It is a crying shame. If schools taught this, they would immediately see gains in their student’s math skills.
An amazing bonus is that this same method of checking can be used for multiplication, subtraction and division. It is about the best weapons you can have in your mathematical arsenal, and it is a huge help on standardized tests.
There is a practice pad that is available for the See-Say-Write method, which insures that you actually learn the method, instead of just reading about it and then forgetting it. (After all, what good is it to you to simple “know about” it, when you can actually know it and be able to use it?) That practice pad is normally $5.95, but you can get it free if you order
In the resource page, I’ll also include a special report in PDF file, of how to use the See-Say-Write Method of Addition Mojo to accomplish gigantic additions like the one in the above demonstration-videos.
Nothing will be left out.
In a nutshell, the resource page contains:
- Free audio about basic addition
- Free video about basic addition
- Link to the See-Say-Write Method of Addition Mojo booklet with the special offer for a free practice pad
- Free PDF of how to use the See-Say-Write Method of Addition Mojo to accomplish gigantic additions, quickly and accurately.
Anyone should be able to add large examples quickly and easily with these methods. Students will freak their teachers out with their new abilities.
Fill in the form below to get free access to the resource page for speed-addition.
The reason your e-mail is required, is for me to be able to gauge interest in speed-addition. If there is a lot of interest, I will finish the full course as soon as possible. It’s also so I can notify you when the course is finished, as well as send you free addition tips as I add them to the free resource page.
There is absolutely no obligation for you to enroll in the course, buy the See-Say-Write e-book, or anything else. I won’t share your e-mail address with anyone, either. The form is a double-opt in, which means that when you hit the submit button, you will get a confirmation e-mail. As soon as you reply to it, you will get an e-mail sending you the web-address (URL) and password to the resource page.
If you do not wish to remain “opted-in” there is an easy way to opt out in every message I will ever send you. The double-opt in is just a way to keep both of us free of spam. And I will never, ever share your e-mail with anyone, for any reason.
This is your best way to learn an amazing method. Just fill in the form and submit it now for your free access to the resource page.
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There was a wonderful article in the Wall Street Journal today about mathematics in the former Soviet Union. It is worth reading for anyone interested in finding out a little about the inner beauty of math.
Here’s a short except:
what mathematics really is: “It was a wonderful education… Gelfand amazed me by talking of mathematics as though it were poetry.”
In the mathematical counterculture, math “was almost a hobby,” recalls Sergei Gelfand. “So you could spend your time doing things that would not be useful to anyone for the nearest decade.” Mathematicians called it “math for math’s sake.”
How cool would that be? Can you imagine something like that in an American school? I can’t.
So check out Mathematics in the Soviet Union, at the Wall Street Journal’s website.
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This will not have much to do with math, but a lot to do with mojo.
One of my heros, Soupy Sales, died yesterday.
Soupy was a comedian, who hosted a children’s show in the 50’s and 60’s. He was a master absurdist, with an incredible sense of humor, and a wonderful respect for the minds of his audience. His show was booked as a “children’s show”, but his material was aimed a little higher – over the kid’s shoulders with a nodding wink to their parents.
Soupy is among the other master creators, like Lewis Carroll, L. Frank Baum, James Barrie, and J.R.R. Tolkien, who’s books are sometimes considered “children’s books,” but we get a lot more out of them as we mature. It’s fitting that this week also brought us the movie “Where the Wild Things Are” (from Maurice Sendak’s book), which is another example of this.
He was one of the people who shaped my Idea of how to present my magic show, how to do math-magic presentations for children and adults, and even how to write this blog.
“I’ve never done a pretentious show; it’s always had a live feeling, the kind of thing that comes across when you don’t know what’s going to happen next,” Sales told author Gary Grossman in the 1981 book “Saturday Morning TV.”
I only hope I can live up to that.
His show was aired during an era when live television still was the norm. Other great children’s hosts, like Sandy Becker and Sonny Fox, shaped my Idea of mojo. Mojo isn’t just magic, and it isn’t just about the blues, as a lot of people think. Mojo is just a weirder, more open-minded way to approach anything. And that was Soupy, all over.
I remember watching his show when I was a kid, sitting with my dad and my brother on the couch, the three of us cracking up and mugging for each other when Soupy’d get hit by a pie.
Here are some links where some of you other baby-boomers can reminisce about Soupy, and maybe some younger people can go find some comedy-mojo from a different, less nasty era:
Pachalafaka, Soupy!
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How could I have missed it? Or almost have missed it.
Today is Martin Gardner’s 95th birthday.
Who is Martin Gardner, you ask?
I’m glad you asked that question!
You can read more about it in today’s New York Times Science Section.
I’ll write more about him soon, but for now, do yourself a huge favor and check out that article, then run to a library and check out any math books of his that you can find.
Here’s another good article about Martin Gardner in the New York Times.
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Here’s a dilemma for a lot of parents and other people who are trying to teach their kids math:
The methods that many people use are far superior to the standard algorithms taught in elementary school, yet many benighted administrators and school policy-makers do not recognize this, and insist that students do things “the regular way.”
Of course they don’t realize that other cultures (besides the U.S.) have a different “regular way” that sometimes beat the poop out of our way – which is proven by our low ranking among most other countries of the world in most subjects.
I’m specifically thinking of math. I help teachers, parents and students learn math with methods that magicians have used for years. They are not “magic” – just more effective, which make them seem like magic. Some of these methods are the norm in other cultures (the ones outperform us by far in elementary math).Commonly, someone I am helping will ask, ” But what if we are not allowed to do it that way?” Recently someone wrote in:
“I am fascinated with your approach to math but worry about teaching these kids differently from what their teachers are teaching. Will I confuse them? Because they are graded on the methods taught in the classroom, will I be doing more harm than good?”
Well, let me not be coy – yes, you will confuse them if you teach superior methods. But that is unavoidable, and not as big a deal as it might seem. There really is no learning without some initial confusion. The common “show-and-tell” kind of inculcation that gets kids to jump through specific hoops is not really learning. It is “training.”
If the children aren’t getting it the “normal” way (and all statistics point out that most kids in U.S. public schools don’t really have a grade-appropriate grasp of math), then it is really time to bite the bullet and face a little confusion.
They will get over the bit of confusion, as soon as they finally “get” what they are supposed to get, using better methods. Besides, the alternative methods do not give different answers, they just use different algorithms to arrive at the answer.
Let me give you a trivial, yet representative example:
You know that when you multiply a whole number by ten, you basically just tack a zero on to the end of the number. For example; 34 x 10 = 340.
It seems like a “trick,” but any streamlining of a method seems like a trick to the uninitiated.
Would anyone really expect any child to write out the example, complete with partial products, each time they were to multiply by ten? That would be ludicrous.
As long as the child understands the concept that there are ten groups of the number, therefore the number is to go into the tens column instead of the units column, it’s fine – no, it’s necessary – for him or her to just “know” the answer is 340.
So when you teach them a better algorithm for the standard algorithm to perform multiplications like 28 x 63, it would be appropriate – no, much better! – for the child to be able to simply write or call out the answer “1,764″, without showing any “work.” (For the algorithm for this, check out this post about the inferiority of the “Standard Multiplication Algorithm” – which also has some more thoughts about “showing the work.” )
Yes, some teachers will frown on a student doing things like this. Fortunately, I live in the twenty-first century, where most of the teachers I have shown this to can’t wait to embrace it. There are still some hold-outs, but that says more about them than about the methods, or their students.
The real problem lies with administrators and school-boards who don’t really understand what teachers face “in the trenches.”
There are ways to deal with that, and I’ll have to deal with this in another article, soon.
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I was poking around some old files on my computer this morning, and came across something I’d scanned from our local newspaper back in 2002.
It’s just one of the reasons schools need work.
Get it?
Hotcha,
- Professor Homunculus
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Using magic to present new math Ideas
An insightful reader wrote in:
Susan Grigor wrote:
Good morning, Brian,
I want to consult your wife as one who works with little people.
I have been looking at the Grade 3 and Grade 4 curricula. There is a
lot about looking for alternate strategies such as 26 + 35 = 30 – 4 +
30 + 5 = 61. Note, however, that positive and negative numbers are
not taught until Grade 7.
Kids even up to Grade 7 are literal/concrete thinkers, not abstract
thinkers. How well do they use these abstract ideas? They are
mental gymnastics.
Susan,
I don’t see anything in Math Mojo that is less concrete than the pap they feed kids in “standard curriculums.”
Math Mojo doesn’t use the 26 + 35 = 30 – 4 + 30 + 5 = 61 kind of strategy. I use what I call the See-Say-Write strategy. It is subtly different, but it does not use any subtraction. It is also extensible. I use it for adding gigantic columns and rows in my head, easier than most people can use a calculator. I also use it for advanced multiplication. (More on that in a forthcoming course.)
The only problems I’ve ever had teaching second-graders or above any Math Mojo stuff has been because of what you mention in the next paragraph – some of them apparently “like” to do it the tired, old way.
I see that as one of the most important things I can do in this world – break them of that miserable, school-learned, brain-deadening habit.Naturally, kids like to learn. They like to learn cool and new things. But when you get “partial credit” for showing work that doesn’t need to be done, and you are bent-over and forced through artificial hoops long enough, it just beats the soul out of you.
Here’s my dirty secret – Math Mojo isn’t about any math techniques. It’s about re-humanizing the learning experience. My goal is to get people to realize, “Hey, that’s amazing! I can really learn meaningful stuff if I want to! And it’s always more fun and rewarding than that stuff the drones do!”
Susan continued -
My experience is that kids in elementary school (and high school) do
a lot of math by ritual and rote, rather than real understanding–
and they like it that way. They want to be told the right way to do
things, and then to practise until they get good at it. Only one to
three per class are interested in mental mathematics and alternate
views.
I am working on presenting these ideas. But I wonder about those
others for whom this is not interesting, but frightening, those who
want numbers to be sure and solid, not slippery and subject to
interpretation like story- and essay-writing.
Okay, I’ll admit that some kids get scared of this in the beginning. But those kids are so severely damaged that they need to learn this stuff. It’s so important that we teach kids that math really is a free-ranging, adventurous, imagination-filled world. If they don’t learn to appreciate that in the early grades, they will be the kind of people who grow up to say “I’m just not a math person.” That is like saying, “I’m just not a reading person.”
Kids that insist their numbers be “non-slippery” are kids who are going to have a very, very difficult time with irrational numbers someday. They are also the kinds of kids who get the heebie-jeebies when they are faced with operations with negative numbers.
All of that stress can be avoided by not reinforcing the bad pedagogy that standard curriculums present
So one of the ways I present cool stuff is not to tell them that they are learning the same stuff a new, alternative, better way (which of course it is), but instead to present this stuff to them as an extra bit of “math magic.” Not a trick, but real magic.
For example, when teaching multiplication by 5, I write a long number, with all even digits, on the board, like 68,462.
Then I ask one of the kids who may not be the swiftest in the group to come up for a magic experiment. I them simply ask him or her what half of 6 is, and to write that below the six. Then what’s half of 8, and to write that below the 8, etc. down to the final 2, and then imagine there’s a zero at the end, and to write half of that (which will be zero, of course) below that.
Then I tell the class that little Spatula (or whatever the kid’s name is) has done an amazing magic trick. It’s one that even David Blaine probably can’t do (true). Then I have the kid sit down, and ask for applause.
Everyone thinks I’m nuts.
Then I ask the best math student in the class to come up and be part of an experiment. (It’s still the same “trick”, but I don’t tell them that).
Then I ask the “smart” kid to multiply the original number on the board by 5. Normally the little genius re-writes the number, writes a 5 below it, writes an “x” for multiplication, draws a line, then goes through the ritual of doing times-tables in his or her head, complete with writing the carries, until finally little Pippin (or whatever the kid’s name is) arrives at the very same number that Spatula did, without carries, re-writing or other machinations. (And Spatula even did it from left to right!)
I do so enjoy the little tykes’ “Oh, my God!“ses when they realize what just happened.
They have seen, and convinced themselves, that this new thing “rocks.”
Being a magician, I’ve spent most of my life helping people reach a “suspension of disbelief.” This is one great way to do that with math.
In general, I think this is the way to go. It makes you appear to be less of a “teacher.” It also avoids trivializing magic as a “trick.” The actual magic happens when the kid goes “Oh, my God!” – when the light bulb goes off. It’s that light bulb, not the method, that’s important. As a true teacher you know that already. As a magician, I’m just giving you another way to light that sucker up.
It is questioning like this that interfered with my career, you know
Yeah, I know. That’s why I can’t really even consider working for anyone but myself. But it speaks wondrous volumes towards your human-ness.
By the way, the little people my wife works with are usually more at the stage of being able to tell their nose from their arm, or simply being able to count, than doing simple arithmetic. I’d love to help her with this kind of stuff, but there’s not much call for it with the kids she works with. Her magic with them is waaaay beyond any help I could offer her, anyway.
I think teachers in general (the good ones) are magicians in a sense I never could be – you deal with administrations. That is some heavy mojo (voodoo?)
All the best,
Brian
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The Math Mojo Chronicles have been down for the weekend due to some technical problems .
It’s nice to be back online. Although the site’s been down, I’ve been writing posts all weekend and will publish them soon.
Thanks for your patience. It’s the first time the blog’s been down since 2003. I hope it doesn’t happen again!
- Brian
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