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

“From the National Mathematics Advisory Panel’s Final Report , released yesterday. It is entitled: U.S. Math Education is “Broken and Must Be Fixed”:

“International and domestic comparisons show that American students have not been succeeding in the mathematical part of their education at anything like a level expected of an international leader. Particularly disturbing is the consistency of findings that American students achieve in mathematics at a mediocre level by comparison to peers worldwide.”

As always, there’s something to this story, but it’s deeper than a short blog post can explore adequately. You just have to be mildly conscious to notice that American schools are generally doing a pathetic job of math education. But it’s not that easy to assess “blame,” or “what needs to be done.” There’s no simple answer to such a complex problem.

That it’s “broken” seems clear. But what is “it?” Each state, district, and even type of school is different. One thing that is clear is that creating simplistic “standards” (which are supposed to cover all federally funded schools) is just jaw-flapping by people who understand neither education, math, nor children.

Change for change’s sake is a silly impostor of a real cause. But there must be change for progress’s sake. So a consideration might be, “What kind of change, for whom, when, and how can we implement it – instead of just demanding it?”

I hope we don’t become even more of a nation of people who demand simplistic answers to complex questions. We demonize pretty bad math programs (yes, there are plenty, and I think the article is basically right to call “Everyday Math” one of them) but that doesn’t mean they have no good elements, or that we have to return to “tradition.”

That’s like saying, “We were the greatest car manufacturers when we had to hand-crank them to start them. If we want to be the greatest again, we need to put hand cranks back on cars.”

Although the premise has something to it, and I can certainly empathize with the commentary in the article which asks, “Can we get rid of “Everyday Math” now and go back to the old math?” – I also recognize that is probably not a useful solution.

The world changes. There are much better ways to teach nowadays than one way or the other, and it’s time we start working harder at using them, rather than insisting that there is “one best way,” that would work “if we would just do so-and-so.”

A first step might be to look at what works in each system (I imagine there are even parts of “Everyday Math” that don’t suck) and find out why, when, and for whom they work. Then put that in each teacher’s “toolbox” and go and find some more.

And then, for godssakes, let the teachers teach! Keep the textbook lobbyists and the politicians where they belong (in jail?), and away from young minds.

Another thing we might keep in mind is that the people who work on “Advisory Panels” tend to come from the industry they are advising (naturally). This sometimes leads to very myopic visions of what is wrong as “what is to be done.”

Everything with a grain of salt. No?

Hotcha!

Brian (a.k.a. Professor Homunculus )

Hey, you droogs,

There was an interesting post on the Whallah! blog about an article in the Associated Press, concerning the education of math teachers in public schools.

Apparently the National Council on Teacher Quality has done a comprehensive study to come to the conclusion that everyone who is not an “expert” has known for years: Teachers are not being taught math adequately, and generally fail to teach it well to their students. (Do tell…)

Isn’t it funny that the “establishment” will never admit that? It takes an expensive academic “study” to show what is already known, yet Universities (in general) will not do anything about the way they teach teacher how to teach math. They will try some new, expensive methods that some textbook company has lobbied for, of course. But they won’t try anything that might actually work.

That’s why homeschooling and afterschooling are becoming more and more important. Taking an interest in your own child’s education is more important than ever, as public schools tank in their ability to actually teach, thanks to the natural entropy of society, and the idiotically simple-minded ways some people like to deal with it, as with the subtly(?) sardonically named “No Child Left Behind” act.

According to the AP article:

“Author Julie Greenberg said education students should be taking courses that give them a deeper understanding of arithmetic and multiplication. She said the courses should explain how math concepts build upon each other and why certain ideas need to be emphasized in the classroom.         

“Teacher candidates know their multiplication tables, but “they don’t come to us knowing why multiplication works the way it does,” said Denise Mewborn, who heads the University of Georgia department of math and science education.”

This is the key to most of what every student needs to know…

… – how multiplication works. Addition is almost intuitive. It is an extension of counting. Once you extend addition to multiplication, (be careful, this does not mean that multiplication is simply an extension of addition) though, you need a good understanding of how the base ten system works, and the commutative, associative, and distributive laws. You don’t need to know the names of those laws, of course, but you need to understand how to use them in order to understand multiplication.

That’s the big issue. Just being able to recite multiplication tables is not actually being able to understand multiplication. And just going through the motions and repeating math steps that a teacher has “taught” you by show-and-tell methods, so you can prove that you can jump through the hoops for the big test at the end of the year usually does more damage to your understanding that anything.

So what is there to do about it?

First, as a truly concerned parent or teacher, make sure you, yourself understand some of the nuances of multiplication. Like why when you multiply by a fraction, the product is smaller than the multiplicand. (Did I get you with that one? Leave a comment below requesting the Math Mojo take on that one, and I’ll cover it in a new post).

Second, make sure you have at least two ways of explaining to your students how multiplication works. Not just how to do it, but how it actually works. I’m working on a video series about this now. Send me a nudge (again, in a comment below) to make it a higher priority to get it done and available to you faster.

Third, make sure you have a way to assess if your child or students understand what you taught them. The assessment doesn’t have to be a test. Tests are more about beating kids over the head. Asking questions and asking to demonstrate, in a non-threatening way would be my first strategy. If you must beat someone over the head, start with someone in an administrative position.

Here’s one of the reasons why:

According to the AP article:

“Since states oversee the preparation of the nation’s school teachers, the report recommends they set tougher coursework and testing standards.”

Why is does the solution always involve browbeating the learners? Why are the words “tough” and “testing” so often involved? How on earth does that teach or inspire? The problem isn’t that, “those who can’t do, teach.” The people who run those studies and teach university level education courses usually can do the math they are supposed to teach quite well.

The problem is that “those that can’t teach, teach.” Then they “train” teachers, instead of teaching them. No wonder those teachers have problems teaching. And no wonder the

As I always say, look up when you look for where the problem lies. You can’t blame a third grader for not learning. If it’s behavior problems, there might be an issue beyond the teacher’s scope, but most behavior problems are dealt with by good teachers. Also, I’m sure you understand that I am not talking about children with neurological damage. That is an issue outside the realm of my expertise.

But beyond those things, start looking up the chain for someone who needs the butt-kicking. If the teacher can’t teach, was  s/he taught well? (Are they even allowed to teach well in that school?) If the teacher’s teacher can’t teach, was s/he taught well? Is the administrator constantly putting monkey-wrenches in the teacher’s teaching techniques? Is something going on at the School Board mucking up the school? Is the state requiring more tests, but providing less resources for teachers and students? Did some idiot in the White House set everyone else up to fail so he can push some hidden agenda?

Keep looking up. Here’s a hint: Besides the handicapped, who’s got the parking spot closest to the school entrance? Start with him/her.

Remember - when things are looking bad, begin to look up.

I hope to hear from some of you soon,

Brian (a.k.a. Professor Homunculus)