How to Present New Math Ideas

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