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“In mathematics the art of proposing a question must be held of higher value than solving it.”

Georg Cantor

Here is an except from that comment:

“Frankly, I don’t care if an elementary school child can add long columns of numbers in their head - it is an almost worthless skill. I do care if they can think about mathematical concepts.

Better to teach them to come up with simple proofs (not memorized proofs) of basic facts in math.

Better that they should understand what a prime number is, and why we care about prime numbers.

Better that they should learn to enjoy slow, deep thought about puzzles and concepts.

That is where the gold standard in math education is.”

I wanted to revisit this thought, because Penny brought up some great points. I don’t disagree with any of them. But I must say that I, as well as a lot of the readers are coming from a different place. Penny is a brilliant research mathematician. A lot of us, on the other hand, basically have a history of thinking that we sucked at math (at least until we came upon Math Mojo, and learned that almost no one sucks at math, but some sometimes the way math is taught sucks.)

I wanted to address some of the points Penny made, because those points made me think a lot this month. Here’s

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Okay, admittedly, this post has nothing to do with math. But I got distracted.

We had visitors over from my wife’s family, and the young father of a four-year old boy was teaching his son how to spin a coin on the table. He said, “I think a coin can be spun with one hand? Can you do it?”

The reason he asked is because he knows I am a semi-retired (not semi-retarded) (okay, maybe a little) magician.

I had never tried, but it didn’t seem too daunting. So I gave it a try, and it was pretty easy. But while thinking about it, I came up with what I believe is a novel way.

Check out the video. It’s easy to learn, and is seems more difficult than it really is.

Have fun,

Brian

(note: At some point I misspoke and said John Kennedy was Ted’s younger brother. Of course, Ted was the younger brother.

I know that in the last post I mentioned that it is pretty much impossible to explain to immature minds what the benefits of learning math or any other skill is.

But I assume if your a Math Mojo reader, you have a pretty mature mind. (Cool sentence, eh? I get to flatter both you and me at the same time!)

So here are a few examples of concrete benefits I have gained from using “strange powers of the mind.” These are not necessarily the same benefits you will have. Everyone will experience different benefits. (Mileage may vary.)

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That the heck does writing backwards have to do with math?

For me, it’s a sort of warm-up exercise to get me into the creative, non-judgemental flow of opening my mind. This helps let answers come to me that my mind would otherwise have blocked out. It makes thinking less of a chore and more of a “party in my mind.”

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With so many things in bloom here in rural upstate New York, I figured it’s time for some new Ideas with Math Mojo.

One of them is the addition of a new segment, called, “Strange Powers of the Mind.” Look for a lot more weird stuff like this at Math Mojo. Sign up for the Math Mojo Monthly (”Comes out Quarterly, Mostly!”) Newsletter to keep up with the additions.
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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.

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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.

Something’s been on my mind for a long time. It’s the whole “public school atmosphere” thing.

I didn’t generally like school when I was a kid. I guess I went to pretty good schools, as far as schools go. I liked a lot of my teachers. I just didn’t like the “set-up.” I thought that whoever designed the whole process must have been a bunch of ignorant, arrogant jackasses.

Year after year, teachers and students complained about the same things. Some were reasonable, some weren’t.

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Surely most readers have had thoughts and observations about boys’ and girl’s differences concerning their typical learning strategies.

A reader (Susan G.) has been corresponding with Math Mojo for a week or so, and I’ve noticed that she’s made some great observations. She’s also written a e-book on word problems. I’m in the process of reading it, and it looks right-on-target. It will be a resource that teachers and home-schoolers will want to have.

I’ll be writing more about it in the future. In the meantime, if you want to find out more about it, please shoot me an e-mail (use the contact box on this page) asking about it, and I’ll put you in touch with her.

Susan had been kind enough to offer some of her expertise about education in general, and she’s been one of the readers who’s taken my request for proofreading to heart; she’s pointed out some typos in Math Mojo materials, which I’ll be correcting a.s.a.p. (Thanks for the heads-up on this stuff, Susan!)

She’s kindly given me her permission to publish some of the thoughts we’ve been sharing about math-ed.

Here’s and excerpt from a recent correspondence we’ve had:

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Today a concerned reader took issue with what he understands my methods to be. (See comment #4 at Augends, Addends and the Commutative Law of Addition.)
Fair enough, but I think he may have misunderstood my methods.

That could, of course, be due to the way I communicate them (or miscommunicate them). First let me say that none of the algorithms (ways of solving math problems) I teach are “mine.” “Math Mojo” is the name of my attitude, not the methods. The methods have been either gleaned from better sources than me (and most are hundreds, if not thousands, of years older), or I have “re-invented” them. That is typical for most people’s alternative methods.

Now to the issue; the reader stated:

After all these years (30) of struggling to teach children math, I finally realize why it is so difficult. A brief perusal of some of the mathematical girations you go through to multiply two numbers together explains a lot of why kids are poor at math. Commutative and associative properties are more easily understood when you have the basic tools to work with without adding zeros then subtracting the number from your cousins name on your mother’s side of the family. Teach the basics by rote then progress to the more abstract. Simple to complex seems to work.

Professor Homunculus’ reply:

I’m sorry you’ve come to that conclusion. If you’ve been teaching math for 30 years, you surely have some insights. But I can’t see see how you’d say, “simple to complex” seems to work. May I ask where it seems to work? And if it does, why is it a struggle for you, and why is it so difficult? Have you been teaching with the “girations” (sic) you say I use to make it so frustrating?

I’m not quite sure I understand the logic of your position.

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