Introduction to these Chronicles

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May 7, 2004

Hi. I am Professor Homunculus. Brian Foley created me, and now I am helping to create him. Sometimes he will make entries here, and sometimes it will be me. Generally we won’t differentiate between who is who.

I am helping him sort his thoughts about Math Mojo. The site is becoming a little overwhelming, and we’ll be using The Math Mojo Chronicles to help him get his thoughts together and also give you an Idea of what Math Mojo is, why it’s here, and where it may be going. Warning: there may be a lot of rambling along the road to clarity. Let’s start from the beginning:

Brian here. It’s nice to finally have this forum to explain about Math Mojo.

When I was young, going to school in the 60’s, I was a very bad math student. That doesn’t mean I was bad at math. I don’t believe that how you are as a student necessarily has anything to do with your “natural” ability to do math. But I had bad study habits, and a bad attitude towards math.

I went to school in a suburb of New York City, and the schools were pretty good, as American public schools go. It was a progressive district, and even though I didn’t like school too much (who does?) I have to admit - I got a fairly decent education.

In those days, in our school district had you in elementary school until the sixth grade. In fifth grade we had our first taste of “departmentalized” classes. Departmentalized meant that you went to a separate class for each subject.

Until then, we had one teacher in each grade for all subjects. In fifth and sixth grades, though, we got to have a different teacher for math.

That was the first time the schools made us feel that math was “different” or “separate” from other things. It wasn’t till much, much later when I realized that math is really a part of just about everything. It is just the schools that set it up as something “hard.” That isn’t a good move on their part, I think.

Each teacher should really understand basic math, and have a good attitude towards it. I mean, if you don’t have an appreciation for at least basic arithmetic, what would you be doing teaching?

In those days, like these, your teacher’s attitude towards teaching in general, and teaching math in specific, didn’t effect them much. It did (and does) effect the students, though.

There are a lot of weird myths about math. One is that if you are good at English or art, you won’t be good at math. (Total B.S!) Nowadays it is trendy to talk about left and right brain learning. There is something to it, but it is usually misunderstood and used to propagate the myths that weren’t true before, either.

Educators, theorists, and even students love to use myths to rationalize why they don’t learn particular things. It makes them think that it’s not their fault that they can’t teach or learn. It gives them an excuse to fail.

I bought into that myth about myself back then. Someone made me think that because I was good at some things, I couldn’t be good at others. Although thatlie is so destructive, it is still so prevalent.

Pondering point: If this is one of the main reasons why some students get stuck in educational traps, how come there isn’t a lot of effort to make teachers, parents, and students aware of it? Why isn’t there a subject called “How to Learn” in schools? Why isn’t that taught in all grades? Why are we constantly fed information, but given so little guidance as to how to process that information?

My math skills remained poor until I was deep into my thirties. I never passed math in high school. There’s a long story behind how I even got a diploma. But I did get one.

In college I took remedial math, and I had to drop it because I didn’t know what the heck they were talking about. I never finished college, either. But I did have a good time there. So now you know - Math Mojo is not run by a mathematician.

I have no degree in math or anything else. (Professor Homunculus has a Theoretical Degree in Mathematics - but it’s just theoretical). I am not interested in math because it is an academic subject - I am interested in math because it
is so beautiful and fun.

Mathematicians don’t own math. (They don’t want to.)
Teachers don’t own math. (They usually don’t want to, either).

Educational administrators, boards of education, test-makers, and especially politicians who pretend they care about education don’t own math. (Unfortunately, all too often they think they do. That is the main problem.)

Math was a mystery to me until a lucky break came in my thirties. I am a professional magician by trade and nature. I specialize in high-end sleight-of-hand tricks with cards and coins. Decades of practice have made me fairly good at what I do. Besides, I love it. Not just the entertainment part (I don’t like that all that much), but the creative part. One thing a real magician has to do is look at things
and say, “How can I accomplish that so it will look like it should have been impossible?”

Another thing we have to do is to look at things that are impossible, and make it look like we actually accomplish it. Another is to take things that are practically impossible, and actually do it.

The lucky break came while reading a magic book. In that particular book, there were some math-magic tricks. I had seen that kind of trick in books before, but for some reason, this time I tried it. It turned out to be pretty easy to learn. The next time I had a show, I tried the trick on the audience. It was my turn to be amazed - it went over even better than my other effects!

What a strange thing it was to realize that something I had practiced for an hour had a bigger effect than the things I had practiced, rehearsed and performed for years. It turns out that math is such a big mystery to most people, that they think that doing some easy things with it really are impossible!

Since math is something that most people have to use every day, they are under the impression they know what should and shouldn’t be possible with it. Multiplying 693,324 by 125 in fifteen seconds, without a calculator or pencil or paper, appears not to be possible for a “normal” human, or even a magician. Whereas making a Two of Diamonds turn into a King of Hearts seems possible for a magician to do. I mean, that’s what they get paid for, right?

Bolstered by positive reinforcement, I learned another simple math trick, and it worked like a charm in my next show. I started getting a reputation for being a “genius.” I got so much bang for my minimal investment in time and effort, that I decided to learn more math tricks.

Magic books usually have no “agenda.” They don’t want to make you feel bad if you don’t learn. They don’t grade you. The only test is if you enjoy doing the trick, and the audience enjoys seeing it. By that standard, I was getting GREAT grades, with math! That’s the wayto learn, I think.

Things just snowballed from there. I realized that the methods I learned in school, and the atmosphere of testing instead of teaching, were totally bass-ackwards.

From then on, I sought out better ways of learning math, and better methods of accomplishing the things I wanted to with math. I don’t really think the term “alternative” math is what it was that I investigated. Just because something is different, or “alternative,” doesn’t mean it is good. It might be, but just being different is not a sign of necessarily being better.

The point is to TRY it and see if it is better for you. Besides, most of the things I checked out are things which have been around a lot longer than the ways that are taught in most American public schools. Some of the methods are taught in other countries, where the average pupil is better at math than the average American pupil. (Don’t laugh, that is practically every country on earth!)

Never accept “alternative” as better until you have tested it. By the same reasoning, never accept the “accepted way” until you have tested it, either. You must try more than one way (many more, usually) until you can establish if one or the other makes more sense for you. Math is not “one size fits all.” The results may be, but there are many ways to get the same results. Some ways are better than others.

For example, if you wanted to multiply 10 x 68, you could write it out, with partial products, zeros as placeholders, adding up the rows of partial products, etc. Or you could just stick a zero behind the 68. One makes more sense, doesn’t it?

Naturally, it is important to know the other way, in order to understand why the easy way works. But that doesn’t mean you have to write it out the long way every time.

It turns out there are easier ways to do every multiplication than that old way with the partial products. Why aren’t they taught and used in all schools? Why are we given the impression that there is ONLY one way to do it, and that’s the way you are going to be tested on it, and, by God, you better “show your work”?

Really want to know why? Because it is easier to teach and test that way. It is not easier to learn that way, though. So whom does the system benefit? Teachers, testers and administrators. Where does that leave students? The same place it left me — alone, to fend for ourselves.

That is why I created Math Mojo. To leave you less alone while investigating math. I would like to share some of the methods I learned with students who would like to get better at something that is so important (and cool). The world of math is so fascinating when it is not spoiled by being turned into a “subject” that must be “graded.”

The other reason I created Math Mojo is because I realized that if you can understand the reasoning of math, you can use it to understand other parts of your world. Math can be a tool for understanding the world around you and the other “secret” tools for how it works. In the introduction to the great work “Introduction to Mathematical Thinking” by Friedrich Waismann, the mathematician Karl Menger wrote, “This does not mean that by the wider dissemination
of insight into the methods or mathematics more intelligent things would necessarily be said than are said today, but surely fewer unintelligent things would be said.”

I firmly believe that that last quote is one of the most important things that you can say about the use of math and reason. It takes math out of the realm of “subjects” and puts it right at the head of dealing with our world — critical thinking.

Imagine having a system for figuring things out. Imagine if this system was fun to learn and use. Imagine sharing it with other people to make the world a more agreeable and interesting place. I imagine just that, and I call the
system Math Mojo.

More later…