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 )

Be vewwwy quiet! I'm hunting Math Mojo!

This is the first of a series of Math Mojo podcasts. They’ll range from “math magic” to the what math can mean to you, and how to use it for your personal development.

After you’ve listened to it, please leave a comment. This is just the beginning, and anything you can tell me to help make it better would be appreciated.

Click on the arrow below to begin playing the podcast.

]]> http://www.mathmojo.com/chronicles/2009/07/27/the-mission-of-math-mojo/feed/ 0 the Math Mojo Podcast,The mission of Math Mojo Math Mojo will be aimed at helping anyone who either feels a bit intimidated by math, or would like to learn interesting ways to think about some of the math that they already understand. Math Mojo will be aimed at helping anyone who either feels a bit intimidated by math, or would like to learn interesting ways to think about some of the math that they already understand. The Math Mojo Chronicles no http://www.mathmojo.com/chronicles/2009/06/09/what-if-i-fail-9th-grade-math-part-6/ http://www.mathmojo.com/chronicles/2009/06/09/what-if-i-fail-9th-grade-math-part-6/#comments Tue, 09 Jun 2009 11:51:09 +0000 Brian http://mathmojo.com/chronicles/?p=742 This is a continuation from the previous posts:

At the [...]]]> This is a continuation from the previous posts:

• What if I Fail 9th Grade Math? (Part 1)
• What if I Fail 9th Grade Math? (Part 2)
• What if I Fail 9th Grade Math? (Part 3)
• What if I Fail 9th Grade Math? (Part 4)
• What if I Fail 9th Grade Math? (Part 5)

At the end of the previous post, a reader wrote in:

“i have the same problem. i am in grade 12. i used to grasp those integers, algebra and simple geometric problems with lot of ease and faster than others. then i started falling down not only in grades but also in work ethic. now i got 70 in grade 12 and thats the highest ive gotten in high school, with lowest being 53 in grade 11. I am not able to break the 80 barrier and 70 is a great struggle. I know it isn’t about marks, but in university i need to maintain a nice gpa and need the idiotic marks. I have a stigma “i suck at math” stigma and can never get A, because after i got 60 in grade 9, 10 11 and 12 ive been frustrated and slow to understand concepts. now ppl tell me that my brain is too old to improve. im not a kid, so obv i don’t believe BS like that. But what do I do? Do i Start from grade 9 scratch and work my way up as if I just graduated from grade 8? Or what??”

Professor Homunculus sez:

Tommy,

Well, you’re on the right track. What kind of idiot would tell anyone they’re too old to learn anything? Only someone who’s own brain has prematurely calcified. Modern research has shown that it’s time to get rid of that myth.

I’m going to suggest that there is a possibility (just a possibility, OK, I don’t know your situation well enough to be sure at all) that age is related, but in a totally different way.

You’re at a great age in life when you probably are developing your mind in fantastic, independent ways. Your interests are probably turning to things other than algebra.

You also may be noticing things about how the world seems to work that are a little disappointing to how you imagined. Like, say, that things aren’t fair, and that adults don’t always have your best interests at heart.

At that stage, sitting in a boring-as-hell math class and learning axioms and theorems that are presented as something to be accepted and learned by rote is not exactly what thrills your imagination.

If that’s the case, let me make a suggestion – it may be time to realize that math is not what you are being taught in school. School is basically there to make little drones out of unsuspecting kids, and to disappoint new wide-eyed teachers who think their chosen profession is there to help them change the world for the better.

Because most school systems have bought into the drill-and-kill, inculcate-and-test mentality, the art and romance of real math gets killed so bad it has to get buried twice.

So what can you do? You have to re-kindle your math mojo from an external spark.

Once you’ve done that – once you’ve discovered (or re-discovered) the real mental-magical journey of math, you’ll find a new interest in math class, I suspect. That interest may not be a new-found appreciation for math class, though. Let me explain:

Unfortunately I didn’t find my math mojo until deep into my thirties. I wish I had gotten the math-bug while I was still in school, though. That way I could have played a little game – put a bug up the system’s ass.

What I mean by that is that while suffering through the unit about quadratic equations, I wish I had gotten some information from books (not textbooks) about them, and learned about some uses for them (maybe some unconventional ones) and then when listening to the next boring lecture about them in class, enjoyed the realization that I was actually becoming the kind of person who actively investigated my world, instead of being one of the drones in the front of the class, sucking up to the teacher, getting the great grades, and understanding nothing, only to forget the few crumbs of informations that I’d gathered by the time the tests were over.

There is a crazy old book that was one of the pillars of the “self-help” movement in it’s early stages, in the middle of the last century. It was called “Success Through a Positive Mental Attitude” by Napoleon Hill and W. Clement Stone. In it there was a term that I think hits the nail on the head about how you can take something that bugs you and make something good out of it – it’s called “inspirational dissatisfaction.”

Inspirational dissatisfaction isn’t just complaining about things that bug you. It’s taking them and making something out of them. Ever see “Rocky?” (God, I can’t believe I am going to reference some Stallone trash.) Remember that scene where he decides to compete, and goes into “hyper-training” mode? He was dissatisfied with his situation, but made the choice to embrace the work and sacrifice that would make him better.

A more subtle (and less pop-crap referenced) example would be some of the works by great authors. At the moment, I’m thinking of Hermann Hesse, and the wonderful book, “Demian.” I don’t think I’ll spoil it for you here. It’s a great read, and you’re at the perfect age for it. Get a cheap paperback copy of it. (Hesse also wrote one of the most important books concerning public education ever written, “Beneath the Wheel” (“Unterm Rad”).) These books are almost a hundred years old. Good luck finding something as well-written or meaningful today.

Ostensibly, Demian has nothing to to with math. It has everything to do with learning, growing up, and mojo, though. It’s on my top 10 books of all time. (But so are 20 other of Hesse’s books!)

While we’re on books, may I suggest that you run, not walk, to a library, and try to find any of the books by Martin Gardner? He is a wonderful magician/mathmatician, and a fantastic writer. He is truly a legend in his own time among his colleagues. Check out a book of his called, “Mathematical Carnival.” He’s got many other great ones out, but that is a good place to start. It’s about weird math and magic. It’s not like anything else you’re likely to have read about math. That book just may give you the spark you need to see that math is not what they’ve been beating you over the head with in Math I, II, or III.

Now let’s get more concrete. You may have to go back to the grade 8 books as far as your classwork goes. Maybe not. Brainstorm what you know and what you don’t know. (See What if I Fail 9th Grade Math? (Part 5) for how to do that). I can’t tell you the answer to that here, and no one can really tell you as well as you can figure it out yourself if you brainstorm it.

But remember, get yourself some kind of motivational math book to guide you through the BS. Don’t get bogged down in the textbooks – they are killers. You need some other kind of book to get you into the “soul” of math.

So here’s a concrete suggestion - Get your butt out to a bookstore and order a copy of Robert and Ellen Kaplan’s “The Art of the Infinite.” It’s in paperback, so it shouldn’t set you back too much. The reason I suggest you buy this one, instead of getting it from a library, is that if you invest a few of your own bucks in it you’ll be more likely to actually read it.

I can’t recommend that book highly enough. It may change your whole view of math. It should. I first discovered it yesterday, and it saved me a lot of work and research. I wanted to write one of the greatest math books ever, which would help show the beauty, adventure, romance and history of math, and what it all means for your mind and the development of mankind. The Kaplans have saved me that trouble! (Get that book!)

On to the work-ethic. Hmmm. You came to the wrong place for that one. The only advice I can give you is to not beat yourself up for your perceived work-ethic problems. I’m sure enough other people do that for you. You obviously care enough about your mind and future to seek help, so you are way ahead of the crowd on that one. Maybe you should check out “Success Through a Positive Mental Attitude” by Napoleon Hill and W. Clement Stone. It’s been in print longer than I’ve been alive, so there’s got to be something to it.

Tommy, thanks for writing in, and getting me to talk about this stuff this morning. I truly hope this helps. Please comment again in a few days on this post and let us know how you are doing. We’re all rootin’ for ya!

Hotcha!

- Professor Homunculus

Di-llama

Many mathematicians and some math educators are aware that a lot of the stuff that passes for “math” in schools is simply number manipulation, or rote memory of math “facts.” 

If we “teach to the test” or use some state-sponsored curricula, or bureaucratically sanctioned “standards,” we are just providing some hoops for students to jump through, which may or may not have anything to do with actually engaging their minds and leading them to mathematical thought. 

There are great insights to be gleaned from mathematics, which fall by the wayside as we instead try to inculcate the greatest amount of students with “material that must be covered this semester.”

Here’s a little dilemma:

It’s probably true that in most cases students have to be able to proficiently master basic skills. It’s also probably true that the insights should come during that initial learning phase. 

On the other hand, for some of the reasons mentioned above, as well as others, most schools are not set up to handle fostering actual insights. There is no time and there are no resources to try to do that for most of the students. 

So what can we do? 

I.

I’d say the first thing is to do no harm.

If you just teach the basics, at least make it clear to the students, over and over, that there is more to learn, and that learning does not end when you learn a a certain way to perform a particular operation. 

Let me give you and example of what I mean: When you teach addition of natural numbers, addition will always give you a greater number than any individual addend. 

In other words in a + b = c, c will always be greater than a or b. 

That may lull students into believing that “addition always makes bigger.” 

Exactly that myth is what leads to frustration when you teach them about adding negative numbers.

So even though you may not be teaching the “negative numbers unit” yet, you must take it into account, and mention to the students that they should not get the impression that “addition always makes bigger,” because there is more to learn. 

That way, even though they may not get the deeper insight about negative numbers yet, you are preparing them for it. At the very least you will not be damaging them by teaching that “addition always makes bigger.” That was a common mistake among teachers in past years. 

II.

The second thing we could do would be to make sure that to get each student to master those basics. 

Good enough is not good enough. It is very easy to make sure that the four basic operations are understood and mastered by every non-neurologically damaged student, and many damaged ones as well. 

I know I am setting myself up for some frustrated souls to rant at me about this, but I feel it’s necessary to say it:

There is a much higher percentage of teaching-disabled teachers than learning-disabled students. 

That is not a dis at teachers. If someone is learning disabled, and you recognize it, you are not saying something mean about them. On the contrary, it is mean to know someone has a disability, and not try to get the the help they need to help themselves, and then expect them to perform, although we practically have set them up for failure. 

The same goes for teaching-disabled teachers. If we do not get them the resources they need (because we are to timid to point out that they need some new resources), and then send them out to teach without those resources, well, then we are setting them up for disaster, and of course, then everyone will blame them for the problem. 

That is tragic. What I am pleading for is that we should make sure the teachers have the means to teach every child in their classrooms at least the four basic operations very well.

It should be considered a crime for an elementary school to send children on to middle school unless those children can confidently and accurately add, multiply, subtract and divide positive and negative whole numbers, fractions, and decimals (at least). 

III.

The the third thing would be to find more than one way to teach those basics, and that at least one of them be superior to the one that the district usually teaches. No matter what method a school uses, one can always find a better one. There is no one best way – that means no matter what way you have, somewhere there is a better one. 

It would be reasonable to ask what those ways might be. Of course it’s not possible to list the definitive set. It’s not even possible to list a partial set, because each case is different. 

What I’d like to offer is a short set of tenets that we might take into account when coming up with alternative solutions. 

1) Respect the student’s minds. Assume that there is a way they can “get” the material. Strive to find a way that’s better for them, and try to let them know that you expect them to be open-minded enough to give each way a chance. Of course it won’t always work out, but beats any mind-set I’ve heard about yet. 

2) Remember, it’s about the students, and not the standards. We are there to help students, not promote any particular curriculum. 

3) Don’t patronize students. Don’t teach down to them. Don’t dumb-down the material because you think the child is too slow to grasp it. You can present it in ways that may be more accessible, of course, but non of them should involve the Tele-frikkin’-Tubbies, if you follow my drift. If you’re teaching math, teach math. Don’t make them think that learning isn’t do-able if it isn’t sugar coated. It’s like bribing a tantrum-throwing tyrant with Coke and ice-cream. (Sheesh, I don’t even know how we got to the stage in our society where that isn’t considered child-abuse.)

4) Keep it human. Ask you students what they have learned, and how they might apply it. That might pre-empt any of that “why do we have to learn this stuff, man?” baloney. Put the onus on them, and let them know that you are really curious about what they can learn from what you are teaching them that you didn’t plan on teaching them. 

5) Consider that the dilemma of math skills versus math insights is probably a false dichotomy. They can go hand-in-hand. Keep looking for ways that that combine the two. You don’t have to look in textbooks, rubrics, etc. If you keep your eyes and ears open, and listen to what the students ask about and talk about, you may find some insights yourself. It’s a two-way street. (Yeah, that’s vague, but how the heck should I know what your students are going to talk about?)

6) I dunno. I’m just a lonely blogger. You tell me. What have you got? I’d love to hear from you. I just think these Ideas are a jumping-off point. They may all be crap. They work for me, in general, but I could use all help I can get. I hope some of these thoughts helped you, too. 

Sound off!

Professor Homunculus 

Thought you might enjoy this bit of math “logic.”

So if you can have the items related to each other, it’s easier to remember them. It’s certainly easier to make sense out of them.

Now, when you consider the following numbers from the point of view of a child learning them:

9, 18, 27, 36, 45, 54, 63

they seem to have nothing in common, except that they are on a chart of “the multiplication tables” that the child is told to “shut up and memorize!”

On the other hand, if you show the child groups of objects, which have nine in each group, and you put them next to each other, they can readily see how nine grows into 18 if you add two groups, then into 27 if you add another group, and so on.

This increases the child’s appreciation for what he is learning, and decreases resistance to that learning. So showing the concept definitely helps learn the skill.

The school of thought that says, “Teach the skill and the concept will be easier for the child to understand later” is based on what we want the child to learn, not how it’s best for the child to learn it. This is utterly misguided.

It’s the “authoritarian” way. It’s the same school of thought that says, “You will do as I say whether you like it or not, because I know what’s best for you.” That is the most counterproductive way that was ever thought of. It is the default, brain-stem, neanderthal way. And it doesn’t work to produce intelligent children.

It may produce obedient drones if that’s your goal. But I’m pretty sure that if you read this blog, that’s not exactly what you’re after.

Actually, the “authoritarian” way doesn’t even create obedience. But it’s a great way to produce anti-social rebels who will revolt against the thing you are trying to teach them. I don’t mean that they’ll become the creative-rebellious types who produce great things for society, I mean they’ll become the destructive little shits who only complain, and then grow up to be exactly the kind of disappointed authoritarian types as the dunces who tried to inculcate them with “facts” and “skills” that became neither to them.

A Theory of Relativity…

Imagine giving your child a list of names, like: Mark, Simone, Leonora, Derrick, Romulus and Matthilde. Now tell them what each looks like and acts like, and that Mark and Simone are married, and Mark is their father’s brother, and Leonora and Derrick are their children, and Romulus and Matthilde are Derricks friends from school. You can even make a chart of all their relationships and characteristics.

Or, you an invite them all over for a barbeque and letting the child play with them and get to know them. They gradually learn how each is related to whom, and they get a personal relationship with each. Those people become meaningful to the child (imagine that!)

Which do you think will stick with the child more? Which would he rather do, sit and stare at a list and a chart while you grade him on his progress, or play and interact?

I hope this little analogy, imperfect as it is, nailed the difference between understanding and drilling for you.

Respect your Mind

When we teach concepts first, and skills later, we are reinforcing the Idea of respecting the minds of the children we teach. It may take a while, but when you do that, the child slowly gets the Idea that it’s okay to trust your brain. They’ll see that when you don’t expect them to memorize something and then use it quick (because, say, you have to “cover material”, and it’s in this “module” of the “curriculum”, and that “it will be on the test soon”), that they can actually grasp it, and understand it more deeply. That way, everyone gets more satisfaction from the teaching/learning endeavor.

Tomorrow I’d like to mention a kind of caveat to all of this, concerning a bit of Zen philosophy.

Apropos of nothing:

I’ve recently gotten into the “Twitter” thing. Not sure if I like it, or what it will bring, but it is new, interesting, and a great distraction from work. I’m supposed to be using it as an organizational and motivational tool. We’ll see.

Recently I read a “tweet” from http://twitter.com/bcubbison. He asked, “What kind of people would name their planet after dirt?” It made me wonder what the people who named their planet “Uranus” are like.

BTW, do you use Twitter? If you do, check me out at twitter.com/Prof_homunculus, and follow me.

Addendum

On Thursday, July 31, 2008 I read an interesting blog post at The Amazing Mind blog, entitled Learning Mastery 5 – Back to the Basics. You might want to check it out. The blog is very interesting in general as well. He bring up many topics and points about them that everyone should ponder now and then. Have fun.