Stephen Downes tells me I shouldn’t teach math. (I did preserve his comment, by the way, on my 40,000 talents post, though I did edit the entry. No point in leaving wrong information up. One of my schools former financial officers once told me, “I can only remember five things a day. I would like for them to be right things, and not wrong things”.)
He’s right, too. I shouldn’t.
I feel that I am exceptionally poor at math, doing things by rote, and I have a tremendously difficult time recognizing when my answers are way off base.
In this particular 40,000 talents problem, I converted talents (an ancient measure) to pounds, and then to kilograms when Wolfram Alpha converted “pounds of silver” to Pounds Sterling (₤) as I tried to convert “pounds of silver” to “US dollars”. And in the process of converting pounds to kilograms, I forgot what kilo- meant, and wound up assuming an object the size of a semi-trailer was actually the size of my town’s “downtown”.
Argh. I deserve to be taken to task.
Stephen’s more recent entries involve the importance of becoming master learners, and modeling what good learning involves.
So here I am. I’m publicly asking for help. I clearly need to work my way through a general mathematics course. I work pretty well from books, but not particularly well from textbooks.
What should I do? So I can model learning to the next generation, AND become better at math?
[…] And that third inner ring can be turned, as well, of course, which means that you can wind up with combinations like Bucephalus speaking in the Senate with his scepter and orb. Five rings of thirty letters allows for 150 combinations just at the AAAAA. level, and millions of combinations when all possible combinations are considered (I think it’s 30-factorial, or 30!, but I’m not ever as sure of my mathematics as I should be). […]
[…] through some form of geometry or visualization: comparison of areas, imagining piles of money (though I’ve really screwed that up often enough), and so on. More and more, I solve mathematical problems […]
I’ve been tutoring a student in math recently (I know, I’m an English teacher), and I’ve been fascinated by the ways in which basic mathematical concepts are taught in 2010 versus the way they were taught in the late 1980s and early 1990s when I was in elementary and middle school.
He came in last week having tried to learn a relatively simple task: subtracting mixed numbers. I was going to teach him how to do this the way I learned how to when I was in school, but then I looked at his math book and saw that his teacher had taught him a completely different way. Here’s the thing, though: I looked at his notes and looked at his notes and looked at his notes but, for the life of me, I had no idea what the hell she was teaching him.
So I went to one of our middle school math teachers. “I need to teach Ethan how to subtract mixed numbers,” I explained, “but I have no idea how to.” I told her that I would just as easily convert them into mixed numbers and subtract that way.
“If you do that,” she said, “the numbers will get too big. Here, let me show you what to do.”
The process — finding a common denominator, doing the multiplication, etc — was the same until we got to the part where I had to BORROW 1 from a mixed number by adding x/x (where “x” is the denominator) to its fraction. She wrote this out for me, and I said, “Sorry, Debbie, but could you do that again? That makes absolutely no sense to me.”
I’M 30 YEARS OLD AND I WAS CONFUSED BY ELEMENTARY MATH. PLEASE SHOOT ME.
But Debbie taught me again, and then I taught Ethan. He was literally jumping up and down with excitement when he figured it out — and so was I.
You should totally hold a tutoring session where kids come teach YOU math. Have them create lessons in a way that THEY THEMSELVES enjoy being taught.
This will give you insight into what they enjoy, help you learn math, and make your math teacher mighty grateful.
I like the idea of a tutoring session where the teacher gets math instruction. I think I’ll do better with a book.
I seem to care about civility…I just read Stephen Downes post and I think you should teach math. Math is not about being right all the time. You can blame a system for leading so many to think they are outsiders. Scott Buchanan in Poetry and Mathematics says something that is burning in my mind (go to the amazon preview–pg 34). “a great many sometime students of mathematics try to persuade themselves that they haven’t mathematical minds, when as a matter of fact they have only had nonmathematical teachers. Mathematics is not what most mathematics teachers teach.” I had non mathematical teachers until grad school:( Got to run the bell just rang:)
If you go by the fact that my 9th grade math teacher was a former English teacher ‘repurposed’ and my 10th grade math teacher was a history major… I think there’s an enormous disservice done to say that I should teach math.
There’s a famous story about George Washington and the cherry tree. It’s false, I believe, and it’s been demonstrated to the best of anyone’s ability that a negative can be ‘proven’ (yes, I have enough logic under my belt to know that you can’t prove a negative).
There’s a more truthful but less famous story that as a young man, he knew his weakness in mathematics, and bought a book with which to teach himself math. At the end of a year, his exercise book and his notes in the margins were enough to guarantee him a commission as chief surveyor for Cobbs County, Virginia — it was his first job.
Mathematicians should teach math. Not hacks. And the proof of it is in poorly taught students who grow up to be math-illiterate teachers. Like me. 🙂
At least I’m going to try to correct my error. Thanks for the book recommendations.
Two texts that come to mind are wonderful–Fostering Geometric Thinking and Fostering Algebraic Thinking both edited by Mark Driscoll. The mathematical territory is beautiful and challenging–you will find problems that allow you space to wonder and develop habits of mind. I think the biggest thing for me is the development of those habits of mind. His work helped me ask questions like, what is changing, or can I find the relationships…If I had to choose two books to help me learn (still working on it) and help my students learn, it would be these:)