What my semester looks like

Sorry it's been quite a while since my last post. Classes started at the end of August, and life has been pretty crazy.

On that same note, my schedule will give me a good number of future post topics; I presume that's the occupational hazard of completing a college (double) major in what the blog is supposed to be about. My classes for this semester are as follows:

1. Multi-Variable Calculus
2. Linear Algebra (both for my Math major)
3. Adolescent Development
4. Computers, Teaching, and Math Visualization
5. Secondary Education Practicum
6. Jewish Science Fiction.

I know the last course seems a bit out of place, but it's a break from classes that I specifically need for my majors. Anyway...

The first five courses are fitting together surprisingly well. The straight-up math courses certainly teach the stuff they're supposed to, but it gives me some opportunity to play with ideas from the other three classes. And then topics covered in one of the education classes give me something to focus on from the other two.

An example of what's been on my mind:

In Adolescent Development, the 2nd chapter we covered was cognitive development. I forget which researcher it was, but someone talked about the stage at which kids are able to make leaps from the concrete to the abstract. In terms of implications on math education, that would be when students are able to understand the concept of a variable. So, depending on whether the student is an early- or late-maturer, he may get lost in class if the teacher introduces variables before he can really get it.

I witnessed a possible instance of this first-hand as I observed a classroom through my practicum: 7th grade Advanced Pre-Algebra. The lesson of the day was the Properties of Addition (Associative, Commutative, Distributive, etc.). The teacher talked about grouping like terms, and why students couldn't simplify the term "x + x^2". He asked a student why it wasn't possible, and the student replied that it was because they "don't know what x is." This sounds right, but it could be that the student thinks that "x" has a different value at both places in the the expression, which it doesn't. From a practical viewpoint, is there a good way of diagnosing cognitive misconceptions, or whether or not the student has reached the level of understanding in order to get what a variable is in this context?

So today in my Math Technologies class, we got into a discussion about whether or not technology should be used as a crutch to help students that are lagging still get something out of a lesson that may be over their head. The consensus was that if a student has a hard time carrying out the algorithm to compute a problem, they may still be able to benefit by viewing the problem more conceptually using a graphing calculator or Geometer's Sketchpad. In the above example, is there some way that a certain technology could be used effectively by the teacher to help the student visualize the logic of "grouping like terms" before they understand how variables are used?

And then when I don't feel like thinking about (relatively) little kids anymore, I can apply the same mindset of a teacher to my own math classes. Even once we reach college, the same things still apply. I find it interesting to contrast the teaching styles of both of my current math professors, mostly to find some justification in really not liking, at all, how one of them teaches. (The fact that I can't understand his accent half the time doesn't help, either.) A review book will be desperately needed for that class.

On that note, I should be studying. Any feedback would be enjoyed.

How's about those positive role models?

My friend showed me this video of Patricia Heaton at Guest Week on "Who Wants to Be a Millionaire". (Skip to about 3:00.)

It isn't often that I yell at videos, but this is ridiculous. As soon as anything with numbers showed up on the screen, she completely shut down even before looking at the question. This is a grown woman freaking out about middle school math. A kid would look at the video and say, "She can't do math and got to be famous. I can do that too!" Never mind the fact that when Regis walked her through it, she was perfectly capable of solving the problem.

A defeatist attitude is lethal to learning math or any other subject. Unfortunately, mathematics often gets the short end of the stick in situations like these; that's what credit cards are for, right? It's a lot easier to get away with never doing simple, mental calculations than to get through life unable to write a cohesive paragraph. Who cares that you can't balance your own checkbook, as long as you can write thank-you notes to your generous donors. 

Does anyone know of a celebrity who likes doing math in public, and is proud of it? Who knows, maybe Patricia is just stuck in a junior high mindset and doesn't want to be called out as a nerd. 

Welcome to MathEd Out!

“For Today’s Graduate, Just One Word: Statistics”  (NYT 8/6/09)

“I keep saying that the sexy job in the next 10 years will be statisticians. And I’m not kidding.” -Hal Varian, chief economist at Google

Math stole the front page of the New York Times today. In short, it claimed that a good number of the careers that will pop up in the next decade are going to be based on a math-heavy education, namely the field of statistics. With the growing number of technologies born to process huge quantities of information, we need more human intelligence to do something with all of it, and to make those technologies more efficient.

One example:

A while back, MIT experimented by giving 100 students Blackberries that tracked their movements and actions on campus. One small step for Big Brother, one large step for statisticians. It’s one thing to have a massive amount of data on record about your student body; the hard part is focusing on a specific trend, and extrapolating from it. Humans come into play by deciding how to organize the information into something useful, or at least interesting. 

The headline for the general public, or least for school-age students, should be shouted loud and clear: Math is everywhere, not just in your textbooks. You don’t have to be a typical “nerd” to find something that catches your attention in the field of mathematical applications. Most people take advantage of forms of advanced mathematics every day, and anyone with the right kind of analytical mind could contribute to the field in ways yet unimagined. 

For once, math education is being glorified based on something other than only salary! (Though, going by the jobs mentioned in the article, that part doesn’t sound too shabby either.) Soon, the secret will be revealed that math can, in fact, be cool to study. And that it involves far more than learning techniques and regurgitating them on worksheets. You could land a gig delving into technologies we take for granted, and making them even better and more user-friendly. Who wouldn’t want to take part in that? I don’t know how many pre-college students are going to read this article, but I would encourage them to do so, before they make up their minds to dismiss math completely.

“You’re Leaving a Digital Trail. What About Privacy?”  (NYT 11/30/08)