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:
- Multi-Variable Calculus
- Linear Algebra (both for my Math major)
- Adolescent Development
- Computers, Teaching, and Math Visualization
- Secondary Education Practicum
- Jewish Science Fiction.
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.
