Presentation matters

Next semester, I'm going to start off by placing a much higher emphasis on presentation to my algebra classes. My experiences this quarter indicate that this is actually a foundational part of their math education. It has a number of benefits:

1. It sets the standard of reading and following directions carefully
2. It forces students to think about what they're doing and exposes their lack of thought
3. It makes the papers significantly easier to grade
4. It outlines a style of thinking that encourages logical and organized thought
5. It prepares them for more difficult and more complicated algebraic maneuvers down the line

I've made some adjustments and most of my Math 097 students are on board with the presentation (and I hope they're seeing their current material of adding/subtracting/multiplying polynomials as a clear extension of these things). Jason is considering writing up a document about these algebraic presentation things, and I might help him out if I can.

My first stumbling block

I'm now just about two weeks into the semester, and I've hit that first bump that I've been anticipating. What is the problem? It's complicated, and I think it's the same problem that everyone who teaches developmental/college algebra runs into. The students don't get it. Simply stated, the students are underperforming by a wide margin. Why? I'm not entirely sure. I have some conjectures:

1. Bad teachers: I can probably blame other teachers for teaching sloppy, lazy math to students and probably be right. But that doesn't really help anyone.


2. Bad habits: Consider the following musical analogy -- Students of music who are classically trained from the beginning learn their fundamentals right away and develop the good habits early. Students who sort of pick it up as they go along develop bad habits because they simply do not know better; it's a matter of making it work however it does. Classically trained musicians who stick with the program all come out consistently good, with some very high caliber exceptions. The self-trained musicians are generally not so good, but those with natural talent and musical instinct still come out of it playing exceptionally well. Those musicians who are self-trained and are not doing so well have a difficult time when put into a formalized classical setting because their bad habits prevent them from doing better. It takes considerably more effort to break bad habits than to form new ones from scratch.


3. Bad self-assessment: I asked my students on the first day of class to rate their mathematical ability. Most students rated themselves in the 5-8 range out of 10. However, the work that I see puts them in the 3-6 range or even a little lower. Why do they think they're better than they are? Probably because they don't have a full vision of what the range of mathematical talent is. Most of them have probably only been in classes where they were average or above average. They have probably only seen students as good as a 7, and so they see their talent as about 50%-80% of that (3.5-5.6) and so they are working on an broken scale.


4. Bad expectations: I think they just don't know what is expected of them. Because they don't know what's expected, how can they reach that goal? I think this is where I need to begin. I don't know how just yet, but I'm working on it.