GL(s,R)

May 22, 2010

Here we go

Filed under: Uncategorized — Adam Glesser @ 11:46 am
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Inspired by Dan Meyer, Sam Shah and, most recently, Shawn Cornally (as well as Kate Nowak, Mr. Sweeney, David Cox, etc.) I’ve decided to start a blog, cleverly self-titled \mathrm{GL}(s,\mathbb{R}). No, wait. They didn’t inspire me to start a blog; they inspired me to radically question the way I approach teaching. If you ask my former students, I’m sure that they would tell you that I wasn’t such a bad teacher to begin with, but I know better. I’ve wasted opportunity after opportunity to enrich the lives of my students because of a silly need to cling to a system that I fondly remember rebelling against. What’s up with that?

A Story

I taught multivariable calculus in the fall of 2009 and had a student who, despite prior mathematical success, simply didn’t engage. Being a college teacher, I didn’t feel responsible for making her engage. After a horrendous midterm, she came to me to ask about what could be done to improve her lot in the class. I crunched the numbers and even with (unlikely) respectable numbers the rest of the way out, she had little hope of passing the class, much less getting the grade she actually wanted. Being rational, she decided to cut her losses: she shifted whatever attention she had wasted on my class to her other classes and simply conceded the F in my class.

It seems to me that if I teach for long enough to have 100 students face this same predicament, I will end up with 100 students choosing the same road. Please, help me save just a few!

Standard Based Grading (SBG)

Actually, this is telling the story in reverse order.  The changes to my teaching started in the classroom, not on the syllabus. However, there is not too much I can say about how to teach (generally, anyway) that isn’t already in the textbooks, blog-o-sphere, or whatever. Watch Dan Meyer’s TED talk for just a few minutes and you will learn more about pedagogy than I could ever teach. No, I want to start with Standard Based Grading because that is my big change for the fall and that is what the majority of the posts in this blog will be about (more on the minority later). In a nutshell, SBG takes the point of view that if the goal of a class is to learn (and to learn to apply) certain material, then your grade in the class should be a measure of how well you are meeting that goal. Important in the last part of the last sentence is the word are (present tense). If you were doing well at factoring, but are now unable to do so, your grade reflects that reality. If, however, you were unable to recognize a difference of squares, but now you can, your grade will reflect it. This is so intellectually satisfying to me that I can hardly believe I didn’t think of it before. What is the cost? Obviously, there is the cost of me having to pay attention more closely. Also, I have to give up the notion that my students need to learn how, when and where I tell them too.  For the former, well, it is what I should be doing anyway, isn’t it? For the latter, oh darn. I’ve argued for years that college is about learning how to learn. Yet, all I ever do is enforce arbitrary barriers to learning.

What will this blog be about?

Here is the plan. Probably, I will find a dozen other things to talk about, but my goal is to chronicle my journey from what I have been to what I will become. Along the way, as a way of breaking up the diary monotony as well as to create a convenient reference tool for myself, I will publish a few tricks of my trade. Some of these things will be shortcuts for computation, mnemonics and perhaps a bit of insight from the point of view of a practicing mathematician.

Why not just read Think Thank Thunk?

Well, that isn’t a very polite question to ask on the first real post. All the same, I’ll try to answer it. First, Cornally’s blog is designed to…um…actually be good. I have no delusions of grandeur here. My writing is terrible, but I will be brutally honest. You will read the good and the bad from my experiences. Second, the majority of excellent math edublog sites (at least of which I’m aware) are written by and for high school teachers. I am a college professor and so my perspective and challenge is slightly different. For instance, I get to teach cool advanced math courses (e.g., complex analysis and differential equations) and, at this level, the interaction with students is far from the psychological exercise of dealing with freshman algebra students. Having said that, this fall, I get to teach precalculus and finite mathematics. While science majors almost exclusively populate the first class, the second is full of students for whom mathematics is torture. By the way, if you see a post or two on here about probability and combinatorics, it is because of that class.

What’s coming next?

I’ve already started preparing my classes for the fall and so my next post will tell you about the process of selecting standards for my courses. I will also have my first Tricks of the Trade post entitled: Log rules!

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4 Comments »

  1. Why is finite mathematics full of students who hate math? It should be taught for the computer science students, with lots of mathematical induction to prove things about algorithms and data structures. Combinatorics and mathematical induction are the foundations of computer science, and teaching them to computer science students can be a lot of fun (I’ve done it a few times, but not recently).

    Perhaps the pre-req structure needs to be changed, so that first-quarter calculus is a pre-req for the discrete math—not because the calculus is needed, but because a certain level of mathematical sophistication is needed to be able to handle induction.

    Comment by gasstationwithoutpumps — June 11, 2010 @ 10:56 am | Reply

  2. We have a separate discrete math course for computer science students that covers the topics you mention and (I think) calculus is a prerequisite for the course. Our finite math course would not satisfy the math requirement for any science or business major; I suspect we get a lot of theater and government majors.

    Comment by Adam Glesser — June 11, 2010 @ 11:25 am | Reply

  3. Ah, so the “finite math” course is a remedial algebra course for those who failed it in high school. What is the purpose of the course (other than to provide a barrier to theater majors)? It is very hard to teach a class when none of the students see any point to the material and there is no carrot to entice them with, just a stick to beat them up.

    Perhaps it would be better to design a “math for theater majors” course that covers some of the same material (or other material, since there seems no particular reason for this specific material) but with a specific focus on applications to theater.

    That said, most of the theater-obsessed kids I know (through my son) are also pretty good in math, so are not likely to be in classes like that one.

    Comment by gasstationwithoutpumps — June 11, 2010 @ 2:48 pm | Reply

    • Yes, it is a bit tricky. In principle, we should be able to take the three subjects (linear equations and inequalities, financial mathematics, and combinatorics and probability) and make them quite relevant. However, in the first subject, we cut linear regression, in the second, we essentially teach them how to plug things into equations and in the last one, I’m not sure how the teachers are trying to connect to the students. The material isn’t necessarily bad material for the class, I’m just not sure if the implementation is optimal. Since this is my first chance to teach it, I’ll have a much more informed opinion in December on whether the class needs to revamped.

      Comment by Adam Glesser — June 11, 2010 @ 3:11 pm | Reply


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