Spring 2008 reflections

I don't think I put thoughts in this blog nearly as often as I did in the first semester, but now that the semester is over, I have the time and energy to put a lot of thought into how things went this semester.

First of all, Math 124 went a lot better this time around. I still don't think I connect quite as well with that class as I do with the Math 097 students. It is true that I go into the classes with different mentalities. Since Math 124 is a college level class, I treat them more like how I think college math students should be treated. I do less hand-holding and I let the students work on their own more.

Math 097 went very well this time around. I think I found the right level at which to try to meet the students and the introduction of more worksheets seems to have had the effect of helping the students to understand the material.

The homework cover sheet was a pretty good addition. Some students didn't really take to them, but I'm going to keep using them anyway. I changed them slightly so that they interact with the course content more, so that should be a positive change. I also need to write a more defined homework policy and let the students know much more clearly what I am really expecting from them in the homework.

There were a number of interesting comments that I received on the unofficial evaluations I handed out to the students, and even though the probability of them actually seeing them here is very small, I believe it is a useful exercise to reflect on them, and then to take my thoughts from here and put them into the next syllabus and work them into the class content. (Side comment: I'm always amused by the level contradiction from different students about how things have gone in a class.)

"I do not think quizzes you be a part of attendence." The same student also wrote "I like participation credit for [the] test." This is the type of comment that I feel deserve little attention. I know that Jason gives credit for attendence (he also has 'detention' where he forces students to show up to the tutoring center for specified periods of time to make up for missed classes), but it seems like extra paperwork to me. This is a college level course in which the emphasis is on learning content. What part of that description implies that credit should be given for simply showing up? It's very much like a work environment. Do you expect to get paid simply because you show up for work, and not because you actually perform your job competently?

"Quizzes should be at the beginning of class." Over the course of the last year, I have started to agree more and more with this, and will probably implement it during the summer session. This will also be used to make sure class actually starts close to 'on time' and only punish the students who show up late to class.

"Too much homework." No student actually used that phrase this time around, but a couple students commented on it. Students who say this are usually the ones who aren't very good at math, and they often spend far too much time on their homework because they spend all their time being lost and making zero progress. These also tend to be the students who don't come to office hours or ask questions to get help. Even though students will probably make this comment as long as I'm teaching math, unless the response is overwhelmingly stating that the assignments are too long, I will tend not to give much weight to these comments. (There was another comment from another student: "The amount actually helped me to learn the material." That's the whole point of the homework!)

I had a spot on the evaluation where I ask the students to write themselves a short note to themselves at the beginning of the semester. I find this quite amusing and I will definitely have to talk about this on the first day of class for the upcoming semesters. I added my own comments in parentheses:

• "Do your homework." (This was the most frequent comment)
• "Stop slacking!" (Do I need to say more?)
• "Do not miss any classes, you will get behind."
  
• "Be prepared for the quizzes." (If you spend the 5 minutes before class glancing over the homework, the quizzes will be significantly easier because the ideas will all be fresh in your head.)
• "Don't take this class if you are taking other hard classes." (Straight-forward, reasonable advice. Math classes take up a lot of time if you're not as natural with it, and this is worth considering at the start of the semester.)

Math 373 was a fun class this semester. With such a small class, I handled it very differently. I left a significant chunk of time in class to doing numerical explorations as these are really key in number theory. A lot of the results came out of 'playing' with the numbers, so that's how I tried to approach it.

You're not doing math

I had an interesting conversation with a student after class today. The essence of the conversation was that he did not receive full credit on a problem on his exam even though he arrived at the right answer. My reason for not giving him full credit was that he did not demonstrate how he arrived at his answer and that the work that he showed did not make sense.

The problem gives some relationships between various angles of a triangle and asks the students to compute the angles. This student's first step was to divide 180 by 3 because "there are three sides on a triangle." Now, it happens to turn out that one of the angles of the triangle is 60 degrees, but the fact that 180/3 = 60 has no bearing on this. Nevertheless, the student continued to insist that this makes perfect sense.

Upon further attempts to argue with me, he reached the point where he declared that I'm not giving him credit because he "did not do it [my] way." To this, my response at the time was that he did not receive credit because he did not demonstrate how his calculations give him the correct answer.

Afterwards, I decided that I had the option of taking the much more confrontational route, which is the "what makes you an expert in math?" route. Am I not the teacher in the class, the one who is being paid to determine what is and what is not math? Did I not spend 9 years of my life studying math? And yet he believes what he is doing is, in fact, math. And because he thinks it's math, I should therefore defer to his understanding of math? How absurd. Does this happen in other fields? Do physics students try to convince their physics professors that they know physics better? That doesn't make sense (but I'm perfectly willing to believe it happens).

Whether this second option is any better doesn't seem like a good debate. Obviously, it's more edifying to me to simply pull rank to shut him down, but it does little for the student besides pulling further into the grave he has dug himself by being unteachable. My basic conclusion is that I really don't care what this student thinks. He's wrong and he's unwilling to admit it. So how can you work with such a student?

I offered him a challenge: I changed the numbers slightly and challenged him to show me how dividing 180 by 3 is a correct first step towards arriving at the answer. If he can do that he will get back his two points on the test. I changed the numbers so that the answer will end up with fractions, so he's not going to accidentally stumble across the right answer. I gave him until next class to come up with something, so it should be interesting to see what he says. Part of me thinks that he's simply going to walk away from the class, which is perfectly fine by me.

There's a principle in play here that is part of Gershon Harel's formulation of learning mathematics. It is the "necessity principle" (if I'm remembering right). A mathematical concept will be accepted as true by a student until he discovers that it is necessarily false. Necessarily false means that the two ideas are inherently contradictory and so one must eliminate one of them in order to maintain a logically coherent understanding. The purpose of the challenge is to force the student into a position where he is unable to solve a problem using his random techniques. Until he realizes that his toolbox is insufficient for the task at hand, he will never look to new tools. So now I just sit back and wait to see what he comes up with.

I scared my student...

I had was I guess I would consider to be my first big mistake as a professor, although I'm not sure if it really was a mistake or if i'm allowed to fault the student for this. I had a student who I knew was having a tough time with the math and I believed that it was mostly a result of her unwillingness to think about things before she just started randomly guessing what she should do. For example, we were looking at equations of circles and we were trying to write them in "standard form." She knew that a square had to go *somewhere*, but she had no idea where and just sort of stuck on the end. This is bad news from a mathematical perspective because it violates many of the precepts, in particular that every step has logic behind it and that nothing is purely random or haphazard.

With this in the background, she made a post on Webcampus asking me to post solutions to an earlier quiz over the weekend before the midterm. I explained to her that I would be unable to post it until at least Monday (after getting back to campus), but also directed her to the book and other quizzes to use as a guide. I also warned her against the misuse of solutions, namely trying to just memorize them for a test and making sure that she thought through her problems.

She responded by accusing me of criticizing her publicly (her post was public and my response was public) and felt insulted enough to drop the class before even taking the exam.

I had a chance to talk with Sandip about this incident (chair of the Physical Sciences), and it was a constructive conversation. I'm not sure if I agree with his approach, namely that I should treat every student as if they were the most fragile person in the world, but I do know that there can be a bit of a rough edge around me because when I make an observation of the type described above, I tend to believe that I stand on a fairly solid analysis.

I don't know whether I should I feel responsible for a student misinterpreting something like that as a criticism. There's nothing in my reading of what I wrote that I believe is talking down at her or insulting her. I also don't know how else I can communicate the teaching without giving the teaching. This is something that I'll just have to feel my way through in the future, I guess.