I don't understand this

I just finished grading my Math 097 exams this afternoon. There were two parts to the exam. The first part was a 125 minute in-class exam with one page of notes. This is the standard sort of in class final that you would expect from a math class. The second part was a two day take-home final, where students could work together in groups, talk to tutors, and do whatever it takes for them to figure out what's going on (except asking me for help). It's also exactly the same test as the in-class exam.

The average for the in-class: 42.5
The average for the take-home: 55.5

13 point improvement... That's not too bad. However, the exam was out of 94 points. That means that even if the students were allowed almost unlimited resources, they were still only able to get about 60% credit. I find this very disappointing. I also don't understand why the students couldn't pull off at least a solid finish. This is even more confusing to me because the take-home part was worth a full 13% of their final grade!

Sadly, this result on the final exam means that over half the class failed. There were a couple of bright spots. I had a couple students who worked very hard and came away with a well-deserved B.

Coming to the end of the semester

Even though there's another week left in the semester, I've reached the point where I have no more teaching to do. At least, no more planned teaching of new material. I have one more class this evening to teach, but we're just doing review. I've got a couple hours right now with no specific plans, so I'm going to spend the time rambling away with my thoughts on how this semester has gone in order to prepare myself for next semester. I'm pretty sure some of this stuff I have mentioned before, but it's worth reconsidering again.

General things

I'm not going to be using WebCampus for my homework postings next year. Doing it this year was too much of a hassle without enough benefits to make it worth my time and energy. I think by hosting it on a normal webpage will make my life much easier. (Hopefully, I can figure out how to get proper FTP access from home to make this part even more flexible and accessible.) Along the same lines, I need to get better posting quiz solutions and that sort of thing.

I let myself get lazy with my bookkeeping and grading, which was a little bit frustrating just because I don't like to have stuff like that hanging over my head. I also found myself about halfway through the semester not having my quizzes ready until just before class. I think if I get myself a little more organized (the point above with the homework posting frustrations comes into play here), I should be able to make that happen a little more regularly (and efficiently).

I made a homework cover sheet that I think I will have my students use. The point of it is to increase the impetus on my students to be organized. It has questions on the front that I want students to answer, which will force them to think a little bit about what they did with their homework instead of just turning it in. I also gave them a space to ask questions. I didn't leave myself any room to make comments in return, so maybe I'll change that.

I want my students to check their answers in the back of the book. I don't feel that grading their homework is actually something that is particularly benficial for them. I think they need to learn how to use the tools they have to assess themselves. Of couse, I need to explain this process to them on the first day of class.

Math 097

I feel that I need to change my approach to this class completely. I almost want to break it into two different sections: One hour lecture and one hour lab. That might even need to be broken down into two half hour lectures and two half hour labs. I want to keep the daily quizzes, though I may change them into weekly quizzes. There's something about giving them a problem to do and forcing them to show what they know that has seemed to help things stick in the minds of some of my students.

I think the first 4 weeks of the class are the most critical as the foundational algebra must be set up by then for any of the rest of the stuff to have a real chance of making sense. But this doesn't just mean the mechanics of algebra, but a sense that the algebra is actually connected to real life (as a way of representing real values). I've got some ideas that I'm working out right now, but nothing solid yet. It has to do with starting the class using just numbers and then introducing variables *after* they have a sense of seeing patterns and *after* they have a notion of what it means to generalize a pattern.

I am also going to be less ambitious about the number of topics I cover in that class. I need to think a little more carefully about it, but I've got a preliminary schedule that feels like it's only about 2/3 the speed as I had this semester. I would like to follow the "teach less, teach better" mentality this time around and see if I can cut back to the core essentials.

There are things I want to do, but I don't know of any textbooks out there that do it. Maybe I'll write my own someday...

Math 124

There is a move right now for us to get rid of this class. The entire math department wants to do it. We've got a proposal in the works to make it happen.

The problem is that the course has turned into a terminal course, meaning that most students who take this will have this as their last math experience. Unfortunately, the content of the class doesn't really climax very well as a mathematical exeperience, and just leaves students with the feeling that math is a bunch of nonsense that doesn't go anywhere or have any real application. That's all very disappointing because it continues to perpetuate the sense of how hard and weird math is.

As far as how I might change how I teach this class, I'm really not sure. The difficulty is that this class has less time than the other one, so I can't break it up into lots of little pieces and have time for things. However, I still like the idea of breaking it into a lecture/lab combo, but I need to spend time working out how much information I can put in front of them in a 20 minute span and have them make sense of it.

Math 283

This was my fun class all semester long. I hope my number theory class next semester goes just as well if not better than this one. I don't really have too much to say about this one just because it was the one that I could relax the most in (even though it was the most difficult content) and everything that happened in that class just seemed to be very enjoyable.

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.

A chance to refelct on the first half of my first semester

I'm taking some time right now to think about the first 8 weeks of the semester. I'm doing this now, right before the big onslaught of graind that is to come next week. There are certainly a number of things I want to do differently next semester.

#1 - Homework: I'm going to try something new next semester. I'm going to make part of the homework for my algebra classes simply copying the examples out of the book. This is first to force them to read the examples and work through them. Secondly, I want to give them the opportunity to circle parts of the examples that doesn't make sense to them that they would like clearified. I also want to force them to compare the examples to their own work that follows. Hopefully, this will help them get into a good routine of using the book effectively instead of just a source of homework problems. Thirdly, I think giving students a full week to do homework is simply an excuse for them to put it off. Only a couple students ever start the homework ahead of time like I ask, and so I need to force the issue a little with them. Finally, I need to assign problems from previous sections with much more regularity than I have been. This will hopefully reinforce the necessity of not forgeting past concepts.

#2 - Grading: I made the mistake of making homework out of too many points. It really only needs to be worth 3 or 4 points. I had a student ask me why she lost 5 points out of 20 when I only marked one error on her homework. My response was that her error demonstrated that she didn't understand a particular concept very well. She argued that she did lots of other problems correctly, and I agreed with her that she did. However, the point is that she failed to grasp one of four or five concepts for that section (which she agreed didn't make sense), and that her grade reflected that reality. However, there's a psychological difference between 15/20 and 3/4 that she had a hard time getting over.

#3 - Quizzes: I might do the quizzes at the beginning of class and schedule class start time 10 minutes after the start of the class. It's a much more regular routine that way. I might also cut it to one quiz per week.

#4 - I want to buy "The Inner Game of Tennis" and read it so that I can potentially send some of that message to the students on the first day of class. Many of the students have already defeated themselves by coming in with an attitude of failure. I've heard this sports psychology book is very good at discussing how players lose before they even begin. I think I'll jump to Amazon right now to do that because I'm done posting.

I'm glad I'm not a researcher/teacher

I'm finding it very hard to find the time to put my thoughts together in this blog. I meant for it to be a habit of professional reflection, and I guess by "habit" I meant it to be somewhat regular. But reality sinks in and there's just not all that much time. I really should be making more of an effort to carve out time for this, but since I'm already starting to fall behind with my grading (gone all weekend at a wedding), I can expect the remaining semester to continue to be hectic.

Changes that would allow me more time:

1. Different homework grading system
2. Quizzes weekly instead of daily
3. Not having to write lecture notes from scratch (future semesters)

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.