Measure Theory Interblog

The advantage of having only two students to tutor is that I can manage to learn their names. Though I don’t actually know how to pronounce one girl’s name. Anyways, one girl that I’m tutoring hasn’t taken math in about three years. Usually this is pretty common. When there’s been a pretty big gap since the last time the person took math, I ask the person if they’ve heard of a term or formula before I define it. Sometimes they have heard of it and sometimes not. But if they’ve heard of it, I can expect that after we go over the definition and do a few examples it’ll start to come back to them. If they’ve never heard of it at all, I go into a lengthier explanation. After which, the student usually says “Oh yeah!! We DID do this…”

Back to my story. One of my students had a three year gap since her last math course. And she was now in introductory calculus. She’d learned math in high school in a french immersion environment, so she wasn’t familiar with the english terminology even though she’d done some of the concepts before. We started with basic exponential and logarithm rules which she seemed to get alright. And then I talked about what a derivative was and visually explained where the formula for the definition of the derivative came from. After a while it was clear that she didn’t really know what a function was. And it took about 20 - 30 minutes to get across. I think she was getting bogged down thinking that f(x) meant “f times x”. That took me about 10 - 15 minutes to figure out. She was a bit rusty on factoring, but we did a crash course in that. So, I think that she’s starting to get the hang of functions. And we start on the formula:

The question gives a function and says to use the formula to find the derivative when a = 4. Ok.

“What’s a?”

“Well, a is a value of x. Like a particular value”

“So a equals x?”

“Kind of. The x there is talking in general about any value of x. And the a is talking about an actual number for x”

“…so a equals x?”

“Kinda..”

That went on for a while. A long while.

“So x is 4?”

“No, x is x. a is 4″

“But isn’t x equal to a?”

“Um..”

This semester, I was a teaching assistant for a third year economics course - mathematics for economists. Or economical mathematics, or something. The prof wanted me to attend the actual lectures so that I knew what was happened. But, they conflicted with my class, so I could only attend the first half and then leave in the middle. So, I’d usually get to see the introduction, or the motivation for what he was about to do, and then I’d have to leave. It was like every class was a cliffhanger than I never got to see resolved. Anyways, the prof assigned several homework questions and then added a few of his own (not from the textbook). The ones he made himself were to be solved using the “classroom version” of one of the textbook theorems. I missed the part of class where he mentioned the classroom version. And during the last 4 tutorial sessions, at least one person asked about these. So, I pretty much borrowed someone’s notes and winged it (wung it?). “Here’s how he said to do it…I don’t know why this works at all…Something he did in class, I guess…”

Someone just came up to me two minutes ago. He missed the review session. He wrote down the wrong day and wondered why the room was empty.  Anyways, he asked me that same question that everyone else asked. He seemed to be satisfied with my answer though.

Their exam is tonight. At the tutorials, some people were struggling with things they should have known from two years ago.

I also do work tutoring people online. Sometimes people send me a bunch of questions and I solve them and send the solutions back. A year or so ago someone sent me some problems. Some very typical problems of 11th grade math. I solve them and send them back. They email me upset that they can’t figure out “what the answers were.” I was busy that day and I didn’t get a chance to reply until a few days later. By that time, they had emailed me another few angry emails. They couldn’t figure out that the final answer appeared after the last equals sign. As in:

(Original equation)

= (stuff)

= …

= (final answer)

No, they couldn’t figure that much out. It wasn’t a case of me going part way and then saying “…and then you just factor it and you’re done” or “and then the rest is obvious”. No, the whole solution was there and they couldn’t figure out where the end was. Somehow, I think they had more problems than just math.

My last tutorial is tomorrow. Last one of the year. The prof assigned several questions from the textbook and then made up a few himself. The past three tutorials, I’ve been asked to solve the questions that the prof made up. They look innocent enough. But, the tricky part is that part a is really the hardest one. If a question has several parts, I usually do part a since I can figure it out on the spot. Not so. Part a lands me in nowheresville with a bunch of complex eigenvalues. No good. So, I try a different part. It seems to work out. But, then the students want to know why they cant use a different theorem to solve it instead. Well, I don’t know why. This way works and that way doesn’t. Also, the book uses asymptotically stable instead of locally stable. To me, asymptotically stable sounds more like globally stable. But, it’s not. Good thing that the prof didn’t see my undergrad marks in differential equations

I hate differential equations.

Firefox is informing me that nowheresville is either not a word or is not spelled correctly.

In the tutorial last week, someone asked if Fibonnaci numbers would be on the test. For the record, I have been told nothing about the exam. I preceded any comments about the exam to the students by saying, “The prof has told me nothing. I really don’t know. Please don’t quote me on any of this. Do not call me after the exam and scream at me saying I said something would or would not be tested and you found out I was wrong.” I told the student that I felt like the Fibonnaci numbers were more of an introductory example and that they wouldn’t be on the test.

Them: “…he did spend a whole class on them though”

Me: “True. But, he spent a whole class on monopoly, too.”

(He really did. A 40 x 40 monopoly markov matrix from hell)

This semester, I’m required to attend the classes for the course I T.A. Last week, one person came up to me in class and asked when the tutorial was. Apparantly, she had come to the room at the right time but the wrong day. So, she came to this week’s tutorial on the right time. We went over some questions. She said she’d try some more questions on her own and she’d come to the other tutorial next week (since I run them on two days). At the end of class I had a thought and said to her “you know that it’s in a different room if you come on the other day, right?” “No! I didnt. What room is it?” So, I told her. I could just imagine how frustrating it would be for her to come to the wrong room, twice.

This semester, I’m running a tutorial for a third year economics course which is basically a continuation of last semester’s course. The good part is that the material is stuff that I’m more familiar with. The only problem was that the tutorial was scheduled at a time that conflicted with my class. The entire tutorial overlapped, not just part of it. But, I really wanted to be a T.A. for this class. So, I talked to the prof who talked to the class. But, they couldnt agree on a time. So, instead of running 1 tutorial, I’m running two a week. Some people can come to the first and some to the second. Also, the prof told the class that it’s mandatory that they come. Ok. So, the first week I get 3 people at the first one and 2 at the second. Out of a class of about 17. I figure maybe it’s just the beginning of the semester and soon more people will come. Next week, 3 people come to the first one and none to the second one. So much for a mandatory tutorial. This week, we had 0 and 5. Five was a new record and I was happy about that. I’m guessing more people will come closer to the exam, but who knows.

I ran my last tutorial of the year on Thursday. I was expecting more people than usual, but only one showed up. The same guy as always. He’s nice though. He said “God bless you” to me for helping him so much and offered to buy me a hot chocolate. Also, I found out that he apparantly thought my name was Matt. I don’t know how that happened. I still have yet to find out if I’ll be T.A.-ing another course next semester or not.

A rundown of today’s thoughts:

During tutoring at lunch, I mentioned that my breakfast had consisted of two tums. My student went on to tell me how tums actually cause cancer and it had happened to a relative of hers. I haven’t heard of this, but I’ll have to quit snacking on tums now.

During the tutorials, one of the students who always shows up always writes his questions on distinctive post-it notes that he attaches to his class notes. I was marking the assignments, and there, on his assignment, was a post it note. It said “can we write as 2x + 2y - 10=0″ or something. I don’t know if he was reminding himself and forgot it or if he was asking me, while I marked it. I’m deciding to write an answer back on his post it note.

I think students mistake being neat with writing big. Writing big and taking up 20 pages is almost as bad as writing too small and not showing enough work and squeezing everything onto a single page. I think a good rule would be “every page turn equals a half mark deduction.” My marking scheme would be something like:

Actual knowledge: 10% of mark
Neatness/handwriting: 45% of mark
Bonus for not infuriating me with large handwriting and/or obvious word for word cheating: 45% of mark

Usually, at my tutorial, only 1 or 2 students actually show up.

Actually, more than that come, either to pick up assignments and leave or to give me dirty looks when I tell them the assignments haven’t been marked yet.

If no one comes, I get a nice quiet hour to myself. Or 40 minutes. After 40 minutes, I assume no one is going to come and I leave. But, I’m supposed to stay for the full hour. Once someone came 30 minutes into the hour and interrupted the nice holiday from reality that I was having.

Anyways, the 1 or 2 students that usually show up, usually have lots of questions. Often about things I don’t know 100% myself. But, we work through it together at the blackboard. There’s two problems:

1. Most of the students are foreign. So, they don’t have total fluency of english. Which means none of my jokes make any sense to them. So, I’ll say some joke and laugh a bit. They’ll do a small chuckle because they can tell a joke had been told, but they don’t really get it (or maybe I’m just not funny), there will be an awkward pause, and then we go back to math. Sometimes it is a long hour.
2. I don’t know if this is because they are foreign and they have different social norms in their home country or what, but often, they crowd my personal space. When I’m writing on the chalkboard and already stressed because the material is seriously confusing to me, it does not help with you being 6 inches away from me.

Two more tutorial sessions until Christmas. I hope we still have the same turnout, but I have a feeling the last one will be popular when people realize they’re confused about the past 3 months of class.