Higher Mathematics

Originally written on Thursday, March 6
One of the problems with going on a working vacation with no plans is that you don’t really know what kind of work you’ll end up doing until you speak to someone after arriving. That makes it impossible to prepare. Along those lines, Claudia’s husband Joel came here with the idea that he’d try to give some supplemental tutoring or teaching at one of the local schools. So on Monday he invites me to come along to the International Window School here in Mbarara. We have no introduction, but Joel figures we can walk in and offer our services.

To me, this sounds a bit presumptuous. Here come the white Americans, offering to teach at the Ugandan school where of course they could use our help. I’m not entirely comfortable with the setup. In addition, Joel’s plan involves me teaching math. He figures I’m an engineer, so I should be pretty good at math. The school is primary up through secondary (essentially elementary school and high school combined), so I really have no idea what I might end up teaching if they want us to do so.

When we got to the school, I discover that it’s a boarding school for girls only. This was something Joel had neglected to tell me. I’m not really sure if that makes me more or less comfortable about the idea. There’s a large metal gate at the entrance large enough to let a small truck through. When we knock, a small door in the gate opens and we introduce ourselves to the gate keeper. He tells us to wait, and a few minutes later comes back with a visitor slip for us to fill out. We write down that we’re inquiring about teaching, and a few minutes after handing it back, are ushered inside.

We’re greeted by Edith, who’s role in administration isn’t entirely clear, but she’s very friendly despite what appears to be some annoyance with this unannounced intrusion into her day. Joel tells her that he’s heard of the school and its good reputation, and that we were wondering if we might provide some supplemental teaching for the students. He mentions that I’m an engineer and could teach math or English, and that he could teach either of those or geography. Quick side note – Joel teaches geography in Portland and his 5-year old son Will has been working on drawing various maps with an earnestness that is absolutely wonderful to watch.

Edith thinks briefly, then tells us that she’s not the person to talk to and goes to fetch Geoffrey. Geoffrey’s exact role in the administration is never fully explained, either, but it’s clear that he has some authority over the curriculum and the teachers. His demeanor also suggests that our intrusion isn’t entirely welcome, but he feels obliged to entertain us and our impression is that he’s trying to figure out exactly what he might get out of this whole business. Joel goes through his pitch again, and Geoffrey talks about the difficulty of having us inserted into the middle of the semester and interrupting what the regular teachers are teaching. We also share that we’re here for only a few weeks, which makes it additionally difficult to figure out how to get involved. Finally, we settle on some after school sessions in which we can answer student questions for the highest level students (Secondary 4 or S4). We’ll each have our own classroom. I’ll do math and Joel his geography. At this point, Joel offers to have us come back that afternoon. He seems to be ignoring the fact that I haven’t really looked at high school math since, well, high school.

Thankfully, Geoffrey suggests we come back after classes the next day (Tuesday), so the students have some time to come up with questions they’d like to ask. I’m thinking he’s just not prepared for our intrusion quite yet. Either way, he takes us along to introduce us to the S4’s who will be invited to our sessions. We interrupt three different classrooms, are introduced by Geoffrey, and then head off.

At home in the evening, I went over what I could remember from algebra and geometry and also reviewed an algebra book that Claudia’s oldest daughter, Madeleine has with her to do some exercises in. She’s only in 5th grade, but quite smart. The book goes from very basic stuff to some more advanced high school stuff, so the latter parts are potentially useful to me. In reality, though, I have no idea what to expect.

Tuesday afternoon, Joel and I head back to the school to meet up with Geoffrey and find our classrooms. This time, we’re let right in when we get there and soon Geoffrey ushers us upstairs to the classrooms in which we’ll teach. The girls in the school are done for the day, but those that wanted to could come to our sessions. Geoffrey asks us to do about an hour and a half, and then we drop Joel off at his classroom. At this point, I’m very aware that I’m totally alone on this, my big fear being that they’ll ask me to solve a problem for them that I have no idea how to do and I’ll be a total flop. Geoffrey’s billed me as an engineer and an “expert” in math, so being unable to solve any problem is going to be quite embarrassing.

I start with 5 students and no chalk. The eraser is a piece of sponge, which works far better than most erasers I’ve used in the US in the past. I start by saying “Good afternoon and welcome!” - which draws a chorus of laughter. Hmm… ok, I’m not sure why that’s so funny, but I suppose it’s just funny to hear my odd American accent. I check to make sure all the buttons on my shirt are buttoned. I then grab a half inch piece of chalk I spotted on the floor, but a few moments later one of the girls hands me some from her bag. I tell them that I’m going to help them with some problems, so if they give me a problem, then I’ll do it with them on the board, however I’m going to ask them to solve the problem and I’ll help them when they get stuck. This is my big secret plan, hoping that they won’t get stuck and I’ll just write on the board what they tell me. Maybe they’ll jog my memory a bit.

Ready for a good algebraic equation to solve, I ask for the first problem and am given one with the height and vertex angle of a cone, needing to find the surface area. Naturally, I have no idea what the formula is for the surface area of the cone is. Sure, I used to know it, but that was about 15 years ago, so my big secret plan is put to the immediate test. I ask the students what the formula is for the surface area of a cone, and one of them mumbles something so quietly that I’m not sure if she’s thinking to herself or really trying to answer. Thinking about it, I’m not really sure how much interaction they normally have with their teachers. Maybe it’s all lecture. Maybe wrong answers are so embarrassing to them that they’re afraid to state something boldly. They’re almost certainly unsure of what to make of their muzungu teacher.

I manage to coax a formula out of the student and proceed to use basic trig functions, at the students prompting to solve the problem. About halfway through it, someone from the school delivers some brand new chalk to me, allowing me to return my other chalk to the student. Of course, as soon as I use the new chalk, I break it, and find out later that Joel had the same problem with his chalk, so it’s not just me. Anyway, the students are pretty bright despite how incredibly shy they are with me. While I started out with 5 students, more keep coming into the room. I continue to get occasional burst of laughter as I’m writing something on the board, but just have to ignore it and keep going.

Filling the hour and a half turns out to be fairly easy, but I’m very grateful when it’s over. By this point, I’ve got about 40 students in my room, and I’m working on a 4th problem. I had another cone problem (find the volume of the solid left by cutting the top off of a cone) and an algebraic expression to factorize which looked really hard at first but proved to be very easy. The last problem, however, is one that I wasn’t sure at all about. I was given a circle and two secants meeting at a point outside the circle. Some additional lines are drawn, and given two of the angles in the drawing, we need to find two others. I’m really not sure where to go with this. The angles I’m given don’t give me a lot of information, and I can’t remember the properties of angles inside a circle. The students also instruct me to give one angle an incorrect measure. I tried to show them why their mistake wasn’t possible, but they continue to ignore it, and happily, that’s when the time is up. Happily, because I know their choice is wrong, but I don’t have a correct answer for them.

We’re going back on Friday, and I promised to follow up with them then, but unfortunately, I still haven’t been able to solve the problem. I’ve researched some of the properties of the triangles and keep coming back to the conclusion that there are multiple solutions to the problem. In other words, I need another predefined value in order to come up with a unique solution. Joel looked at it too and came to the same conclusion, but he admits that his knowledge of the subject isn’t beyond mine. It’s entirely possible the solution is not intended to be unique, but the way the problem is defined, it looks like it should be. Maybe they copied it down wrong and left something out, I don’t know, but it’s very frustrating! We’ll see how it goes tomorrow.

Epilogue (written Monday, March 10)
At some point you’ll hear more about what happened on Friday during the day, but for now I thought I’d just finish this post by telling you how my experience returning to International Window School went on Friday afternoon. When Joel and I got to the school, it didn’t take long before we were off to the classrooms, along the way greeting the students we recognized from last time. Although we were there at 4:30, the S4 students were still in a class, and as a result, we didn’t have any students at all for a little while.

Around 5 pm or so, a few students walked in to my classroom, but they were all younger students, so I decide to wait with a repeat of my geometry problem until some S4 students showed up. After all the preparation and agonizing over the problem, it turned out that not a single S4 came, so I never did the problem with them! I am going back tomorrow afternoon (Tuesday), so perhaps I’ll see them then, but I don’t have any idea if they’ll still be interested or not.

In many ways, I enjoyed the Friday session more than the first one. The students that were there numbered about 6, and the small number allowed them to cluster around the front of the room and interact far more with me individually than the larger group did. The problems were all algebra problems, which was fun and fairly easy, and I felt like they got a better understanding of how to do the problems since the group was small. They also were very good about asking questions and responding to mine, which really helped me feel like they were learning.

EDITOR'S NOTE: I just wanted to say that for some reason, our slow internet connection has made it difficult to post pictures on the blog from here (although the one above seems to have taken). We'll post if we are able, and certainly put some up when we get back, but for the meantime, you'll have to deal with text only. Sorry!