More Problem-Solving

Last week I came in with a presentation prepared, but Ms. Tran wanted to spend the whole class period working through past homework and in-class problems to help them prepare for a quiz the next day. Toward the end of each class, there was about 10-15 minutes for an in-class worksheet on conditional statements and reasoning. The students in 2nd hour are the least awake and therefore the least likely to communicate a need for help, so I tried walking around and looking over their shoulders to see what they need help with, and there was only one student who had a question that I could address. Third hour was much different - before class even started, one of the students, A, told Ms. Tran that he didn't understand the homework. She was busy, so I went over to A and asked him what he needed help with. He seemed very enthused to have my help, and I helped him walk through the first two sections of the homework assignment. Later, when the students had an in-class worksheet to do, two of the students immediately got up and came to sit by me. It seemed like they just wanted the constant reassurance about what they were doing, and I sat with them as they went through it for the first half of the time allotted. I then decided to get up and answer a few questions on the other side of the room, just to be fair. I don't think any of the students in the non-accelerated classes were able to finish the worksheet in time, but I think that I was able to help a few of them understand what they were doing. I asked them to reference their notes frequently, and showed them where they could find the information they need... as they say, "teach a man to fish, he eats for a lifetime." In the other courses, I did feel like I was able to help out during the in-class problems, and I think that made those particular students trust me a bit more.

At the beginning of each class today, I gave a talk that drew off the previous one about problem solving in the case of hanging curtains. I started by showing some images from the last talk and asked for someone to summarize what we discussed. I then asked the students what we did to solve the problem, and inevitably someone would say that we tried a bunch of tools. In second hour someone actually used the term "trial & error," which brought me to my next point quite nicely, which was that we used the tools that we had (in the curtain case, screwdriver, hammer, pliers; in geometry, definitions, theorems, postulates) to solve the problem. I said that this class should actually be easier than other problems that they encounter in life because they KNOW that every problem in the book can be solved using the definitions, postulates, and theorems that they are learning. Next I showed them another example of a problem, where I was helping a friend of mine move his couch out of an apartment. After we tried many times unsuccessfully to get the couch out the door (and after tearing a big hole in the wall), we decided to modify our goal. Instead of trying the get the couch out of the apartment so that he could move it into his new place, we just needed the apartment to no longer have the couch in it. So, I proceeded to show them some entertaining photos of my friend and I beating his couch apart and ripping it into many pieces. I then asked them how this problem was like solving a math problem, and I wrote their responses on the board. They initially came up with some if-then statements, which were good, but not exactly what I was looking for. I was looking for the way that we used the tools that we had to solve the problem, and how we don't always know what the outcome will be, and how we used trial & error to come to a solution, and some students even made some analogies to variables, saying that we were solving for variables. Second and sixth hours (accelerated geometry) went very well, and students in both of those classes were attentive and able to guess my next moves. Third hour was more difficult, partially because several of them got up and left to get their school ID's made right before my talk. I had a couple of students put their heads down during the talk, which isn't too bothersome when there are 30 people in the class, but when we are down to 15 students, it makes the discussion circle and opinions that we can get much more limited. Fourth hour was actually more difficult than third. There was a full classroom, and it felt like even more of the students weren't paying attention. This indicates to me that this was a poor presentation for those audiences, as it clearly did not capture the audience like the previous talks have. Some of them were clearly entertained, but I think that they were a minority. I think a big part of where I lost them was at the beginning when I tried to bring in geometry parallels. It seems like that type of discussion equates to boredom for many students, and that causes them to zone out, thereby making my job of drawing entertaining parallels to geometry for them that much harder!

During my talk, several students asked the question about how my friend had gotten the couch into the apartment if we can't get it out, and I explained that the way the stairs and doorway were situated, he was able to use gravity to wiggle it down, but when we tried to reverse it, it just didn't work. A minute or two after I moved on from this part during fourth hour, a student, S, looked at me and said "how'd you get it in?" I chose to ignore S because (1) she didn't raise her hand, and (2) I had already answered that question at least twice. She noticed that I ignored her and said: "you gonna look at me and not answer my question?" I replied, "I already answered that question," and moved on as she put her head down for the rest of the class period. I guess I could have said: "who can answer S's question for me," and then she would have felt dumb when other people had to explain it to her. I feel bad for S, but I also think that she is an example of a very common student that has been frustrating me since I started here. This is the student who feels like she doesn't have to listen to anything until she has a question of her own, and then she can interrupt everything to rudely ask her question and expect an immediate answer. When responded to negatively, she feels like the world is out to get her and she gives up on school/math. I don't know what to do about these students, and trying to deal with them makes me angry, which then perpetuates the cycle of her feeling like the world is out to get her. Ugghh!