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!
Tuesday, October 20, 2009
Wednesday, October 7, 2009
The Finite Element Method and Problem Solving in Geometry
The last two weeks have gone well in Ms. Tran's classroom, and I am starting to feel like the students appreciate my presence. Yesterday, there were students in both of the first two classes who looked around for me at the beginning of the day to see if I was there. A highlight occurred yesterday in fourth hour just before my talk, when a student came up to me and said: "You would make a good teacher." That made me feel like I am doing good things in this classroom, and that I am getting through to at least some of the students. Last week I came in with a talk about nodal networks and finite element models, for which I recycled much of a powerpoint slideshow that I used last year, with an iteration of improvement. This week I came in with a new discussion on problem-solving, showing them an example of a real-life problem that I encountered just a few weeks ago. This will be the basis of the students' first project of the year, which I helped Ms. Tran formulate.
My talk last week was pretty successful. I had been talking with Ms. Tran the week before and asked her what topics would be good to cover. She actually remembered the talk that I gave last year around this time, which discussed nodal networks, which was something that they covered in class last year. This year, the curriculum changed, so they did not talk about nodal networks, so that was my opportunity to give them their only exposure that to the topic that they'll likely get during high school. My title slide included a figure from their assignment the previous week, which had a bunch of points connected by lines, and I told them that it was a network of nodes. I then asked them what they knew about networks of nodes, and most of them knew very little, so I broke it down into the words "node" and "network." In all of the classes, at least one person knew what a node was or could guess based on my intro slide; most of the students were able to define what a network is, and I asked them for examples of networks. Many of them came up with the phone company's definition of your "in" network, the internet, and facebook. This was great, so in each case I asked them what the nodes would be in their network; respectively, those were the individual cell phones, the computers and servers on the web, and people's profiles on facebook. I then showed them a few more examples of what I view as nodal networks, including rollercoaster truss structures, the human circulatory system, and an ipod's circuitry. I then introduced the students to finite element models, where we again broke the phrase down into individual words and then brought them together to define the phrase. I showed them an example of a Ford Taurus model with over a million elements, or nodes, and showed them how the network of nodes is useful for crash test simulations with a quick video animation. We wrapped up with a discussion on the purpose of models and why we simulate them. I thought this went fairly well - most of the students were attentive, and I noticed more students answering questions that had in the previous talk.
During Ms. Tran's lesson after my talk, there was some time for in-class problems, and for most of the classes I was able to go around and help students work through the problems. I was rather disappointed that some of the students (particularly in the non-accelerated classes) don't seem to know basic algebra, which is technically a prerequisite for this course. Not knowing how to solve problems of the form (3x+1)/2 = 5 is a real problem, and I have a feeling that the students who don't get it now will have a hard time getting it in the future, when they're fully expected to know it. Being able to get a variable by itself is so important, and it seems to me that the root of the problem is not understanding multiplication and division. There were at least two students that I was trying to help, and when time was up I still didn't feel like they understood what we were doing. I want to help them, but I get such little time with them that it is difficult to make any lasting impact. I spoke with Ms. Tran about this yesterday during the planning period, and she said that some students in the regular geometry classes actually failed algebra, and there weren't enough spots in the algebra classes, so they were placed in her geometry class. I told her that I will let her know who these students are so that she can push them to seek help outside of class, but I am still concerned about these students.
Yesterday I came in expecting time in class to help the students with in-class problems, but there was a change in plans and Ms. Tran gave a test yesterday. She told me when I came in yesterday morning that I could present for the last 15-20 minutes of each class, so I prepared my slides while the first class took their test. We had discussed this topic beforehand, when at the beginning of the year Ms. Tran asked me to help her come up with a project for the first half of the first term. I thought about it for a while, and I came up with an idea while I was helping a friend move into her new apartment. After hanging a curtain rod, we spent maybe 20 minutes trying to solve a problem that we had with a protruding bracket, and when we finally fixed it, I had a real sense of satisfaction from solving the problem. We went through several steps before finally fixing it, and I thought of this as a good example of real-life problem solving that students don't often think about during math class. I also thought that there was a good way to link this with geometry "logic," which mostly revolves around conditional statements. So I proposed to Ms. Tran that the project be to find an example of a real-life problem and discuss the steps and methods for solving it; then, the students could write 5-10 "if-then" conditional statements about the problem solving process, such as "IF this method doesn't work, THEN try this other idea."
So it wasn't a huge surprise when she asked me to do it yesterday morning, and I already had a bunch of photos prepared for it, so I sat in the back of the room and put together my powerpoint while the first class took the test. The slide show started out by defining what problem solving is and asking the students if they've ever had a problem or ever solved a problem (I may or may not have mentioned that Jay-Z had 99 problems). I also posed a question here about how problem solving relates to math, and I had an opportunity to discuss how math is really just a language that we can translate real problems into so that we can solve them. I then presented the curtain-hanging scenario, and walked the students through the three ideas that we tried before finally solving the problem, at each stage asking them for suggestions on how to fix it - they almost always came up with the same ideas that we did. I concluded by asking them to come up with some if-then statements about what I just did, and then I put a few examples up on the board. The classes got a little bit rowdy because many of my pictures were cheesy and kind of goofy, but I think because of this, more people paid attention. My first time through it, in second hour (accelerated), took a lot longer than I expected (maybe twenty minutes), but the students seemed engaged for the most part. One of the students actually gave a really good conditional statement that I hadn't thought of, and I later added to the slides: "If I don't solve the problem, then my friend is unhappy." Third hour (non-accelerated) is shorter than the others, and I only had 10 minutes to breeze through it, which rushed me quite a bit. The bell rang right before I got to the conditional statements part, but we told them to hang on one minute so I could get through it - the downside of being rushed was that I wasn't able to ask as many questions and give them time to respond. Fourth hour (non-accelerated) seemed to really get it, and I was impressed that most of them were engaged throughout and had really good answers to my questions. This was the only class where a student guessed where I was going with it before I got to the "if-then" slide, which made it go a lot quicker (too bad this didn't happen in third hour when I was rushed!). Sixth hour hadn't yet been exposed to conditional statements, so I felt like the part at the end didn't get as much feedback or response. Overall, I think this was an excellent exercise, and I'm looking forward to seeing what kinds of projects the students come up with.
My talk last week was pretty successful. I had been talking with Ms. Tran the week before and asked her what topics would be good to cover. She actually remembered the talk that I gave last year around this time, which discussed nodal networks, which was something that they covered in class last year. This year, the curriculum changed, so they did not talk about nodal networks, so that was my opportunity to give them their only exposure that to the topic that they'll likely get during high school. My title slide included a figure from their assignment the previous week, which had a bunch of points connected by lines, and I told them that it was a network of nodes. I then asked them what they knew about networks of nodes, and most of them knew very little, so I broke it down into the words "node" and "network." In all of the classes, at least one person knew what a node was or could guess based on my intro slide; most of the students were able to define what a network is, and I asked them for examples of networks. Many of them came up with the phone company's definition of your "in" network, the internet, and facebook. This was great, so in each case I asked them what the nodes would be in their network; respectively, those were the individual cell phones, the computers and servers on the web, and people's profiles on facebook. I then showed them a few more examples of what I view as nodal networks, including rollercoaster truss structures, the human circulatory system, and an ipod's circuitry. I then introduced the students to finite element models, where we again broke the phrase down into individual words and then brought them together to define the phrase. I showed them an example of a Ford Taurus model with over a million elements, or nodes, and showed them how the network of nodes is useful for crash test simulations with a quick video animation. We wrapped up with a discussion on the purpose of models and why we simulate them. I thought this went fairly well - most of the students were attentive, and I noticed more students answering questions that had in the previous talk.
During Ms. Tran's lesson after my talk, there was some time for in-class problems, and for most of the classes I was able to go around and help students work through the problems. I was rather disappointed that some of the students (particularly in the non-accelerated classes) don't seem to know basic algebra, which is technically a prerequisite for this course. Not knowing how to solve problems of the form (3x+1)/2 = 5 is a real problem, and I have a feeling that the students who don't get it now will have a hard time getting it in the future, when they're fully expected to know it. Being able to get a variable by itself is so important, and it seems to me that the root of the problem is not understanding multiplication and division. There were at least two students that I was trying to help, and when time was up I still didn't feel like they understood what we were doing. I want to help them, but I get such little time with them that it is difficult to make any lasting impact. I spoke with Ms. Tran about this yesterday during the planning period, and she said that some students in the regular geometry classes actually failed algebra, and there weren't enough spots in the algebra classes, so they were placed in her geometry class. I told her that I will let her know who these students are so that she can push them to seek help outside of class, but I am still concerned about these students.
Yesterday I came in expecting time in class to help the students with in-class problems, but there was a change in plans and Ms. Tran gave a test yesterday. She told me when I came in yesterday morning that I could present for the last 15-20 minutes of each class, so I prepared my slides while the first class took their test. We had discussed this topic beforehand, when at the beginning of the year Ms. Tran asked me to help her come up with a project for the first half of the first term. I thought about it for a while, and I came up with an idea while I was helping a friend move into her new apartment. After hanging a curtain rod, we spent maybe 20 minutes trying to solve a problem that we had with a protruding bracket, and when we finally fixed it, I had a real sense of satisfaction from solving the problem. We went through several steps before finally fixing it, and I thought of this as a good example of real-life problem solving that students don't often think about during math class. I also thought that there was a good way to link this with geometry "logic," which mostly revolves around conditional statements. So I proposed to Ms. Tran that the project be to find an example of a real-life problem and discuss the steps and methods for solving it; then, the students could write 5-10 "if-then" conditional statements about the problem solving process, such as "IF this method doesn't work, THEN try this other idea."
So it wasn't a huge surprise when she asked me to do it yesterday morning, and I already had a bunch of photos prepared for it, so I sat in the back of the room and put together my powerpoint while the first class took the test. The slide show started out by defining what problem solving is and asking the students if they've ever had a problem or ever solved a problem (I may or may not have mentioned that Jay-Z had 99 problems). I also posed a question here about how problem solving relates to math, and I had an opportunity to discuss how math is really just a language that we can translate real problems into so that we can solve them. I then presented the curtain-hanging scenario, and walked the students through the three ideas that we tried before finally solving the problem, at each stage asking them for suggestions on how to fix it - they almost always came up with the same ideas that we did. I concluded by asking them to come up with some if-then statements about what I just did, and then I put a few examples up on the board. The classes got a little bit rowdy because many of my pictures were cheesy and kind of goofy, but I think because of this, more people paid attention. My first time through it, in second hour (accelerated), took a lot longer than I expected (maybe twenty minutes), but the students seemed engaged for the most part. One of the students actually gave a really good conditional statement that I hadn't thought of, and I later added to the slides: "If I don't solve the problem, then my friend is unhappy." Third hour (non-accelerated) is shorter than the others, and I only had 10 minutes to breeze through it, which rushed me quite a bit. The bell rang right before I got to the conditional statements part, but we told them to hang on one minute so I could get through it - the downside of being rushed was that I wasn't able to ask as many questions and give them time to respond. Fourth hour (non-accelerated) seemed to really get it, and I was impressed that most of them were engaged throughout and had really good answers to my questions. This was the only class where a student guessed where I was going with it before I got to the "if-then" slide, which made it go a lot quicker (too bad this didn't happen in third hour when I was rushed!). Sixth hour hadn't yet been exposed to conditional statements, so I felt like the part at the end didn't get as much feedback or response. Overall, I think this was an excellent exercise, and I'm looking forward to seeing what kinds of projects the students come up with.
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