Challenging Students

This week I observed Mr. M teaching an hour and a half probability and statistics class full of seniors. For the first 45 minutes of the class, he had the students do a "word wall" in which he split the students into pairs and had each pair write a word and its definition on a paper and put it up on the wall. One student remarked that it was a "middle school project" and it was obvious that the students thought it was a little silly. After a 15 minute fire drill, we returned to the class and Mr. M wrote a formula on the board. He then gave the students the remaining 30 minutes of the class to work on three plug-and-chug problems.

Overall, I was very interested and discouraged that a teacher who has been in the profession for so long planned this class in this way. I have read articles and heard about schools that have high school students color pictures--because the school believes they are not capable of more--but I was very sad to find an assignment for students that is only a few steps above that. I could tell that the students were not challenged. As a result they put minimal effort into the word wall and many students did not even start the problems that were assigned. This taught me a valuable lesson: teachers must challenge students and provide them with tasks that are age appropriate. This is also something we have discussed in class, but I really saw that it is really important through this instance at school.

If I were teaching this lesson, I would have made up some kind of game (or better yet, have the students make some kind of game) to review the vocabulary and discuss its meaning. I then would have had the students match symbols with the definitions and explain a way to remember what each means. Then, I would have given the students the formula and had them explain to me why it worked. I would then have students come to the front of the class to work through word problems for the entire class, explaining how they went about each step. I think that would be a more challenging adaptation of the current activity. When I am a teacher, I will make sure I challenge my students.

Making Connections and Learning Something New

Today I observed an AP Calculus class for an hour and thirty-five minutes with Dr. R. (different from my mentor teacher). They were covering the second derivative test, which tells the students whether critical values are minima, maxima, or neither. I had never heard of this test, so it was interesting for me. In general, I was very sad to find that the teacher spent the entire class going over homework problems (which I've heard in both methods classes is not at all how we should teach). He didn't collect the homework until the end of class, so the students were copying the work onto their homework the entire class. Also, the students have solutions manuals with the odd numbered problems, but they only went over odd numbered problems in class. The teacher admitted to me that many of the students copy homework straight out of the solutions manual, but he didn't seem concerned about it. I had to wonder how much of the homework the students actually understand. I was especially surprised that the class did not cover any new information, especially since it is an AP class.

Another thing that stuck out to me was that while they were discussing the second derivative, one student asked a question about inflection points (which can be found using the second derivative). The teacher said, "No, forget what you know about inflection points and only think about the second derivative test." I was really surprised by his reply because I have had a conversation with my mentor teacher and have heard from Dr. Manizade's class how important it is to make connections between concepts in math. Had I been asked that question, I would have praised the student for making that connection but explained that looking at the inflection point would not help us in determining maxima and minima.

From this experience, I have learned a few things:
First, it is extremely important to make sure that homework is completed at home. It should be something that builds on student understanding rather than a way to teach students because there was not time to cover new material in class. I feel very strongly against spending much class time to go over homework, so I would have simply asked them what problems they did not understand. Also, I would make sure to assign even problems similar to odd problems so that students actually had to complete the homework rather than just copy the solutions manual. By doing that, I would provide students the opportunity to look at examples similar to the problems they are doing and look at their assigned problem so that they could get help on how to solve their problems. In addition, I will make sure that I collect the homework at the beginning of class so that students won't be able to complete their homework in class.

Another thing I learned about is the importance of reinforcing connections in mathematics. In Dr. Manizade's class today we learned that most high school students will have jobs in 2010 that do not exist right now. This means that no one has done what they will be doing, so they will have to be able to think on their own and make connections between concepts to solve problems. When I am a teacher, I will encourage my students to try to discover how each topic we cover relates to previous topics (and will make a point to show them that myself). I will certainly encourage students for trying to make connections so that they will be able to see how new information builds on previous material. That will encourage my students to take learning into their own hands.

Proofs gone wrong

This past Tuesday, I finished teaching the lesson I began last Friday in Geometry CP on proving isosceles triangle conjectures for the hour and a half class. Part of the lesson that I had planned involved completing two flowchart proofs together, both from the textbook. In both of the proofs in the book a lot of information was already given to the students, leaving them to only have to complete some of the remaining information themselves. I decided to take out some of the information to challenge the students to think. I went through them and took out about one piece of information from every pair given. I used the think-pair-share method of problem solving so that they students would have to think by themselves, work with each other, and share their reasoning with the class.

While we were going over the proof, I discovered that I should have been more careful and strategic about the information that I omitted. There were two adjacent boxes dealing with linear pairs: one of which had the reason of the definition of a linear pair and the other of which had the reason of the linear pair conjecture. There was one student who absolutely could not understand why the reasons for the two boxes could not be interchanged. I tried having the students explain first, followed by myself explaining that the definition was in one box and the conjecture was in the other box, so the reasons could not be changed. We must have spent at least ten minutes going over just that part of the proof. I didn't know what to do because it was only one student who was really struggling with the concept while the others seemed to have grasped it. I tried to explain a couple of times and then had to move on, but I went over to her individually afterward to ask if she had any other questions. The entire experience was a bit frustrating for both me and the students as we found it very difficult to communicate with each other.

Looking back, I think that I perhaps should have given them both reasons so that the students would not have been as confused. From this entire experience, I have learned the importance of really thinking through each problem to detect any potential problems that students may have and to create/edit problems accordingly. From now on, I will try to look at each problem in the students' eyes to see how they will approach the problem and think about explanations that address these ahead of time.

Finding Balance

Yesterday I was at school for nearly seven hours, an hour and a half of which I taught Geometry CP. I was teaching on Proving Isosceles Triangle Conjectures and, overall, it went very well. I was a lot more comfortable this time and the students all behaved very well. During the lesson, we somehow got into a discussion about different dimensions and planes. The students were all asking very good questions and it was a mathematically rich discussion. It did not really have anything to do with what we were talking about, but it is an interesting topic and most of the students were actively engaged in the discussion, trying to grasp the concepts. That diversion went on for probably about 20 minutes, and I did not get to finish my lesson as a result. To me, it was more important that the students were thinking mathematically and asking lots of questions that it was for us to steam through the topics that we were supposed to cover.

During lunch, I talked with my mentor teacher about the lesson. He told me that he thought it went very well and that he thought I handled things well. At one point, they asked me a question that I didn't know, so I told them that I didn't know. One of the students commented that he really appreciated my ability to admit that; my teacher later told me that he agreed. I was glad that went over well with the students. However, I know that students would not like it if a teacher said that every day, so it's something that I'd have to use sparingly. My teacher reminded me that with the Promethean Board, you can access the internet and said that would be a very useful resource in the future--something I'll have to keep in mind.

We also discussed how to balance between rich mathematical discussions and covering standards that must be met. Obviously this issue is important to me because I love when students ask questions stemming from topics covered in class that shows their curiosity and interest in math beyond what's being covered, but we still have to cover certain material. He asked me if the tangent we discussed addressed any of the standards covered in the lesson I taught and pointed out that if side topics build a stronger foundation of understanding, they are worth it. Otherwise, it will not be as beneficial to the students and they could use that to try to get the teacher sidetracked so that they never really have to do any work (kind of like in Mr. McCourt's classroom in his book). I know that students are smart about trying to get out of work, so I will have to work to see when that is the case. As a teacher, I will try to be open to talk about other topics to the extent that it will be helpful to the students. Otherwise, I need to limit those conversations to ensure that my students will know the material they need to know for End of Course exams and other tests.

Parent Override Forms

This morning, I observed my teacher's Geometry CP class for an hour and a half. I got to school early and was talking to my teacher when one of his Algebra II Honors students came in to get extra help working on problems. He told me that the student's parents filled out an override form to get him into the honors class, but that he really should not be in that class because he is very behind and struggles a lot. It takes him much longer to work on problems, so even though he comes to school 20 minutes early, they are only able to go over one problem. He told me that it will only end up hurting the student in the end, which is really sad to me. The student seems so willing to work hard to catch up, but he is so far behind that he may not be able to be at the ability level of his peers while in this class. For that reason, this topic of conversation was really interesting to me.

Talking to my teacher about that really made me think. I'm sure that at some point in my teaching career I will have a student placed in one of my honors classes because parents signed an override form. As a result, the student will probably be a bit behind the other students and will struggle a little bit more. I will have to make decisions about how that student's understanding affects the pace of the class--especially if all of the students understand things. Like my mentor teacher, I will be willing to help students who come into school early by working on problems and talking about concepts with them, but that required effort on the part of the students. What do I do if the student cannot come to school early or stay late? I would be willing to work with the student during lunch if that was possible. One thing that I have learned in my math methods class is the importance of creating activities that challenge students of all ability levels. I think that will be a key factor in helping that student succeed, but I am not sure how to go about creating activities like that. Thus, I will try to consult many other teachers and look at technology resources for guidance. I really want to help all of my students succeed and plan to do everything I can to help students to learn.

First Time Teaching

On Monday of this week, I taught for the first time in my school. I taught a lesson on parallel and perpendicular lines in my teacher’s Algebra I B class of third year high school students, all of whom are only freshmen or sophomores by credits. I observed the class for three school days prior to teaching so that I would have a really good feel for where they were in terms of the information they had covered. The class lasted for an hour and a half, and I taught the whole time. At first, that seemed a little daunting, but I actually ran out of time and did not get to do everything that I had planned. I found it hard to plan for how long activities would take, so I did not write out the amount of time I wanted to spend on each activity. Next time, I think it would be helpful to at least guess and give myself a range of times so that I can make sure we get to do all of the topics I have planned.

Overall, I think the lesson went fairly well for my first time teaching. However, there were several behavior issues that I had no idea how to handle. I found myself getting a little frustrated with myself while I was teaching because I didn’t know what to do about it. I would say that that was probably the only major problem I encountered while teaching though, which was encouraging. My mentor teacher took notes the entire time I taught, including both good and bad things, and most of the bad things dealt with classroom management. He said I did a very good job about getting students involved and not giving up on them when they were struggling to come up with concepts. I wanted the students to come up with the idea that the slopes of perpendicular lines are opposite reciprocals so that it would be more meaningful to them than if I just told them that. I asked them questions for several minutes and thought that I was going to have to end up telling them the relationship, but they eventually discovered the concept on their own, even using correct terminology—which was very exciting to me. He also told me that I did a good job of praising students for good ideas that they voiced. He had the students write a few sentences about how I did and most of them said that I did a good job, but several students said I was too quiet. That is something that I will try to remember the next time I teach.

Reflecting on teaching, I think I did pretty well for my first time and that I was very comfortable with the content. Also, I tried to include different activities that required the students to come up with examples and solve problems on their own and then show their answers on the board. In general, all of his students love coming up to the board to show their work, even volunteering to do so when my teacher doesn’t ask them to do that. I wanted to be able to keep the students engaged in the same way that he does, and I did so fairly well. I am still a little disappointed about the classroom management aspect of my teaching, but my teacher told me that it is something that comes with time. To improve my ability to deal with situations, I plan on paying closer attention to how my teacher handles issues and to ask him about certain situations that arise about which I have questions. This teaching should be a learning experience, and I look forward to improving as I reflect on the comments made by my teacher and by the students. Teaching on Monday was a little nerve racking, but it made me excited to have teaching as my profession.

Lesson on Classroom Management

On Wednesday I observed my teacher’s Algebra I B class for an hour and a half. I normally observe his Geometry CP class, which has a very different dynamic. This class talked a lot more and seemed to be a bit more disruptive in the sense that at least half of what they were talking about was not completely related. My teacher told me that all of the students in that class are in their third year of high school but are still in that class and that two of them had just gotten out of jail over the summer. His Geometry class stays on topic and is very quiet while working on problems, but this class talked a lot more and had trouble staying on topic. There were even some students walking around the classroom for a little bit (though they weren’t distracting other students). At the end of the class, he and I were discussing the differences in classroom management between normal upper middle class classrooms and minority classrooms. He told me (and I agree) that minority students are a lot more verbal and joke a lot more. As a result, he does not constantly hush his students but often jokes with them and tries to get them back on topic when they digress too much. He told me that the last thing he wants is for one of his students to drop out of school and end up on the streets, so he has to adjust the way he deals with his classes to keep them in school. His students are still eager to learn and frequently volunteer to write their answers on the board.

I told him that I feel nervous about next year because I do not believe that my education at Clemson will thoroughly prepare me to deal with a classroom full of minority students. He told me that he felt the same way and that his first year was very painful, but he has learned to approach things differently with his students. He constantly asks his students during class if they are doing okay. From this I have learned the importance of building relationships with students so that they will feel like you genuinely care and know that you are there to help them, not torture them. My teacher told me that he has learned a lot about dealing with minority students from doing lots of reading about it, so I plan on trying to do the same. I have learned that I will probably not have a cookie cutter classroom in which all of my students behave perfectly, but that you have to meet your students where they are at to help them learn. When I am a teacher, I will keep this in mind and prepare myself by knowing that my classroom of minority students will be a little more rowdy than other classrooms. I have learned that it is very important to evaluate how the strategies you use work with your students and to know that I will probably need to do things differently than my current classmates.