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.

Textbooks: to Use or not to Use

On my last visit to school, I observed a Geometry class and an Algebra I B class and was there for two and a half hours. While there, I was discussing textbooks with my teacher since I was asking him for suggestions for planning my lesson to teach. He told me that he tells his students to take their textbooks home and leave them there; in other words, the students are to use the textbooks as extra resources. In his classroom, he has several different kinds of textbooks for the classes he teaches. He showed me a workbook that came with one of the books and told me that he doesn't use it for any of his classes except for one because that class is very textbook dependent and they begged him to use a textbook.

This issue raises an important question. I think that teachers should not let the textbook dominate their teaching, but what do you do if your students are dependent on them? I really don't think that making them go completely without a textbook in one class when they're used to having one is the best thing to do. I like the idea of having students use textbooks as an extra resource rather than as the main tool of instruction. After studying about vocabulary in class, I think textbooks could be useful to have students look up the technical definitions of words and as sources for some problems. Other than that, I think I might have students only use it more if they want to do so. I had a teacher who required us to read the textbook the night before and take notes on it and used that as our main form of instruction. I definitely don't think that is the most effective way to use textbooks unless you give students some sort of training on how to read textbooks and get the most out of them.

In general, I have learned from all this that my views of how textbooks should be used might be different from the students' views of how they should be used. Thus, I will need to find a happy medium for which I am satisfied and they can best learn. I know for sure though that I will probably use the textbook as a resource, but not as my main tool for planning lessons. I think that there are so many resources available that it would be a shame to only use the textbook.

Effectiveness of Technology Depends on the Teacher

I was at school today for two and a half hours, observing students before school for about 20 minutes, Geometry CP for an hour and 35 minutes, and Algebra I B for 35 minutes. During the Geometry class, the students used laptops to complete a project on Geometer's Sketchpad. There was such a difference between the behavior of my teacher's students and the students I observed using the laptop last week. At the beginning of the class, Mr. Delaney told his students that if he saw them working on anything other than their project, they would not be allowed to use computers for the rest of the year. Since they use computers once a week, that would be a huge loss of privileges. The students were on task and working hard for the entire period. Another thing I noticed is that he has his students put their work into portfolios: both electronic and paper. I thought this was a very good application of what we talked about in class. Mr. Delaney encouraged his students to work at their own pace and told them that he offers extra projects for extra credit at the end of the year. I like that idea a lot because it rewards students for working quickly rather than punishing them in the form of giving them extra work without rewarding them for it.

Observing class today was very encouraging to me because I saw that is is possible to have a classroom full of students working on computers and staying on task the entire time. After I observed the class full of students not doing their work when there were two teachers in there last week, I was very discouraged and wondered if it was possible to have that many students doing what they are supposed to be doing. After observing today, I felt hopeful that I could have students working diligently on their assignment. I learned today that it is important to clearly state your expectations in the beginning so students know what they are supposed to be doing. Also, Mr. Delaney treated his students like adults in the sense that he only once told them to remain on task and then trusted them to do what they were supposed to be doing. I will apply this to my classroom by clearly stating my expectations in the beginning to make it easier for my students to succeed. I want my students to know that I trust them because then they will be more likely to do what they are supposed to do. I also want to have confidence in incorporating technology in my classroom and get my students actively involved.

Productive Classrooms

On Tuesday, my teacher had me observe another teacher because his class had a test. I was at school for two hours, observing the time students were waiting in the cafeteria before school and observing an Algebra I A class with Mr. B that lasted an hour and thirty-five minutes. His class was taking a pretest to assess their prior knowledge of topics in Algebra on individual laptops and then were going through lessons on multiplication, addition, subtraction, and whole numbers on the laptops when they were through with the pretest. There was an inclusion teacher in the classroom named Dr. L who works with Mr. B to allow the special education students to be able to keep up with the rest of the class. So there were two teacher in the classroom for about sixteen students.

First of all, Carolina High School is very strict on not allowing students to be in the hallways during class. As a result, Mr. Delaney (my mentor teacher) absolutely will not allow his students to go to the restroom during class. However, Mr. B had students who just got up from their seats and walked out of the door without even saying anything to him. During the course of the class, three different students did this--some of whom were gone for at least ten minutes. There was also one student who was talking to a student across the classroom and wandering around the classroom for over half of the period, barely getting any work done. There were a couple students who had closed their laptops and were not doing any work at all. Another was playing a pinball game. I tried to encourage individual students to get back on task by telling them that they were doing a good job on their work or telling them that they could do it, but that didn't help. There was one student who came into class late (because of testing) when there were about fifteen minutes left, but neither teacher set up her up to at least some of the work. During the entire class, neither of the teachers asked the students to get back on task more than once or twice. There were probably only a few students out of the entire class that stayed on task the entire period.

I definitely learned a lot from this experience. Mr. Delaney's students are much more focused and well-behaved. He addresses problems when they arise and doesn't let students get away with things, while the other teachers I have observed use the method of trying to simply ignore the problem. From these observations, I have learned the importance of establishing an atmosphere in which students feel like they are expected to be productive and to stay on task when they are given a some independence in their work. I will remember these experiences when I have my own classroom to remember that it is important to not ignore every problem, hoping that it will take care of itself. From the beginning, I will be clear with my students that I expect them to learn in my class and to be on task. I will make sure that it is clear that I will not tolerate students not doing work during class and to explain the importance of everyone participating and taking an active role in their learning.

Latest Visit

I went this past Thursday to observe again, and when I got there my teacher told me that his daughter was having a baby and that he had to leave half way through the class. I talked briefly with my teacher about what they would be covering and then observed an hour and a half of class. For the first half of the class, he went over questions from the homework and covered some new material about polygons and labeling them. He has a promethium board in his classroom that he always uses, and any time he covers new material he leaves blanks that he has the students complete. It is interesting to see that he will ask for someone to go write the answer and usually more than one person gets up from their seat to go write on the board. His students love it and know how to use it very well. I think it is a good thing to have in the classroom and hope to be able to have one or at least to get my students to get up and move (like we talk about in class) and to engage them in this way. Mr. Delaney is very good at this, and his students are usually well behaved and attentive.
Half way through the class, he left and Mr. Mac, whom I observed for homeroom the first day, came in the classroom. Before when I observed him, Mr. Mac never once asked the students to stop talking while hew as talking. He didn't seem to actively engage the students at all. This time, the students were working on a worksheet of word problems that they were allowed to complete together. I walked around the classroom and would answer questions when students asked them. I helped the students break down the problems and look at them piece by piece so that they were easier to understand. I even got to look at some students' work and help them correct it. Mr. Mac walked around and helped some, but he sat in a desk for a while too. There were several students who were talking across the classroom and not doing their work, but he never asked them to stay on task. I would try to ask specific students to help us with a problem, but that didn't really work. I felt frustrated because I don't really have any authority, so I couldn't really say anything to the class about their behavior. Finally, when there were two minutes left in class, Mr. Mac told the students that their teacher doesn't like the noise level to be very high and that they were exceed it. That's all he said to them. I can surely say that I am learning of teaching and classroom management methods that are not the most effective. So, it actually is helpful to observe other teachers and take note of what does and doesn't work.

First and Second Visits to School

Last Monday, I went to Carolina High School in Greenville County to start my Field Placement. I am with Mr. Mike Delaney, who teaches Algebra I B, Geometry CP, and Algebra II Honors and was the Greenville County Teacher of the Year last year. I started the day by standing in the hall with Mr. Delaney for about 20 minutes, where he was on duty and supposed to help with crowd control. He talked to me some about the school and told me that all three of his classes have 15 or fewer students in them. That day was the students’ first day of school, so we first went to the auditorium with the freshmen, where the principal, ninth grade administrator, and various other school officials spoke to them about the importance of staying on track and doing what they need to do to graduate in four years. After that, the students split into homeroom—which they only have for the first two days of school—to learn about some of the school’s rules and policies. Since Mr. Delaney is the head of the Math Department, he does not have a homeroom. I wanted to see what it was like though, so I observed Mr. M, who teaches Honors Pre-Calculus and AP Calculus.

In homeroom, Mr. M explained the forms that the students were given and covered some of the rules in the school’s handbook. I noticed some things about the way he spoke to the class that stuck out to me as things that I do not want to do. At one point, he was describing a woman as being very short and over 200 pounds, which I thought was a bit unprofessional and rude. Some of the students even made comments to each other in disbelief that he had described her this way. Nearly the entire time he was talking, students were talking to each other or had their heads down on their desks sleeping, but he never said anything to them about it at all. At the end, he finished twelve minutes early and spent the remainder of the time sitting in a desk without talking to students at all. He made it clear that he only teaches seniors, so he would not be having any of those freshmen in his classes.

Next, I went to Mr. Delaney’s Geometry CP class. It wasn’t as long as a normal class period because they had gone to homeroom, so he just spent the class going over the syllabus and explaining his expectations of the students. He even had them practice leaving the classroom and coming in and getting their calculators. He told me that he is a stickler for the rules and heavily enforces them. He also made that clear to his students and told them that he will try to earn their respect and they should try to earn his as well. After class was lunch, which I spent in the teacher’s lounge talking to two teachers about why they decided to teach and how they ended up in Greenville. It was interesting to hear their stories and ideas about teaching, especially since one of them had just graduated from college and is teaching for the first year.

The last class I went to was Algebra II Honors. Because Mr. Delaney is a football coach and a basketball coach, he knew lots of students from those activities and from previous classes. He knew most of the students by name in this class and many of them were excited to have him. He again discussed the syllabus, his rules and expectations, and had his students practicing entering and leaving the classroom. About halfway through the class, the bell for the second lunch rang, but he thought it was the end of class and dismissed his students. After a couple of minutes, he realized that they weren’t supposed to have left yet. I was very surprised that eight out of the ten students in that class came back. When they came back, the class started reviewing some things and discussed an assignment that would be due the next day.

I would say that my experience overall the first day was pretty good. It was interesting to see the special relationship that Mr. Delaney had with his students and to see his genuine interest in their wellbeing and learning. He must have known about half of the students who walked past him in the hallways, and greeted and shook hands with several of his students. However, he barely talked to me at all that day and did not even introduce me to his classes except when half of his second class had come back after being dismissed early. That really bothered me, but I didn’t know what to say. I sort of felt invisible. When I got home, I e-mailed him and apologized for being so quiet and told him that I would really like to be involved as he would like me to be. I did not want to just sit there the whole time like I had that day.

This Monday, I went back for my second visit. I was able to observe fifteen minutes of his Algebra I B class and the entire Geometry CP class. He talked to me a little bit more in between classes and let me look at one of his lesson plans. During Geometry, he gave them a worksheet on graphing that the students completed with graphing calculators in pairs. I asked him if I could walk around and help and he told me to do so. I got to talk to the students more and work with nearly every pair—there were only eight students in the class. I worked with one of the students one-on-one for a few minutes and was able to help her understand a problem through inductive reasoning. I really enjoyed my time yesterday and was excited that Mr. Delaney asked me to constantly be involved with the students, whether it be helping them with questions or making sure they are taking good notes when he is lecturing. I am very optimistic about how this Field Placement is going to help me as a teacher.