Diane+and+Ralph

Sept 7th 2010,

About 2 weeks have passed since school began. I feel like I have been in a whirlwind not really knowing what to expect next in our classroom. There have been some changes in the schedules since last year and I think that the teachers and students are still trying to adjust to these longer block schedules. I am observing an Algebra 2 class, a statistics class and a pre-algebra class. This schedule is odd because we see the Algebra 2 students 4 times a weeks for and hour and a half, the statistics class 3 times a week for about forty five minutes, and the pre-algebra students (who are 6th graders) twice a week for about 45 minutes. The first day of school I only got to see the Algebra 2 students and we tried to get some paperwork done but we also wanted to get some sort of assessment done so that we could determine if all of the students in the class should actually be in this class as opposed to geometry. We did a name game where each person was to "form a rectangular prism with 3 faces" out of a note card and write their names on one side, write an adjective that describes themselves on another and then we all introduced ourselves to the class and described ourselves with our adjective. At the end Diane was able to name everyone in the class (she knew most of them before). We then wrote something down on the third face that we didn't think Miss Crimm knew about us and turned them in. We then passed out a problem called the yellow brick road problem which asks how many bricks will need to be used to make a road that is "n" feet long. It was a fun problem for the kids to work on but the worksheet that the problem was printed on had a misleading representation. It had pictures of sets of 3 blocks arranged in different ways. This led the students to try to work in groups of three which made the problem much more difficult than it needed to be. However, the discussion that the worksheet was amazing. The students would work by themselves and then share their findings with their group or with the class. Students would be able to recognize errors that were made in their own work and the class made progress without the teacher guiding them more than asking a student to share what they had found. At the end of class, no one was told the answer. I asked Diane about how I should be helping the students. I noticed several students making incorrect assumptions but I did not know how to react because I didn't want to ruin the problem for them. I decided to ask the student what they had done hoping they would recognize what they had done wrong but it didn't work. Diane explained that she never told anyone the answers to large class problems. She indicated that it is more important that the students learn how to think about how to solve these problems than it is to get the right answer. I have not yet seen how she corrects assignments and tests because there haven't been any but I am curious how important answers will be.

In my Algebra class, there is a wide range of students. I have 7th through 10th graders. I questioned Diane on how she pushes students with more ability than others. She said that the year before she had a student who was very gifted in math. He went to the mathlete nationals in Disney world. She often had him teach lessons to the rest of the class or she would pair him up with other students so that he could learn how to explain his thinking and social skills while working with math. She also makes a effort to give students "jobs" to help with keeping attention from students who are easily distracted. She will ask them to come and graph the function the class is working on or to pass out papers or pretty much anything to help them get out of their seat and move around during class. Also if a student is able to solve a problem before the rest of the class she might have the student present his method but not the answer. That way the students will have to do the work themselves and find the answer. I thought another beneficial practice was that she requires the students to clear off their workspaces before beginning a new project. The can have their "tool boxes" (a composition book for their notes) and a pencil and that is all. Diane also is constantly using math and scientific terms in her class. To get the attention of the class she tells them she is gathering data to determine if a seating class is necessary. Also on the first day she used the prism activity (previously mentioned).

Sept 16.

About a year ago, I had the opportunity to be a supplemental instructor at the University for the Math 1010 class, or intermediate algebra. As we went through the course, we came to functions and function notation. I don't remember how I was taught what a function is but we taught it using the idea of a function machine. The teacher would give a list of outputs and would ask what all of the inputs would have in common. An example was when he listed several First Ladies and asked what the inputs would be. This method was meant to help the students understand that there was a relationship between what could go in and what could come out. For example, if someone other than a president was put into the machine, there would not be an outcome. In Diane's class, we actually used a machine, well a calculator anyway, to put inputs into the machine and then to get the corresponding outcomes without seeing the actual function. The students would then list in their toolboxes the values and then plot the points on a graph. The students took turns guessing what they thought the outcome would be for a given input. While some of the students lost interest in the activity after 3or four functions, the majority of the class was having fun guessing what the function would be. I thought that was a great was to incorporate technology into the lesson.

Another method that I thought was excellent was when Diane was teaching the students how to factor quadratics. Some of the students had heard of the "FOIL" method which is not a method at all. Also it drives me nuts when students say, "FOIL it." Fortunately as I found out, Diane also dislikes the term "FOIL." One of the students brought up the box method which I had not heard of either. Diane taught the class a method where you draw a box and create 4 squares inside of the box. Then you place the values of the terms from your quadratic inside the boxes and use the idea of area to figure out what the values should be. A bad description I know but it makes sense if you can see it. It made me frustrated because I had wasted so much time trying to teach students how to factor quadratics while they did not understand what was happening. This method seemed more intuitive than any other method I have seen.

While I understand that there is limited time to teach all of the material in the core, I found one of the discussions in class that did not pertain to the core especially rewarding. After Diane collected an assignment, she led a discussion with the class on how important it is to have neat work and how important it is to be able to have someone else be able to understand each step of your work. Diane had the students re-work different problems and then present them to the class with complements on different aspects of neatness and clarity.

In regards to grading, I questioned Diane as to her grading. While most of the grade is from passports, some is from homework and from quizzes. Passports are basically check points to make sure that the students understand and can perform specific tasks. If the students do not get all of the correct answers, the students will be required to either retake the test, meet with the teacher, create a coversheet that describes why the students made the mistakes they did or all of the above. I thought that it was a great way to ensure that the students truly understand what they are trying to accomplish. The Students can retake the passports as many times as they want.

I also had the opportunity to observe Emina teach a class. It was an interesting experience. The motivation of the students was vastly different from the students at SLCSE. While I thought that the activity the students were presented with was engaging, the students seemed to lack enthusiasm. I was interested in watching the interaction between the students and the teacher. I was surprised to find how much Emina seemed to know about what was happening in each of the students lives. She would meet them at the door and would have something to say to nearly all of them. It was interesting to see her try to restate what the students were saying. Often, she would say the same thing thing the student did but the student would not agree. The students did not seem to understand what they were doing. It was also interesting to see her classroom management. She and her co-teacher would roam the room to see if the students needed help but it seemed like the same students were struggling every time a new task was given. I thought that it might be useful to decrease the time allotted to the students between each new task because there were many who would finish early and then distract others. I wonder if with less time, the students would be more focused. I was also surprised by how much talking was happening while Emina was trying to give the final instructions for the class. Her co-teacher made a comment to reprimand the class which will probably make a difference in the attitudes of the class in the future. I did like how Emina asked for the students input when answers were given. I thought that it was beneficial for the students to see their own work in front of the class and to defend what they had done to solve a problem. Also, when there was a glaring mistake, I saw how frustrating it is to find that the students are lacking in understanding. One of the students made a mistake dealing with different fraction values and either the class did not understand why it was wrong or was too lazy to explain their understanding. I think that they were not clear on fractions and for an Algebra teacher, having to explain fractions again seems silly.

Sept. 26

I don't remember how I learned to add integers when I was in 6th grade. I remember doing an assignment the night before valentine's day with my friends as we worked on a four headed dragon box, but I don't remember how my teacher taught it to me. I think that if he had dressed up as Sally the Sorceress I would have remembered it much better. Although I will not be teaching an algebra class this year, I wanted to see how Diane teaches her Algebra class. During the planning period with Vivian, DIane, Marcie and myself, we discussed how crucial it is for students to have a firm grasp on how to add and subtract integers. While most of the students had been taught this topic, our mentors believe that it is such a crucial topic that they only trust themselves to do it correctly. So they essentially reteach everyone. After seeing how they do it, I don't blame them. We discussed the importance of an "Anchor activity." An activity that the students can refer back to later in the unit and recognize that the work they are currently doing is familiar because they have done it before. So I guess to be effective it should be something that is memorable. For this lesson Diane and Vivian combined their classes, which totaled about 60 students. They had them group up into tables of 4 or 5 and gave them all a calculator that can submit answers to a hub which can show a tally on the smart board, very cool. Interestingly enough, the addition of students did not change the way the lesson progressed. The students were attentive, they were on task, they wanted to participate and by the answers submitted, they seemed to have grasped the concept fairly well.

The memorable part of the lesson is when Diane dresses up as Sally the Sorceress which includes a black hat, cape and bag with purple trim. She clearly describes why she is not a witch and that she is just magical. She tells the students that she makes "brews" using her cauldron but does not use fire because of the bad relationships between fire and magical women in the past. Instead she uses hot and cold cubes to heat her brews up or cool them down. While this does not seem like a particularly complex idea, I think it is fantastic. The students are easily able to understand how the temperature of the brew changes based on how many hot of cold cubes you "take out" or "put in," I liked how the wording is specific.

In Diane's class, she uses the thinking of Mark Wahl who wrote a book called math for humans. She has large posters on the windows which have pictures and common words that are used in place of words like add, multiply, divide, and subtract. She uses hand gestures, specific terminology and sticks to them throughout lessons so that the students can understand what they are doing when they perform different operations. I would like to read the book but as of yet I have been unable to.

Back to Sally, I am interested to see how multiplication is explained.

I had my first opportunity to grade this semester. We tested the students on their introductory knowledge of functions and function notation. As we went through the papers, I thought it was interesting to see that because we are looking for mastery, if there was a mistake at all, the problem was 100% wrong. Also because the students are expected to either retake the test, create a cover sheet for the problems that they missed, or have a seminar with the teacher, or a combination of the three, it was okay. The students were not overly disappointed if they did poorly because they understood what they did wrong and they knew that they had the opportunity to correct their mistakes. The students were not embarrassed to ask us if they missed problems because almost everyone did. I enjoyed this atmosphere of safety. I like how it is okay not to have all of the answers as long as you are working on figuring some of them out.

October 11th

So, when do you deviate from your book? I understand that no math textbook will be able to cover all of the material that you are hoping to teach in a year. Diane has found a book that is very comprehensive. In each chapter, there is a spiraling review which ensures that each student has the necessary ground work laid for that section. The problem that Diane and I have run into is that there is a large amount of review material that the students have not seen before. The book that we use is a constructivist style where the students are expected to discover the material for the lesson through guided work. The problem then is deciding when to intervene with the books course and to go in a direction of your choosing. To me it seems that with traditional texts, where there are lists and lists of problems for the students to work through, it is easier to alter the plan set out by the book. I know that this is not a particularly interesting thing to think about, but I have been trying to identify the proper course to follow with our current book which does not allow much room to reinforce other topics not covered in the section of interest.

I also enjoyed the opportunity to observe and participate in the schools parent teacher conference. This being the first time I have been a participant, I had no idea what to expect. It was interesting to see how the different parents interact with their students when there is another adult present. I thought that it was a little disturbing to see how the parents did not believe in their students. The parents would look to the students with an accusing eye and ask the students why they had not performed the way the parents had expected them to. While I think that it is good for the students to have responsibility for their actions, these parents were acting as though the students had actively engaged in a plot to mislead them. Other parents were very positive and were looking for ways to help their students learn the material or to help the teacher with ideas on how to more effectively communicate with their students.

October 24th

This week we focused a lot on lesson planning. As a math department, we sat down and talked about an effective way to plan lessons and to manage time during the period. Because this is the first year the school is on a block schedule with 90 minute periods and so the teachers have had to adjust their lesson plan schedule. Diane mentioned that she had practiced and taught her lessons so thoroughly that she knew the timing of when to move to new topic, when to use a certain question or when to segue to a new topic. The transition has thrown her and the other math teacher off of their game. We discussed how important it is to have a lesson plan that is conducive to your style of teaching. We created a plan that had a spot for the title, objective, materials needed and a spot for notes to self for reflection. We decided to break the day up into 5 segments. The first is the ATB where we will either introduce a new concept or review the previous days content. The next section is for a review of the homework that was assigned the night before. Ideally there will only be a couple of problems that require discussion. Each section will only require 10 to 15 minutes each. If more time is required, then it will be given. We will then move to the meat of the lesson. We decided to cut the lesson into two 20 minute sections so that the students will not be sitting and working on one thing for too long. It is expected that the students will be actively engaged in some sort of exploration or discovery type of process during this time of the lesson. At the end of this section, we will ask the students a question or questions that reflect the scope of what was taught during the section. This does not mean that it will be the only question, but it will determine if the class is actually ready to move to a different activity or if further instruction is necessary. If the class is ready, we will move to a skills practice part of the lesson. This does not mean drill and kill through a set of problems but rather have the students use what they learned from their discovery to accomplish a task or set of tasks. This section will end again with a question that will sum up the lesson to that point to assess the ability of the students. As we will need to come up with effective methods to assess knowledge, we are working on a sheet of different types of questions so that we will be able to easily come up with meaningful questions. Each of these parts of the lesson will last for about 20 minutes. For the last 10 minutes of class, the teacher will give the homework, and discuss the calendar the school uses. because the math department gets more time with the students than anyone else, they are responsible for making sure the students are kept up to date on their homework for other classes and on events that are occurring in the school. We thought it would be important of the students to have someone helping them remember what was due and when. I am excited to see how the plan works for us.

October 31st

This week I had the opportunity to teach an entire class period for the first time. Diane had created a unit which she called hands on equations. We have decided that it will be my responsibility to teach this unit. It teaches the students how to think about solving for variables. It gives them a picture and and algorithm for them to think of when they are done with the unit. It also reinforces the idea to check your answers to make sure that they have the right answer. I had read over the lesson and had tried to think of some additions but I thought that the lesson was good standing alone. So I decided to go with it. Diane created a program template for the SMART board with a picture of a tetter-totter type scale with boxes with numbers 1-10 on them, which I could move to either side of the scale and then ask the students to balance it for me. I introduced a blank triangle which did not have a know weight and I asked the students what the triangle weighed with different weights on each side. One of the students brought up the word variable and we were able to have an intelligent conversation with a vocabulary lesson built in, which we recorded in our tool box. The next step was to introduce a more difficult problem and have the students guess and check using a t-chart. We worked through a couple problems as a class and then I handed out their home work, a worksheet with the same graphic and style of problems. They were to guess and check on the problems and then show their guesses on a t-chart. I realized a few things afterward. First of all, I should have gone over the homework to have the students work through an example with me so they could see what I wanted them to do on their paper. Also I should have had the students show their guess work better. I was pleased with the vocabulary lesson that had taken place which was unplanned and I think that the students will have a clearer picture of what it is in the future. Diane and I had a similar experience with vocabulary when we discussed the difference between a factor and a term. The conversation gave the students some background and terminology to use when we discussed simplifying rational expressions. We have decided to try to use vocabulary lessons like this in our classes so that the students can use correct terminology with context so that they know what they are trying to say.

I also had the opportunity to attend a stomp at the school, it was the halloween school party. This school is interesting because the school has students from 6th to 10th grade. The patterns of behavior were on opposite sides of the spectrum. The 6th grade boys were running around and the older girls were trying in vain mostly to get their boyfriends to dance with them. It was hilarious.

November 17th

How important is it to be prepared for the beginning of class? How important is it to have all of the details at the beginning of class covered and planned out? Very important. Yesterday I was planning on teaching my class a kind of comprehensive review of a unit we had been teaching our pre-algebra class. I got to a late start and got to school with only 5 minutes to spare before class was scheduled to start. I thought that I had my lesson planned out well enough to have an effective lesson even though I was late. Unfortunately, I had not finished writing up a neat form of my new seating chart. I decided that I would just send the students to their new seats and that would suffice today. Unfortunately I underestimated how fixated this class is on their folders in which they keep their assignments which they had completed. The class was hampered by their lack of paper to do their ATB on. How I forgot about this part of our seating chart gets me. I was forced to waste class time passing out their work from their folders while the kids worked on the ATB in their minds so they could write it down when they got their paper. Stupid! I don't want to go through that again. I should have had the students sit in their original seats and then take all of their work out and move to their new table. Then we had a review of their assignment. The previous day, I had to go through each problem on the homework to make sure that the student were showing their work in a way that others can read and follow. I thought that the same thing would need to happen today. I was wrong. I went through two of the problems and realized that I had lost the class. Instead of stopping there and reviewing the problems a different way, I just tried to finish faster instead of doing something else. Stupid! I should have altered my plan twice and did not. I need to plan better and think on my feet better. It was a good lesson and a hard one to swallow. We lost half of a day because I did not plan appropriately. I know that sometimes things happen in class or from an outside source and I can't help that, but I need to control better what I can control.

More to come.