Wendy+and+Rosalie

__**Week 1 (Aug 23-26)**__ was spent preparing for students, decorating the room, making sure there were enough desks, getting a computer, faculty meeting for policy and procedures, math department meeting, and a numeracy committee meeting. Wendy suggested as a new teacher I start collecting posters from conventions of things I like to hang on the wall. I have not even thought of this as I have never had to decorate a class before. We talked about Wendy's classroom management style. She likes to have students work in a team and so has the desks arranged in groups of 4, called islands. Each group is given a tribal name. The first day of school was a pep talk given by Wendy. She spent a lot of time creating the need for the math class. She had them reflect and write down what their dream is and she helped them see how passing this class was essential to graduation and thus would help them get paid more money. The statistics she shared was that on average students with a high school diploma make $6 more than someone without one. $6 bucks, big deal? But she helped students see that in an 8 hour day you would make $48 more...in a 40 hour work week you would make $240 more...and in a period of a month that would be $960 more...and if you went on to getting your college degree what that would look like and if you got your masters, etc...I thought that this was highly effective approach to creating the need for students to 1. come to class and 2. do their homework. It was an eye opener for the students. Wendy would tell the students that it was not about the math, it was about learning abilities like figuring things out and working together to help each other be successful.

Wendy does not like disclosures and so she did not read it or go over it word for word. She basically told students that there were two class rules. 1. We respect each other! and 2. We work as a team! I think that Wendy did a fabulous job of creating an environment with a positive attitude in her classroom toward students selves and in a subject that most feel they are automatically going to do bad because they feel they are bad at math. She had students write down that they were NOT bad at math. They had only had bad experiences with and had instilled in them that they could trust in her to teach them the math and that they would have good experiences with it. Students that had at the beginning of class shared they hated math and were bad it were by the end of class raising their hands to say they felt they could be successful in this class.

I observed that as Wendy spoke a student that was talking while she was so Wendy stood next to the desk and looked right at the student to get their attention. Also, another student would make comments aloud as Wendy spoke and she would ask the student "Are you on board with me?" and he responded, "Heck yes!" and she would give him a five. Another student that was had a lot of energy, she had him be the class leader to help manage his energy into a positive thing. When Wendy had the class do a "I am...I am looking for..." (find your partner) activity she had this student lead the group in figuring out what they had to do. Which was very effective.

I asked Wendy why she allowed students to use their ipods in class as long as she was not speaking and she said that she did this because she picks her battles and did not believe this battle was worth it. And she wants students to be on board with her. She also does not go over disclosures on the first day because she believes that students already know the rules. She did go over the routine of the class.

I for the most part, was just introduced as a co-teacher and observed Wendy, the class, and helped out when students were working on the "group race review" activity and spoke with students that turned into wall flowers (were disengaged), and helped students out in the "I am...I am looking for..." (find your partner) activities. We observed that we have our work cut out for us when some students were asking me how to divide 32/4 and how to identify the slope or y-intercept in the slope intercept form. I did not know that students had to move on to the next math class or else they would not graduate. Students need Algebra 1B, Geometry, and Algebra 2 to graduate. If they fail, they are still moved onto the next class. Wendy also used this fact to help motivate the students to make their lives easier to do their homework and work hard to learn the material.

This week was getting the students use to the routine which consists of a starter (or ATB) during which time Mrs. Solomon will go around signing students' cover sheet. This is where students points for doing hw (taking notes and starter points) are recorded. I noticed in the first starter I graded that the students were not putting equal signs after simplifying each expression. So I wrote the equal signs in for them. I was almost tempted to address the issue in class while students were working on their in class problems, but then I consulted with Mrs. Solomon before I did so and she told me that this was not a big deal for her. I found out that she feels this way because when students put the equal sign they get confused and thinks this means they need to solve for x. So she does not have them use equal signs in simplifying expressions they just have to box their answer to avoid getting confused with solving for x....After taking classes from Emina, Marilyn, and Kelly, I have to see the equal sign there for simplifying expressions and in solving for x. It is just simply an incomplete sentence for me if it is not there.
 * __Week 2 (Aug 30-Sep 3)__**

In Mrs. Solomon's direct instruction on radicals I thought I would share with you how she taught to simplify squares roots. She likens taking the square root to pairs braking out of jail. And to simplify square roots in the numerator and denominator with constants out front she will say, "insides go with insides and outsides with outsides." I think that this helps students to conceptualize the rules.

Also, Mrs. Solomon made up a song, on the rules for adding and subtracting integers. "When adding integers do this and you'll be fine: Same sign, add them up and always keep the sign. Different signs different rules: Now you must subtract, keep the sign of the larger one and then you'll have the fact."

One thing I have noticed at WJHS is th at the math department here works as a team. They are all on the same floor and each lunch together. They collaborate with each other and are willing to share their material. Mrs. Solomon suggested when I start interviewing for jobs to ask how collaborative is the math department (as this helps to lighten the load).

This week I observed how Mrs. Solomon dealt with the overwhelming task of students not knowing how to add and subtract integers, fractions, multiplying, dividing. She said if students do not know how to do these basic skills by now then there must be something not clicking mentally. So she has decided to allow students to use calculators in class and for tests. She likens it to somebody who has bad eye sight is given glasses to fix the problem. Her thinking is that if students can not perform these basic skills that they have seen from as early as 6th grade and on, then Mrs. Solomon says they need a calculator. I wonder that even though students are expected to know these basic skills maybe they just have forgotten and need to be continually reminded, retaught, refined in hopes that the knowledge will be brought to the forefront of their minds. I am not sure that giving them a calculator especially if they do not know how to perform the task already by themselves is doing a service to them.
 * __Week 3 (Sept 8-10)__**

I was able to get up in front of class to work out the problems from the ATB and read out the answers for last times homework assignment in Alg 2, answer any questions, and work out the problems for them. I tried to probe students with questions that would help them think about why we work out a problem in a certain way. I felt that I took too much time working out the problems. Mrs. Solomon is very good at managing her time in the classroom. Although there was one exception with Wednesday's school schedule having a mentor period cuts our 1st period time short and Mrs. Solomon was unable to get through all the material. Mrs. Solomon gave me some feedback after, she said that I need to work on wait time. Allowing students time to think. I thought I was, but I will start to count to 5 to ensure I am practicing wait time.

I also observed how Mrs. Solomon handled one of our high energy students in Geometry. He was being disruptive while Mrs. Solomon was giving direct instruction and she just asked the student to quit it, because she did not have the energy to deal with it that day. She still had to talk to him a couple more times to put him in his place. But eventually he quieted down and did his work.

I found out this week that one of our students in Alg 2 is legally blind so to see he has to put his notes or paper close to his face to read it. She said he has a buddy of his that sits beside him (that was arranged like this on purpose) who helps him.

I observed that in collecting the cover sheets students had done their homework in their notebooks so students asked if they should tear it out of their notebooks. Mrs. Solomon decided not to have students tear homework out of their notebooks so that their notes can remain in one spot. Mrs. Solomon lets students correct their own homework. Students have the responsibility to do it, score it, and come and get help if they need it. The school has incorporated time into teachers contracted time so that they are available in the mornings to help students. I have observed in the time that I have been there only less than a handful of students come in asking for help on their homework assignments. I realize that students might not all be able to come at 7 am to get help. But I think that students have to be continually reminded, invited, and encouraged to come to this reserved time that is for them and that it is their responsibility to seek the help if they need it. I have noticed that we have a couple of student athletes in our classroom that play football. One of them is not doing well in class and he has not come in for help either. I wonder if every day students need a peep talk. Like in coaching a team, the coach tries to inspire students to be better.

I observed in trying to get the group race review all together and running (we still had to write the tribe names on them and each persons name in the tribe on their packets) to keep things organized I think what was lost in the moment of commotion was making sure clear instructions on the purpose of the race review and why the students needed to make sure they knew the material and were prepared for next's class period. Some students did not finish the group race review and did not make sure that they picked up the rest of the problems to complete at home. It was not evident until next class period that students did not understand what the sheet was for. Most did not complete it. I do not think that students understood that the group race review was given to prepare them for the test. It was to students advantage to complete the group race review because it is similar to the test.

I observed that with a particular student that joined class later Mrs. Solomon was very understanding with him with her tone of voice and willingness to work with him. Also, on his first day, I thought I would catch him up to speed on what that routine was and Mrs. Solomon did not want to overwhelm him for his first day so she made a comment about not worrying about it, which I felt helped the student by taking off the weight of what was going on in the class. He seemed to appreciate that so he could ease into the class. I also observed how this particular students acted on the day of the exam. He was making faces like he was uncomfortable and kept grabbing his throat. I asked him if he was okay and he said that he was not feeling well. He seemed to be exaggerating it to me. I think this is how he was reacting to taking the test. I wondered if he was as prepared as he could be.

During Alg 2 there were two different tests issued so students could stay in their tribes seating (groups of 4, 2 tables side by side in front and in back). When I was grading test I came to find out that a student had copied their neighbors test because they had the answers to the other test...I told Mrs. Solomon and she had me stop grading it and gave the student a zero score and commented on it, "cheating". I also noticed while grading that students would do get the rules reversed for solving radicals or would perform the wrong operation. I wondered why students were not getting the help they needed if they did not know how to do the math. I told Mrs. Solomon my feelings and she said that they needed to have a "Jesus meeting" where the students are called to repentance. After seeing students scores we discussed the decisions teachers have to make to reteach the material or move forward? She seemed to think that reteaching was needed but that she had to move forward. She said that she was going to talk to her department and see what they thought.

Also, I observed that the department created another Alg 1B class to lighten the load of two other classes that were crowded. Also to help these students get the attention they need. I thought that this was a great move. When the day came for this class to meet for the first time our neighbor teacher only had 2 students in class. The scheduling department made some errors with placing students in the wrong period. It was good for me to see how our neighbor teacher handled this.

My thoughts are focused on working on communication and clearing up ambiguity in my speech. I found that communication can be tricky because of ambiguity. Also working on giving clear instructions to students and making sure to stress the need to do their part and seeking the help that they need.

This week I was able to observe Mrs. Solomon address the issue of cheating on the first test (that we did not discover until grading) in 1st period (Alg 2). She addressed the issue to the whole class and let the whole class know someone had cheated but did not reveal who it was. She said, "they know who they are." She let the whole class know how stupid this was to cheat because she distributed 2 different tests, so if you copied off your neighbor, you would have all the answers to the wrong test..."duh!" I noticed that whole class laughed and thought this was funny, except for the one student, he had his head down. But initially he had his head up staring off no where in particular contemplating the consequences of his actions (I thought) as Mrs. Solomon explained from the disclosure what would happen. His parents would get notified and receive a score of zero. I followed up with Mrs. Solomon to see if she had notified his parents and she said that she still needed to do that. I asked her if she was going to talk to the student individually about cheating. So I asked her if she was going to talk to him to see if he realizes the consequences of his choices. She said she could tell him that, “by cheating you are choosing to fail.” This is true, but I was wondering he something could be said to him that would strike a chord in him as to the severity of this bad habit. It is basically dishonest and if when he gets into the work force and goes about doing dishonest things, the consequences of his actions can affect innocent people, the company, etc...
 * __Week 4__ __(Sept 14-16)__**

She also addressed the issue of not having a strong math foundation. She did a good job of shifting the responsibility to the students and also explaining her responsibilities as the teacher. She explained the problem of having the majority of students fail posses to her as the teacher and how she needs to inspect what part of their roots have holes. She explained how students who have holes in their math knowledge need to come and get help because she does not have time to cover the old material because she is bound by the core/new material to move forward. She also addressed that if they thought the material was hard, that it was only going to get harder and that they needed to take share in the responsibility and get the help that they need if they did not understand. In geometry, Mrs. Solomon discussed with her students the need to come in and get help before or after school. I liked how she told the students that their school has built into their bell schedule a late start for students to come in early and get help on their homework or they come after school and get help because teachers are contracted to stay after school as well.

I tried this week in class not to answer students questions if I felt that they could contemplate the material more and wean them off depending on the teacher but to think for themselves. Amid grading and trying to get students to fill out their cover sheet correctly, and trying to answer students questions, I failed to return to make sure these students were able to work through the problems, ultimately owning it. So I will work on being better about that next week. I also learned from my own experience that grading papers can be a head ache. Mrs. Solomon has it organized that students grade their own work. She will read the answers off in class the following time and students grade themselves and record the score on their cover sheet. This way it reduces all the grading that has to be done.

I am also working on a lesson plan for next week about transformation of absolute value. I will let you know how it goes.

This week I had planned to teach absolute value transformations in 1st period- Alg 2. This was the first time they were going to see it. I ran into some road blocks because I need to present my lessons plan in advance to Mrs. Solomon. I was trying to prepare a graphic organizer (GO) for the students to fill in the different transformations but they did not end up using it like I would of hoped. Mrs. Solomon was trying to get software or calculators that worked for the students to use. We ended up using the calculators on the over head projector but I did not get to it. Mrs. Solomon helped me print off my updated version of the GO and also print them onto transparencies. I had not presented my lesson plan in advance to Mrs. Solomon so it was just before class started was when I getting input from Mrs. Solomon. She gave me suggestions on how she would present the material vs what the textbook said. I thought that it was important for the students to see "y=" written as "f(x)=" and the transformed function as "g(x)=" since that is how they would be seeing it in their text book.
 * __Week 5 (Sept 20-24): __**

Mrs. Solomon told a student to stop being disruptive and threatened to have him leave class but did not actually have him leave. He was quite but still not paying attention. I got up while Mrs. Solomon was lecturing and had to go by his side and tell him to put away his camera he was using as binoculars.

One of the algebra 2 students came in this morning and was seeking help. She was getting stuck on solving for y...and on adding and subtracting integers. Mrs. Solomon encouraged her to use her calculator to do the arithmetic. Mrs. Solomon gave the student a similar problem to work out again and she stepped out of the room. I could tell as this student tried to work out the problem she was getting stuck because she did not have the fundamentals down. I could tell she wanted to solve it and I asked her if she wanted to know the rules for adding and subtracting integer. She said she did because she did not want to depend on the calculator. This made me happy. So I wrote out the rules for her with examples and told her to study it and that I would follow up with her on learning the rules.

Some of the feed back I got from Mrs. Solomon about teaching absolute value transformations was how to present the absolute value function and not to spend so much time on the review. Also, this particular day we were on the assembly bell schedule so we had less time to present the material. I did not remember this while I was teaching and I did run out of time. I could of written out the f(x) column for the table for finding the coordinates of the function. Mrs. Solomon said that she liked how I handled the situation when a student that was not quite following what I was doing asked how I came up with a particular coordinate from the x/y table...and another student made a remark that I did not have to write it out...and I said there was nothing wrong with writing it out. We were here to learn so it was okay.

We had a test in Geometry. I graded the B version of the test. I was surprised to see how students would get problems wrong that Mrs. Solomon worked so hard to stress so that they would not get wrong. I think that even though if the teacher stresses points it can be hard for students to digest information if they did not put the time in to digest it and make it become a part of them.

__**Week 6 (Sept 28-30): **__ This week, in preparation for a term project, Mrs. Solomon showed a video on Fractals called, Hunting the Hidden Dimension (http://www.pbs.org/wgbh/nova/physics/hunting-hidden-dimension.html) in Geometry. I thought it was a powerful tool to help students see geometry in the world around them.

They will have a project on how to generate a fractal. This will help them zoom in and see the same process over and over again. The process is reduce (or shrunk), replicate, and rebuild the pattern.

Alg 2 had a test today and I liked how Mrs. Solomon told her students that it is not acceptable to do your homework after the test because it would be the same as the football coach saying, today we will have the test and tomorrow we will practice. Doing your homework is the way we practice for the test. We have a handful of football players in class and others who play different sports so I think this helps to drive home her point on how important homework is. Also, in the early morning a football player came in for help before the test and Mrs. Solomon told him that by giving him these problems he was working out was her conditioning his mind mentally like he does in football conditioning himself physically.

I talked with Mrs. Solomon about the Alg 2 student who is still working on her algebra one skills and she said that she has been coming after school to get extra help and Mrs. Solomon has assigned her work sheets to help her work on the fundamentals. Mrs. Solomon had devised a plan that if she would turn these work sheets in she would allow those points to be applied to a test.

Mrs. Solomon and I spoke about her EL’s students and how I thought we could ask the students who spoke another language other than English in the home. She said we could look that up on the skyward login. So we did and found that at there were 4 students that had Spanish listed as their language. I told Mrs. Solomon this is why I like GO’s to help students that are EL’s acquire the English language. Also, by doing activities that will help them use the 4 language modalities will help them to acquire the language as well. Which are reading, writing, listening, and speaking.

I am also working on a lesson plan to present next week in Geometry class on polygons and perimeter. I went over with Mrs. Solomon on how she would present it and made copies of work sheets the book had prepared. I chose two work sheets. One that focuses on the skills and the other that focuses on EL’s. It focuses on speaking, and writing in this work sheet. I am also going to try and incorporate a vocabulary activity for the students.

__**Week 7 (Oct 5-7): **__ This week I had the opportunity to attend a faculty meeting. The choir director had a group of his singers come in all dressed up fancy and serenaded us to, "I am strong when I am standing on your shoulders" and each of the singers said thank you to a teacher that has touched their lives. It was so powerful it had me in tears. I had never seen anything like this. There was about a handful of singers that had thanked their math teachers that had touched their lives for the good. One of the singers even said that she still remembered the quadratic formula and recited it and said that that was amazing! :)

This week we also had the opportunity to have Udita come and observe us. For Alg 2 I prepared and presented the starter. I chose a basic review problem, a review of last home works assignment, and a preview of a skill they were going to need to use that day. For Geometry I also prepared and presented the starter with the same format as Alg 2. While students were working on the starter I was checking off on their cover sheet if they had completed their homework. In first period most of the students had not done their homework. I asked them why. I wish I would of told them that they needed to do their homework to do well in the class. I did encourage them to do their homework even though they would not get it stamped for credit and encouraged them to come in for help if they thought they needed it. I did think when I had done the starter for geometry that I should of had the students come up to the board and solve it. I could feel the energy level slowing down. Udita did give me feedback to have students come up to the board and show us how they solved the problems.

Mrs. Solomon was very theatrical in Alg 2 class. The topic was on substitution and she had the students laughing and engaged the whole time. When Udita gave me feedback she said that anything we do for these students will help them because they are a needy for various factors, the economy, etc. She said just by cracking jokes (or tell them a story) and making them laugh might be the only time they get to laugh and have fun is when they are in your classroom.

In retrospect I do feel that I should not of got upset at the Geometry class for not being quick to remember that the pythagorean theorem is conditionals to right angle triangles. I did give them think time and two students raised their hands and did get the answer right. I felt that students should know this already and even though I should not have any hint that I am getting frustrated that they do not know if off the top of their heads. I should be more encouraging and have faith that it is in their memory banks and needs a second to resurface. I should of also shown more praise for the two students who had answered the question. Mrs. Solomon did give them both a squibble point for their respect tribes.

While I was reviewing the homework I was getting responses from students and Mrs. Solomon in particular really liked one of the responses. She asked if she could elaborate on it and she told a story on how Pythagorus came up with perfect squares and rational numbers geometrically. She also used a student as an example who was catching on to what a perfect square was and had him stop talking and asked the rest of the class to tell her how he new how to find the next perfect square. Once they figured it out she had students continue to find the string of perfect squares. She also had wait time for students to think which I observed to be very effective. She had more responses out of the class.

Also when I was solving a problem I used the approximate symbol and Mrs. Solomon asked the students if they had seen the symbol before and why I used it. We had a good discussion on this and found that it was because of the nature of the numbers we were using had an irrational number, like pi and so that is why I could not get an exact number.

I told Mrs. Solomon that I was worried that I would not be able to keep the students as engaged as she does when I take over. She told me that I had to find my style and suggested that I observe a neighboring math teacher (who is most likely not as theatrical as Wendy) to see how she keeps her students engaged. So I have made arrangements to observe another class next week.

__**Week 8 (Oct 11-13):**__ <span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">This week I remember feeling particularly compassionate toward those students who are failing. Failing for whatever reason (i.e., cheating on test, not coming to class, etc...). Mrs. Solomon stresses for students to do their homework, come in for help before or after school, and some do, but not all. Most do not do their homework. There seems to be a general feeling of, "I just don't care." So I felt that when students who have cheated on a test and have not been coming to class (or have) and have not been coming in for help (that I could tell) that I would take advantage of the time they were in class to help them. I decided that during the warm-up (or starter) that I would look over those students work and let them know what they were doing wrong so that they could see where they were going wrong. I asked Mrs. Solomon if this was okay and she said that this was fine for me to do this but that she was not going to do that. I feel that this is the least I can do to help them see that they can do it. I want to help them see that they can do it so that they feel a sense of confidence and help them obtain self reliance.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">Also, a student came in this week who has not been showing up so I asked her why she had been gone so much and I tried helping her redeem some potential points by letting her know about the fractal project she could do to drop at test score in place of it.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">This week we also talked about how it is not equitable to require a graphing calculator. The school will rent graphing calculators out for a $20 fee. I suggested to Mrs. Solomon to see if the school has a waiver for students in need.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">Mrs. Solomon is teaching me to use my time wisely. This week a student asked me to grade her homework which is not typical. Students are required to grade their own homework. This took up a lot of time for me to do. Mrs. Solomon warned me not to get into this habit.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">Mrs. Solomon informed me about a student from Africa that has only been in the states for 2 years. He took Alg 1B and struggled to pass it. He is in Alg 2 now and struggling. Mrs. Solomon devised a plan for him to stay in Alg 2 because he needs it to graduate high school and for college. She thought up for this student to stay in Alg 2 he could be an aide for an Alg 1B class but not do aide work and instead would sit in as a student to polish his skills. She talked it over with this student and he thought it was a brilliant idea. So the next step was to speak with his counselor to see if it was possible and we found out that it is. All Mrs. Solomon has to do is speak with his parents now to inform them and see what they think. I was able to join Mrs. Solomon in speaking with his counselor to see that process.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">__**Week 9 (Oct 19-21):**__ <span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">This week Alg 2 had a test. Mrs. Solomon had to remind the students not to cheat and that she distributes two versions of the test. She also tried to discourage them from cheating by telling them that she has her ways of knowing if they do.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">We are also consistently having more students come in for help in the morning time. I try and help students by asking them questions like, "What is the first step", "What is the next step", and "What do you notice..." about this problem? I also find myself encouraging students a lot and telling them I know they can do it. I also find when students ask why they have to do this, they are looking for a purpose, so I try and give them purpose. I told a tribe in Geometry the reason I wanted them to double check their angle measures was because in the real world they need to double check for accuracy. The example I gave them was, in research when taking measurements for the body for accuracy you want to take measurements 3 times and then take the average. Sometimes you even have another person take the measurements to check yourself for accuracy. In Alg 2 I told a student that the reason we are doing this is because it will help you model real world situations whether you go into research or become an entrepreneur for your own company you can use these to model real world situations.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">I am still trying to help this one student gain the concept of adding and subtracting integers. I explained to her the “hots and colds” analogy and even drew the picture each situation we discuss presented and I think this helped her to understand the concept of adding and subtracting integers. I also would remind her of the concept of keeping the scale balanced is what we are doing conceptually when solving algebra equations.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">In Geometry, Mrs. Solomon had an exploration handout prepared for the students. She also had manipulatives for each tribe prepared. The manipulatives were transversal and parallel lines that were made out of colored construction paper that were laminated. The students explored how the lines had to be to more angles congruent. We think this went really well. Students were able to find relationships and come up with conclusion like, “as long as you have two parallel lines it doesn’t matter where the third line in the transversal is placed, two angles on each side will match” (Tribe Algekor). Coming from the Pentanos tribe who has more than one EL said, “draw an equal sign, then diagonal line through them.” Other responses were, to have 4 corresponding angles you need to have two parallel lines that are crossed by another slanted line. One keen observation that was made is that 2 of the angles are acute and the other 2 angles are obtuse. I will use this skill to share with my cohort for our November meeting.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">I met up with a student in the bathroom and she told me that one of her tribe members will not help them during the group race review and how it is frustrating her. I told Mrs. Solomon and she said that it was important for them to learn to work in groups. She plans on switching up the tribes for the new quarter.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">While student were taking the test Mrs. Solomon asked to speak with a student so that she could inform him that he was failing this class and ask him what he was going to do about it. She also pointed out to him that this is graduation that is at stake! She figured he could take an alternative math class called personal finance and then he would eventually have to take Alg 2 (the core math class) for graduation.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">__**Week 10 (Oct 25-29):**__ <span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">This week Mrs. Solomon did something different in her approach with the routine. She still gave Alg 2 the warm-up but went over it before she collected it so that the students could check their work and make the corrections they needed. She also handed out a review to the students for their final next week that they were able to work on in class. She asked students what they preferred, to have Mrs. Solomon work out the problems or work in tribes. Most students wanted to work in tribes, but two students suggested that they work in tribes for a time and then have time to see Mrs. Solomon work them out.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">Tribes will change for the next quarter. We have students that are frustrated and awaiting the change of tribe members and other students not wanting to have a change.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">In Geometry class today, Mrs. Solomon was introducing formal proofs and it went well. She was able to guide the students through direct instruction and asking the right questions to get students to think why yo u could make each statement that consecutive interior angles are supplementary. (Because angle 1 and angle 5 add up 180 degrees because they are a linear pair. Angle 1 is congruent to angle 2 because they are corresponding angles due to parallel lines. Angle 2 and angle 5 add up to 180 by substitution. A student was able to conclude this in class with out even knowing he was doing a formal proof. Mrs. Solomon was trying to get students to articulate why statements were true and students were having trouble but she would not discourage them from digging deeper.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">Today in Alg 2 the students were taking a final for the end of Unit 3. This test was given in a different format, with multiple choice and scantron in preparation for the CRT’s. To encourage the students to work out all the problems on paper, she did not hand out the scantron until later. She also told the students that if they did well on this test, they could erase their bad grade and replace it with this test score. The example she gave is that if their current status for the quarter was failing and if they got an ‘A’ on this test they could get an ‘A’ for the quarter. The reaction of some of the students was, “Really? I’m going to try harder now!” I am not sure why he thought by trying harder now would make a significant difference at this point.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">In geometry class we were starting a new section on slope and Mrs. Solomon explained slope with a time graph and how a businessman would interpret his profits from reading the different pictures (the different slopes). Mrs. Solomon would ask the students after drawing a positive slope how a businessman would interpret this graph? Students would respond that profits were going up and that this would make the business man (or woman) happy. Mrs. Solomon would draw a negative slope and ask what would this would mean to a business man and students would respond that it meant that profits went down. Then she drew a horizontal line and asked the same question. Students responded that nothing changed. Mrs. Solomon was pleased and stressed that it was a neutral graph where he did not lose or gain profits and she still discussed how this would make a businessman feel. He would not feel mad or be happy about this. Then she drew a vertical line with arrows that extended from both ends and asked the same question. One students’ response was that the picture meant that he was rich. Mrs. Solomon response was, “Or is he poor because we do not know which way the graph is going up or down?” She pointed out that because of this confusion this particular graph was a mystery and thus it had undefined slope. I think that teaching slope this way helps students to grasp the concept of slope. She also explained how vertical slope has no run and how horizontal slope has no rise.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin: 0px;">The quarter has come to an end and we feel that the grades do reflect how the students are doing. Geometry lessons are going much better. I witness an “aha” moment for one of the students. He could use logic to explain how corresponding angles were congruent, guided by Mrs. Solomon but he did it.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">__**Week 11 (Nov 3-5):**__ <span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">This week I observed Mrs. Hesterman’s, a neighboring math teachers, Alg 2 class. She was lecturing on transformations for quadratics. The class started out with a warm-up at board. Which was a review from last time. Last time they had a substitute teacher deliver the lesson and she expressed that she had debriefed with him over the phone about how the class behaved and how he delivered the lesson. She praised the class for getting the best report on behavior with the sub. They are starting a new quarter so she went over how the students did as a class. She said how many had ‘A’s’ and ‘A-‘s’ and how many had ‘F’s’. She gave the class an incentive to get no fails for this quarter and then she would have a pizza party at her expense at the end of the quarter.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">After the students did the warm-up she had two students come up to the board and work them out. To expound on the warm-up she explained how when solving for zero’s that there are synonyms for it like, roots and x-intercepts. She went over the work the students did on the board, step by step, and filled in the steps where they left them out. She pointed out the differences on how she would prefer the problems solved and why. Then she showed them how she would get rid of the fractions.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">After the warm-up she had a chart that was written on the board before the class had started. When she started the class she read off answers for homework while the students corrected their own hw. I also noticed that she had the key to the homework worked out and in a protector sheet.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">Then she had the students copy the chart from the board to their notes after when she went over the chart I felt it was a little confusing because the students had no experience with it, and it had a lot of short hand, but once she did detailed examples it became clear to the class. I really appreciated that she would ask the students frequently if it was confusing or not with “thumbs up or down”. I could tell she did this to get a sense of the students understanding. She also used the example with a vertical stretch by saying and using hand gestures to pull from head to toe one of the students to explain that this would make him thinner. Like wise for the horizontal stretch to explain how pulling in this direction would make the student wider. Then she would draw the corresponding parabolas on the board. She also did examples on the graphing calculator and would stop to circulate through the students to see if they needed help.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">I really liked how she explained to the class to distinguish between a horizontal and vertical shift. She likened the parenthesis to a building. You have to be inside the building for the transformations to apply, conversely with being outside the building. If the transformations were inside the “building” or the parenthesis then it was a horizontal shift. Conversely, if the transformations were on the outside of the “building” or the parenthesis, then that was a vertical shift.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">Also, she pointed out the pitfalls of graphing the horizontal and vertical shifts and also pointed out that even though the horizontal shift is counter intuitive (when seen in function form), when seen in the English language written out, you do what it says. <span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">In geometry Mrs. Solomon told the students how the department had came up with a decision to have the students take a step back and review algebra. She asked the students what does “solve” mean? A student’s responded that it means to find x. She clarified that it means, “find the number to replace “x” to make the sentence true.” We could tell that most of the students were excited to work on this, and thought it was easy, because they were getting it. Mrs. Solomon had asked them to put markings that indicated that they knew they were combing the like terms so that she would know when there was a mistake she could distinguish if it was a problem with addition or combing like terms. We also, handed back the test, that most failed. I asked most of the students if they were planning on taking the retake, some said yes. One student said they were content with the D- they got. I really thought he was serious, but I hope he was pulling my leg. It can be hard to tell. I encouraged all of the students to take the retake and study for it.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">For Alg 2, Mrs. Solomon was introducing solving for zeros and FOIL’ing. She taught them the secret to mathematics that no other math teacher will tell you is: the banishment of fractions. The students thought that this was cool. We noticed as the students were working the problems out on their own that it did not mater if they subtracted the constant over first or left it before they undid the fraction. Mrs. Solomon also had a problem that had a constant multiplied by a binomial squared. A student had multiplied the constant through then squared everything. He asked me if this was correct. I worked it out and it we did not get the same answers. Mrs. Solomon worked this problem out on the board for the whole class and she asked them why this was not valid. She explained that by distributing the constant through, you would be squaring it and thus getting the wrong answer.

<span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">During preparation period we discussed the direction of the Alg 2 class which is factoring. She asked me how I was taught to factor: <span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;"> x^2 + 7x +12 and 2x^2 - 9x -18 <span style="font: normal normal normal 13px/normal Arial; letter-spacing: 0px; line-height: 19px; margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px;">We discussed the road blocks in presenting the way I was taught and the advantages to presenting the lesson with algebra tiles and to teach factoring by grouping. She stressed the importance of building on what they already know and how this is a foundational skill for students. We also prepared algebra tile packets for each tribe. Mrs. Solomon feels that it is a good starting point to present factoring by talking about the days of Pythagorus and how they ordered numbers using pebbles and sticks. He noticed that he could order 16 pebbles in 2 rows of 8 to form a rectangle and 4 rows of 4 that formed a perfect square...I am looking forward to see how the students understand the mathematics as this is a very visual way to present factoring. I anticipate that it will help them learn and understand the math.

__**Week 12 (Nov 9-11):**__ Today we will be formalizing what they learned on Tuesday with the manipulatives of playing with their “sticks and rocks” to learn factoring. Mrs. Solomon said that it went really well last time (I had to miss and informed Mrs. Solomon in advance). Mrs. Solomon started out telling them that most people feel that factoring is a pain. She started out the lesson building off of what they know; she said that it was the opposite of “FOIL”-ing also “un”-distributive. She introduced the lesson as to factor quadratics (like an ancient Greek). The initial quadratic she used to introduce was: 2x^2 - 6 She related what to do with what they knew from system of equations: (1) 2x + 3y = 1 (2) 4x + 6y = 2

She talked about how this system of equations are the same line and that the 2nd equation could be reduced by its common factor, 2 to be the show that it is the same as line 1.

<span style="font: 13.0px Arial; line-height: 19.0px; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 15.0px;"> I personally was not taught factoring this way, so for myself I will include her lecture notes: The first step is to “reduce” the GCM first. Second, Go Greek! Referring back to the previous lesson on working with “rocks and pebbles”. Through trial and error the students learned that the x’s (sticks) had to split up such that when multiplied together they needed to equal the constant (or pebbles). She also introduced the “magic box” (a 2 x 2 box) used for factoring. The steps are as follows: a) x^2 stuff goes upper left; ax^2. b) the constant goes lower left; c. c) Split the b so that the two pieces = a multiplied by c (in the other two corners).   x^2 + 7x + 10    Combinations to get 10: 1,10; 2, 5.

Third step, Find GCF for both rows and both columns. <span style="font: 13.0px Arial; line-height: 19.0px; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 15.0px;">(x+ 5)(x + 2) <span style="font-family: arial,helvetica,sans-serif;"> Fourth, write out the answer. <span style="font-family: arial,helvetica,sans-serif;"> Other examples: x^2 + 9x +18 <span style="font: 13.0px Arial; line-height: 19.0px; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 15.0px;">(x + 3) (x + 6) Combinations of 18: 1,18; 2,9; 3,6. <span style="font-family: arial,helvetica,sans-serif;"> 6x^2 + 23x + 15 <span style="font: 13.0px Arial; line-height: 19.0px; margin: 0.0px 0.0px 0.0px 0.0px; min-height: 15.0px;">(6x + 5)(x + 3) Combinations of 90: 1, 90 -> 91; 2, 45->47; 3,30; 5,18; 6,15; 9,10.
 * **x^2** ||  **2x**  ||  **x**  ||
 * 5x ||  10  ||  5  ||
 * x ||  2  ||   ||
 * **x^2** ||  **3x**  ||  **x**  ||
 * 6x ||  18  ||  6  ||
 * x ||  3  ||   ||
 * **6x^2** ||  **5x**  ||  **x**  ||
 * 18x ||  15  ||  3  ||
 * 6x ||  5  ||   ||

x^2 - x - 90 (x + 9)(x - 10) Side note: -9 + 10 = 1 <span style="font-family: arial,helvetica,sans-serif;"> Mrs. Solomon asked the student why they would want to use the magic box. She told them that some of the problems you would not need them but for the most part there would be no more guess and checking. Lastly, she had students put in their notes to double check the signs (especially when ax^2 - bx + c) by distributing the factors. For geometry class Mrs. Solomon had an emergency come up so in place of an ATB I asked students what homework problems they wanted me to work through.
 * **x^2** ||  **-10x**  ||  **x**  ||
 * 9x ||  -90  ||  9-90  ||
 * x ||  -10  ||   ||

A single student asked to do number one. I asked if she was the voice for everyone else. I also asked if any student would like to come up to the board and show us how they worked it out. Nobody volunteered. So I worked it out asking students for help. Mrs. Solomon was shocked they wanted to go over #1and #2 since they went over these in class last time. None the less, most of the students expressed they did not get it. So Mrs. Solomon proceeded to express she did not understand why they did not get it and showed them how she thought it was so simple. Then a student started to express where exactly she was getting stumped. I jumped in to see if I could help clarify using the picture on the board. She still did not seem to get it. So I had the class turn to their neighbor and explain it to each other as Mrs. Solomon and I walked around to assess their understanding. We had to encourage them to try and articulate their thinking. <span style="font-family: arial,helvetica,sans-serif;"> Mrs. Solomon will not be at school on Friday so I got to see her prepare her lesson plans for the substitute teacher. For the most part it was very specific like a letter to the substitute teacher with specific instructions. She did not want the substitute teacher to deviate from the way she was establishing the foundation for factoring. She also had specific instructions on the color of paper to hand out to students for specific periods-as this will make it easier to identify which period is whose for all parties. <span style="font-family: arial,helvetica,sans-serif;"> We also got to discuss about one of her books on her book-shelf, //Flatland A Romance of Many Dimensions//. She said that she will discuss with her geometry class the possibility of other dimensions by relating them the story. <span style="font-family: arial,helvetica,sans-serif;"> We also got to help another teacher in the department by watching her class so the teacher could leave 15 minutes early (for personal reasons). Mrs. Solomon told me, “when in doubt use candy!” She had put algebra equations on the board and if the students could tell her what x was without her solving up on the board for them they could earn a piece of candy. This kept them engaged until the bell rang.