I strongly believe that all of my students were able to achieve learning gains because of their small class size. I was able to give one on one attention to each student almost every day. This was especially helpful for differentiating my curriculum as on of my IEP students was on grade level but really struggled to focus. He really benefited from my help in directing him to do his assignments. When students had questions I was able to address their needs individually which does not always happen in a larger class setting. One student needed extra time on the post assessment and he was given that extra time, but other than that there were no special needs with my assessment.

            From my data I can see that all of my students made gains. The average gain for the class as a while from pre to post assessment was about 34%. The only question I have however is do they really have the math skills to move on to high school math. Conceptually my students really understood what I was teaching them. This is why I used the rubric that I did. They are not so good at basic algebra or multiplication and division. Because of this, many student set up equations correctly every time, but failed to calculate the correct answer. From my perspective however, I do not think this means they did not meet objectives, or are not ready for this math. Conceptually they truly understand these concepts, their basic algebra skills as well as arithmetic skills are not up to where they should be and they make calculation error. Negative numbers are especially confusing for them which makes me question whether or not they are actually ready to move on, but since I am not their actual teacher I cannot make that decision.

           Each individual student also made gains. As I mentioned in the visual representation section, the smallest improvement was student E who only improved 5% but she scored very high on the pre-assessment. I would like to note that when I analyzed the individual questions she improved her score from a 1 to a 3 on question 7 of the post assessment (which corresponds to question 6 on the pre assessment). She also dropped from a score of 3 to a score of 2 on question 3 on the post assessment (question 2 on the pre-assessment), but I believe this was a counting error and not a conceptual misunderstanding. The largest gain was made by student A who improved 68% This student struggled with turning in homework, but did well on all formative assessments and clearly did well on the post-assessment. From this representation of the data I can clearly see that all of my students improved. Student J did not meet my goals and objectives, but he did improve 47%. He was one of my two IEP students, and he did receive extra time on the exam and extra assistance with homework assignments. I think he may have gotten discouraged on the post-assessment when he could not answer all of the questions right away. He left some questions blank that I has seen him successfully complete before. Even though he did not meet all of the goals and objectives he did meet some of them and did show great gains in learning. He met the overall objective of drawing a graph from and equation, writing an equation in slope-intercept form from key information, and the objective of writing a linear equation based on a real world scenario. He met 3 out of 5 overall objectives for the unit, and I truly believe that with a bit more work he could meet all of them.

            The most effective teaching strategy that I used was the cooperative group relay. The students were engaged because it was a game, and it also allowed me to give immediate feedback when kids would brig up a relay card. I also kept all of the cards so that I could look and see what teams had trouble with what problems. This was also nice because the students could get up out of their seats and help each other solve problems.

            The other teaching strategy that was very useful was a note taking worksheet I made for my students. On the first page was a fully completed example. The second page had some blanks for them to fill in, and the third page was a space for them to complete their own problem. I noticed that my students struggled taking notes and therefore would get lost when they tried to complete assignments once class was over. My cooperating teacher really liked this note taking method and said he plans on using the template I created in future classes.

            Strategies that did not seem to work very well with my students was when I had them try to figure out math problems before I actually taught them how to solve them. If they could not immediately figure out the problem they would just quit trying. I only did this once and when I realized that they did not respond to this, I changed my strategy. I still think this could be an effective teaching method, but my students were not accustomed to it, so it was not effective for them. 

          Analyzing this data has helped to show that my students are making learning gains in my math class. With out this analysis I would have somewhat of an idea of how they were doing because of the formative assessments I gave every day, but without the pre and post assessment that allowed me to have empirical data on learning gains, I would not be able to say as matter of factly whether or not my students met my learning gains.

        Looking at each individual question and how they relate to my learning objectives, There were only 3 students who received less than a score of 2 on one or more questions. Student I received a score of 1 on questions 6 and 7. This student did not meet my objective of being able to solve for a missing part of a linear equation. Other than those two questions, this student met all of my learning objectives.

      Student J received a score of 1 on questions 1, 4, and 6 and a score of zero on question 7. This student did receive a score of 3 on question 2 which was covered the same objective as question 1. This makes me think that there was something about question 1 that was more confusing for this student. He obviously understands the basic concept, but cannot complete every problem. I struggle with whether or not that meets my learning objective. I think it meets, but he could still refine his skills. Question 4 was essentially the same as question 3. The student needed to interpret from the graph what the y-intercept and slope were and then write an equation to represent this graph. This student received a score of 2 in question 3 which I determined meets, but once again he has shown he cannot do every problem, so he is still refining his skills. This particular student also has an IEP that allows him extra time on tests because he has trouble focusing, so that may have been why he could not complete both of the questions correctly. Like student I, student J did not meet the objective of solving for a missing part of a linear equation. He received a score of 1 and 0 on questions 6 and 7 respectively. Although this student did not meet all of the objectives, he did so great learning gains.

      Student G received a score of 1 on question 1, but a score of 3 on question 2. Because these questions essentially cover the same learning objective, I have determined that this student meets, but is still refining skills much like student J.

     All of my other students received a score of two or better on every question, and therefore met all of my learning objectives. Some of the students are still working on correctly calculating negative numbers, and basic skills, but conceptually almost all of my students met my learning objectives. Most of the students were always on the same page. It is difficult to pick a student who would be "most typical". Not to say that all of my students were the same either. I had two students who did not meet every learning objective, and one student (student H) who received 100% on the post assessment. Student H, showed understanding throughout the unit. He constantly wrote on his exit cards that he knew how to do whatever concept it was that we were learning that day. He was also one of my more careful students when doing calculations. As I said before, my students demonstrated a lot of conceptual understanding, but many calculation errors. Student H's carefulness is what I think helped him get 100% on the post assessment.