## Impact on Student Learning

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The pdf document above contains both a worksheet on solving linear equations and parallel and intersecting lines (first two pages), as well as a chapter test (last 4 pages) from my first student teaching placement at Lenart Regional K-8 school. These documents were for an 8th grade Algebra course that I taught during that time. The worksheet was completed about 16 days before the chapter test. The worksheet shows a lack of conceptual and procedural understanding of the material, and the other link shows a tremendous improvement of comprehension of the material by the student. The particular student went from getting an F on this worksheet to an A on the test in the span of two weeks.

This student was fairly quiet in class and seemed unmotivated when it came to classwork as well as participation. He always seemed to be focused on other things. The other content area teachers echoed this sentiment as well, noticing that this student kept to himself but would show signs of engagement when something caught his attention. After the first couple of weeks seeing his work, I noticed that he was not showing any of his work and was not understanding basic concepts. I tried to present the material in various ways, working one on one with him and learning about his interests. My cooperation teacher informed me that it was fairly hard to get this student motivated to do his work. After working with him a couple of times, I realized that he really enjoyed various topics in geometry, and also really liked one of the proofs that I showed him in number theory. It was clear that when something caught his attention, he would show more focus and motivation to try to comprehend the material. I urged him to come to math club for one session to experience some interesting and enriching number theory topics I would address, and he loved it.

Afterwards, he seemed to really open up and was motivated to work hard to complete challenging tasks. I gave him more proof worded problems that he enjoyed and seemed to rise to the occasion. The conceptual errors that he was making were fixed easily with a little bit of explaining and connection to geometrical concepts. It was easy for this student to connect all three linear equation forms with the graph once he saw where they came from, and how they were derived. This student was also one of the only students who correctly worked through the proof on the chapter test. This student was highly proficient in solving all three forms of linear equations, solving systems, inequalities, and best fit lines.

I believe that some of the math enrichment I exposed this student to were very helpful in getting this student excited about challenging math topics and showing him some of the creativity and philosophy behind various math concepts. By having a strong content knowledge and feeding off of this student's interests, I was able to get this student more excited about math and impact his learning in a way that I feel he had never experienced before. Before my last day at Lenart, this student and I corresponded back and forth with number theory topics that he enjoyed, and I gave him resources to discover and learn more about number theory, a topic that caught his interest.

**Impact on Student Learning**This student was fairly quiet in class and seemed unmotivated when it came to classwork as well as participation. He always seemed to be focused on other things. The other content area teachers echoed this sentiment as well, noticing that this student kept to himself but would show signs of engagement when something caught his attention. After the first couple of weeks seeing his work, I noticed that he was not showing any of his work and was not understanding basic concepts. I tried to present the material in various ways, working one on one with him and learning about his interests. My cooperation teacher informed me that it was fairly hard to get this student motivated to do his work. After working with him a couple of times, I realized that he really enjoyed various topics in geometry, and also really liked one of the proofs that I showed him in number theory. It was clear that when something caught his attention, he would show more focus and motivation to try to comprehend the material. I urged him to come to math club for one session to experience some interesting and enriching number theory topics I would address, and he loved it.

Afterwards, he seemed to really open up and was motivated to work hard to complete challenging tasks. I gave him more proof worded problems that he enjoyed and seemed to rise to the occasion. The conceptual errors that he was making were fixed easily with a little bit of explaining and connection to geometrical concepts. It was easy for this student to connect all three linear equation forms with the graph once he saw where they came from, and how they were derived. This student was also one of the only students who correctly worked through the proof on the chapter test. This student was highly proficient in solving all three forms of linear equations, solving systems, inequalities, and best fit lines.

I believe that some of the math enrichment I exposed this student to were very helpful in getting this student excited about challenging math topics and showing him some of the creativity and philosophy behind various math concepts. By having a strong content knowledge and feeding off of this student's interests, I was able to get this student more excited about math and impact his learning in a way that I feel he had never experienced before. Before my last day at Lenart, this student and I corresponded back and forth with number theory topics that he enjoyed, and I gave him resources to discover and learn more about number theory, a topic that caught his interest.

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The artifacts above contain a test given to a freshman Algebra Extension class at the end of a unit on linear equations, and the test corrections from one student. The first link shows a lack of conceptual understanding of the material, and the other link shows a much greater level of comprehension of the material from the same student. This particular student went from getting a low F to a B.

This was a very bright student with a great personality who worked very well one on one. When he was working by himself or in groups, he would get distracted and start to develop a habit of being off task. I knew this student had the ability to do the mathematics on his own if he developed the focus he needed to get his work done. I had talked with this student before about him being focused in class, and after grading this first assessment, I realized that he would need some individual attention with certain concepts.

I immediately spoke with the student about coming in for help. We had a conference with my cooperating teacher to determine the best course of action. We all agreed upon him coming in during his lunch hour and going over the chapter 5 assessment and the material from that section in order to ensure he understood the content, without the distractions of his classmates. For the next few days, we went over the material, focusing on the mathematical concepts which would be necessary to understand the material in the class as we moved forward. I took this on as a personal goal to get this student caught up and make sure that he was able to grasp the concepts in that unit.

After working one on one with him, he was able to get a deeper level of understanding of the material. I realized that he knew most of the procedures, but it was the disparity between how to connect them with important concepts we had went over. He was able to see the connection between a linear equation and it’s graph, as well as how the equations worked, their benefits, and where they came from. Because of this, the procedural knowledge strengthened and he was able to work on his own. We also did many examples of linear equations involving his favorite basketball player and used real data to model real life applications. Together we were able to determine that he learned best by being able to ask all the questions he needed to and get extra practice necessary for the material to click. By giving him the background knowledge necessary and providing him with the resources outside of the classroom, I was able to help him succeed within the classroom.

After helping this student with the chapter test, he was more open and engaged in the class and willing to participate. He regularly asks questions in class, and some of the students in the class are starting to follow his lead.

**Impact on Student Learning**This was a very bright student with a great personality who worked very well one on one. When he was working by himself or in groups, he would get distracted and start to develop a habit of being off task. I knew this student had the ability to do the mathematics on his own if he developed the focus he needed to get his work done. I had talked with this student before about him being focused in class, and after grading this first assessment, I realized that he would need some individual attention with certain concepts.

I immediately spoke with the student about coming in for help. We had a conference with my cooperating teacher to determine the best course of action. We all agreed upon him coming in during his lunch hour and going over the chapter 5 assessment and the material from that section in order to ensure he understood the content, without the distractions of his classmates. For the next few days, we went over the material, focusing on the mathematical concepts which would be necessary to understand the material in the class as we moved forward. I took this on as a personal goal to get this student caught up and make sure that he was able to grasp the concepts in that unit.

After working one on one with him, he was able to get a deeper level of understanding of the material. I realized that he knew most of the procedures, but it was the disparity between how to connect them with important concepts we had went over. He was able to see the connection between a linear equation and it’s graph, as well as how the equations worked, their benefits, and where they came from. Because of this, the procedural knowledge strengthened and he was able to work on his own. We also did many examples of linear equations involving his favorite basketball player and used real data to model real life applications. Together we were able to determine that he learned best by being able to ask all the questions he needed to and get extra practice necessary for the material to click. By giving him the background knowledge necessary and providing him with the resources outside of the classroom, I was able to help him succeed within the classroom.

After helping this student with the chapter test, he was more open and engaged in the class and willing to participate. He regularly asks questions in class, and some of the students in the class are starting to follow his lead.