Data Analysis

Student Interviews

This video shows the responses that students had to the questions presented.

I chose to interview my students on their opinions of the different types of instruction we have used in our classroom. Students were also asked about the different types of strategies they had learned during math and about their favorite rotation activities. I wanted this qualitative data to understand each student’s ideas on math and how they learned best. By understanding how students preferred math, I created instruction that fit their needs and kept their interests. From these interviews, I found that students did not really prefer one instruction type over another, but instead found that whole group instruction with rotation instruction gave them the best understanding and exposure to the material. For students’ thoughts on whole group instruction, several students said they found whole group useful because the new material was explained and multiple strategies were discussed. Other students liked whole group because they got to hear other people’s thoughts and learn together. Finally, other students said that they found whole group disengaging because they were not challenged and did not directly do any math problems. For students’ thoughts on rotations, many students agreed that their favorite part of math was the rotations. Students loved getting to work with each other, use a variety of materials to solve problems, solve real-world problems, and being challenged based on their needs.

This assessment really showed me that using one style of instruction does not work, and that there needs to be a variety of instructional settings in order to best serve students. Before this assessment, I would have thought that all students preferred rotations and did not value whole group, however, the results of my student interviews said differently. From this, I learned that students felt that both forms of instruction are needed to help them understand and do math. This impacted my students because it showed me what they found necessary to make them successful and helped me understand what works best for teaching them. By learning what they liked best, I was able to create instruction around their interests and needs, which in turn helped them learn. Another way this impacted students was that it showed me that my higher-achieving students felt they needed to be more engaged or challenged during whole group. To combat this issue, I added more opportunities to engage with other classmates and created movement activities with many lessons to keep them engaged and focused on the content.

Pre and Post Tests

During my study, I wanted to get data on how much my students were growing during each math topic. To do this, I gave the topic test before and after each topic. This gave me insight into if my students’ achievement was increasing due to the use of rotations and differentiated math groups. I kept track of students’ initial scores as well as their post-test scores in order to track student growth. The differences between the pretests and the post-tests are found in the bar graphs. The pre-test data shows that many students had very little prior knowledge of these math topics, with anywhere from 13 to 20 students receiving a score of 50 percent or less. In fact, on topics 6, 14, and 18 several students got zero answers correct on their pretests. This information impacted my instruction and my students because it helped me to understand how much support each child was going to need to be successful. From this data, I formed my math rotation groups. Students that had very low scores received more guided practice and gradual release of instruction during their rotation, while my highest scoring students were given less guided practice and more enrichment tasks to challenge them. By understanding what my students’ needs were I was able to give them more individualized instruction and address every student's needs. I found that by using the differentiated math groups and assignments, I had 20 to 22 students show growth on each test with many students also showing a large amount of growth. For example, 4 students grew over 10 points during topic 9. In addition, 15 students grew more than 10 points during topic 6 and 18 students grew more than 10 points during topic 18. This showed that differentiated math groups and rotations improved students’ understanding and achievement because across each ability level that is growth, and in many cases, major growth.

When looking at the graphs, I noticed that during each topic, there was one to three students who did not grow or even had a lower score after each topic. One reason for this lack of growth may be that many of these students missed several days of instruction due to illness or travels. This was the case for student 2 during topic 9, student 15 during topic 6, and student 21 during topic 18. Each of these students missed three or four days of instruction, which means they did not get small group instruction, time to work with peers on real world activities, or any opportunities to manipulate and work with the new topics and strategies. I think that missing these opportunities played a large factor in these students’ lack of growth. I also noticed that I had a common outlier in several topics, student 17. This student received special education services and also struggled with changes in routine. Due to the many snow days that occurred during this study, the student had a very hard time staying focused and had to be removed from the classroom several times due to meltdowns. Because of this, I think this student was not able to get as much out of each lesson as we were focusing more on getting back into a routine than we were on schoolwork.

Reflection Video Data

I assessed my students’ knowledge of the material that they were studying each week. Everyday, students created a reflection video of themselves solving and explaining a math problem based on the day’s lesson. To track how well students were explaining their thinking and comprehending the math, I created a rubric that focused on students showing their math in a variety of ways, using mathematical vocabulary, and explaining their process and thinking. The highest score students could receive on the rubric was a 9. What I noticed was that all students, no matter their ability level, grew as the weeks went on. No matter if students started with a score of 3, 5, 7, or 8 all students grew and only four students did not receive a score of 9 during week 7.

This bar graph shows 2 students from each of my ability groups. Students 2 and 19 represented my high-ability students, students 13 and 22 represented my on grade level group, and students 17 and 23 represented my struggling, or below grade level students. The data from each of these students showed that no matter their mathematical ability, all students were able to explain their thinking and use a variety of methods and strategies. Though there are four times where these students did not continuously grow, most students received a higher score as the weeks progressed. I believe that the reason that students 13 and 19 both saw a drop in the middle of this study this was when we switched topics. During week 3, we moved to area and perimeter after working on shapes, and student 19 had very little prior knowledge about area and perimeter. For this reason, I think he struggled with the switch and needed multiple opportunities before becoming fluent in these math concepts. Similarly, during week 6 we moved from input and output charts to solving algebraic expressions, which was difficult for student 13. Because of the change in topics and a lack of prior knowledge in these areas, these students struggled with applying the learning and explaining their thinking in their reflections. The other student, 23, experienced two drops throughout the study. Both of these I believe were due to illness and missing several days of school. Since this student did not get as many opportunities to apply the math and use it in a variety of settings, he struggled to explain his thinking and correctly apply the mathematical vocabulary.

All in all, the data showed that students’ abilities to discuss math and apply it increased when they practiced solving and explaining math problems every day. The reflection videos impacted my students because they were able to apply their learning to more challenging problems and to a variety of settings. One of the biggest challenges for my students before the study was to take their daily practice problems and apply that knowledge to their assessments that were mostly story problems. By having students solve more complex problems and story problems every day, all students were able to apply their new strategies to a variety of question types. The group that displayed the most growth though was my struggling students. These students all started the study at a 3 or 5 on the rubric, but by the end, all but one student received a 9 in week 7. In fact, by week 5 many of these students were receiving 9s on the rubric. These students were also able to take these skills of explaining their math and their thinking to other areas, including whole group instruction, math investigations, and teacher time. I noticed that these students were more confident in discussing math and working independently after starting reflection videos as well as that they were able to apply more of the skills we worked on during their tests. In conclusion, I think that this strategy was effective at increasing my students' achievement in math.

Student Engagement Data

The last assessment I used during my study measured students’ time on task. A large part of increasing achievement is having students be engaged and focused during math. Therefore, I wanted to see when students were most engaged and where they were the least engaged, so that changes could be made. To measure engagement, my mentor and instructional coach counted students that were engaged in learning every three minutes throughout three lessons. The data showed that students were engaged more during math rotations than they were during whole group, with the exception of one rotation. This information supported my study because due to the high interest and quick paced nature of math workshop, students spent more time learning and engaging with math than they did during whole group. The data showed that on average, student engagement increased 1.45% during rotations. This showed that rotations were more engaging to students, which in turn, means they were learning more during this time.

This assessment impacted my instruction because it allowed me to make informed decisions on how and when to make changes. One thing I noticed from the data was that students were less engaged during the second and third rotations, so I knew that I needed to keep students’ motivation up and create high interest activities for every rotation to avoid this drop. To do this, I created more games, real-world problems, and partner activities to each station, so that students would not get bored or restless. This assessment impacted students because it helped me understand what my students needed in order to stay focused and learning, and therefore I could make necessary changes. When engagement falls, learning does too, which in turn, affects student achievement. By always changing up and adding engaging activities to rotations, I was able to support students’ needs and keep them engaged in learning.

Remaining Questions

There are several questions I had throughout my study and some remaining questions. One question I had during my study was why student 17 was not making growth from pretest to post test? After analyzing the data and reflecting on this student’s behavior during the study, I believed that there was a lack of growth because this student was struggling with an inconsistent schedule due to snow days. This student had a diagnosis of autism and one of his challenges is handling change. Due to seven snow days and never having a full week of school during this study, I feel that he was struggling academically because he was having a hard time staying together emotionally. Another question I had during my study was why students' engagement dropped dramatically during the third rotation? After reflecting, I think this was due to several students leaving and coming in during this rotation. I have several students that leave for resource during this time as well as an enrichment group that comes back. I think that having so many students leaving and entering caused the others at rotations to be distracted. Because I did not have the data to prove these inferences, these were the questions that I had and would want to look into if I were to continue my study.

Triangulation

When reflecting on my data collection, the Math Workshop model was proven to be effective in building students’ math strategies and engagement in math. Students were able to verbalize their thinking process and explain how to solve problems, which in turn lead to increased achievement on tests. Such evidence was cited through a review of my data sources. The reflection videos demonstrated that my students were able to communicate the strategies they were using to solve problems as well as their knowledge of vocabulary. The student interviews and time on task data revealed higher engagement during math rotations, which in turn showed that students were focused on learning math. Finally, the topic tests administered throughout the study demonstrated my students’ growth. The growth from topic tests, students’ feelings from the interviews, data of increased engagement during rotations, and students' use of strategies during the reflection videos revealed that students were able to comprehend and apply their knowledge to math problems.