Capstone Project
Pre-tests and Post-tests
Figure 5 - Topic 11 Student Results
Topic eleven has only eighteen students compared to nineteen students in Topic nine because a new student joined my class during the duration of the Topic nine unit. From the beginning to the end of Topic eleven (Figure 5), all of the students reached more than a passing grade of 70%. Student two, three, twelve, and fourteen made the most growth from a score of 2/20 to 20/20. Student eight made the least growth from 12/20 to 20/20.
From the beginning to the end of Topic nine (Figure 6), twelve students received a score less than 70%. seven students received a score of 70% or more. Student one made the most growth from a score of 5/13 to 13/13. Student ten made the least growth from 7/13 to 5/13.
Figure 6 - Topic 9 Student Results
Students grew in Topic eleven because I taught students how to write in math. I taught students how to write in math for the first week before starting Topic eleven. During the Topic eleven unit, I gave students more opportunities to explain and describe their answer compared to the Topic nine unit where they had to only justify their answer. In Topic nine, I chose to do this because I used writing questions from the district’s math curriculum. One of my internal stakeholders told me to add the writing questions to the curriculum. These questions were justifying an answer rather than explaining the process for the answer. For example, in Topic nine I would provide them with a question such as “Is an equilateral triangle always an isosceles triangle?” This kind of question required students to reinforce why the statement is true. As I was planning lessons for Topic nine, I did not believe students needed as many questions where they needed to explain their answer. The lack of questions where students had to explain their answer impacted my students' results on the post-test because there were lower scores on Topic nine. The data for Topic nine came out lower because students had not reached a deeper understanding. The questions where students were required to explain their answer allowed students to show their deeper understanding. This deeper understanding was correlated to their high post-test scores in Topic eleven which increased their student achievement.
There are many reasons to why four students scored lower on the post-test than the pre-test for Topic nine. The first reason is the amount of times students had written in their math journals. Student eighteen had attendance issues during the study, which resulted in fewer journal entries. This student had a total of six journal entries compared to a total of eleven journal entries done during the study. This student had less opportunities to show their deep understanding.
Due to the timing of Topic nine post-test and attendance, this student had limited opportunities to think deeply about their math understanding which affected their post-test scores. Student ten received a lower score because they showed less understanding in their math journals. For example, from looking at this student’s journal during the study, they received an average score of two which means the student got the answer correct but could not explain their answer on a deeper level. This score correlates to their post-test score because they could not show deep understanding. Student four received a low score on their post-test because they were a new student before the study began and were being identified as having receptive language problems. This student’s receptive language correlated with their scores on the post-test because language was a barrier on the test. Student seven received special education curriculum during the study which resulted in the same score on both tests.
The reason why some students received a higher score on the post-test for Topic nine is because they were developing a deeper understanding. These students had an average of three as their writing score which means students were showing more deeper understanding of the content. This deeper understanding in their math journals was correlated to their increased student achievement on this post-test.
Math Journal Entries
Figure 7 - Student Math Journal Scores
Students’ writing communicated to me that I needed to go over with students how to write in math with deeper understanding, provide sentence starters, and let them practice with partners before having them write independently. There are nine students who did not grow in their deep understanding but ten students who did grow. Growth in writing score means students were explaining their answer with a deeper understanding than before. This deeper understanding was correlated to student achievement.
During the study I got to see how much students were using their vocabulary. For example, in the fourth math journal entry, students were explaining why they do not add the denominator of a fraction. I had one student use the word denominator and the rest of the students used “bottom number” when explaining their answer. This gave me information on what misconceptions or vocabulary to go over in the next lesson. The math journals also gave me information on when to adjust instruction. For example, I would adjust instruction by teaching line plots in the next lessons if students could not accurately explain line plots. The math journals allowed me to adjust which students participated in which groups. By reading the writing entries I knew which students required more teaching and I would put them in the correct skill level group. I used this information to change my groups during instruction.
Sometimes when students were answering the question, they were writing down words to help connect student to teacher or would write “I really don’t know.” Math journals allowed students to become more honest with the teacher. An observation I made from the math journal entries is students' were writing down more about the answer than they would say in class. For example, one of my students who was an English Language Learner, would not participate in class discussions but would write down one to two sentences in their math journals. The math journals made each student accountable for their answers.
Reasons why nine students did not grow included attendance issues, amount of support given, and the length of the study. Like the post-test, Student eighteen stayed the same in scores because they missed more school than others. Another factor is the amount of support given to these students. I had outlined in my action plan the support I was going to give students who were significantly below grade level. I did not account for students who are on grade level. The nine students who did not grow in their level of understanding might have needed more support such as more teaching of how to write in math or verbally explaining their answer instead of writing.
Another factor of the study is the interruption of snow days during the study. There were a total of eight snow days throughout the study which interrupted the flow of how many times the math journals were used. The nine students who did not grow might have increased in deep knowledge if the math journals were continued to be used after the study.
Student Interviews
Figure 8 - Survey Before Study
Figure 9 - Survey After Study
Before and after the study, students were asked their thoughts about math. According to the survey before the action plan, 15/19 students said they disliked math because it was “boring” or “hard”. This means 78% of the class did not like math and 21% of the class did like math (Figure 8). 68.75% liked math and 31.25% disliked math from the survey after the action plan (Figure 9). Over half of the students enjoyed writing in math journals after the action plan (Figure 10). Only a fourth of the class did not enjoy writing in math journals and thought they were “boring” or "hard" (Figure 10). For these students I wondered if I did not provide them enough support. These supports include more teaching of how to write in math and verbally explaining their thinking instead of writing. I wondered if I gave these students the same support whether they would have enjoyed the math journals more.
Figure 11 - Students' Comments before Study
Figure 10 - Math Journal Feelings after Study
Figure 12 - Students' Comments after Study
Triangulation
I believe the study was successful in increasing student achievement because it helped students create deeper understanding. I believe the study helped students in understanding how they got their answer in math by explaining their answer in writing. I believe this also provided me an opportunity to adjust instruction if there was a need shown in the math journals. I believe students changed their attitudes about math because they were engaged with the writing part of the math journals. Many students had said during the interviews that they would rather explain their answer to one problem than do worksheets. After doing math journals, I noticed students can apply math skills in areas other than worksheets. From my informal observations, I saw students become excited when the math journals were being passed out and when they received feedback. The study was effective in allowing students to become engaged and increasing their achievement in math.
Impact on Students
Students’ attitudes about math after the study and their deeper understanding were connected. Students' deeper understanding increased from the beginning of the study to the end because students enjoyed writing and enjoyed receiving written feedback. Giving students feedback after each writing entry allowed them to self-reflect on how they were doing when explaining their thinking. Students were trying to connect with me by writing in response to my feedback, which facilitated relationships between students and I. I know based on this that students enjoyed reading the feedback. Students’ increase in deeper understanding also related to their post-test scores. When students were developing a deeper understanding of the content, they were writing with more understanding which led to increased student achievement. Many students showed growth and the other students did not show growth due to the lack of deep understanding in the post-test or lack of involvement. Not all students got the opportunity to explain all of their answers because of questions where students had to justify an answer, attendance issues, and the limited time of utilizing the math journals.
Practices and Interactions of Researcher
During the study, my teaching was broken down into three different sections. First, I did a warm up relating to the content with the whole class. This was where I discussed misconceptions I saw in the math journals. Then the whole class was split up into differentiated math groups according to their pre-test scores and writing entries. During the educational video students were either watching alone or with partners. Students went back to their seats and would do the math journals towards the end of the lesson independently. I would pose the question and students would respond to that question in writing. The math journal entries and post-tests were done by each student individually.
One of the factors that affected my study was the amount of snow days. During the study, there was a total of eight snow days. This affected how the study impacted students and their progress in math. There should have been more time to use this strategy because it was effective for students in the middle of the study. My goal was to use math journals three times a week. Some weeks were only twice because of the snow days. I stuck with the schedule I had planned but some days were changed.
To conclude, writing in math does increase student achievement by developing a deeper understanding through writing their thoughts. Writing in math does increase student achievement if students get plenty of opportunities to explain the whole reasoning instead of just the answer itself. Writing in math allowed my students to become comfortable with math and to be open to learning math which related to increased student achievement.