Data Analysis

Pre-Test and Post-Test

Pre-Test and Post-Test Per Student

The pre-test, shown in purple, was given to students before the beginning of the action research project. The post-test, shown in blue, was given after students received instruction in writing about math. Student scores were converted to percent correct to accurately compare pre and post test performance. The graph shows that all students grew from the pre-test to the post-test. There are varying levels of growth in the students who participated in the study. No student was able to get all questions correct on the post-test. This may be due to the deferred start of my study caused by back-to-back snow days. The snow days caused a delay in the pacing of lessons and students were not able to receive any math instruction on constructing multi-step equations based on word problems. This concept accounted for 17% of the total questions on the pre and post tests. Students three, four, and five all grew from the pre-test to the post-test, but did not show mastery of the topics covered throughout the study. For the purpose of this study, mastery was defined as achieving 80%. These students missed three or more small group sessions due to sickness or other required interventions. Student growth may have been more significant if they were able to attend all sessions and respond to written prompts. Since they missed three or more sessions, they also missed multiple opportunities to receive specific feedback regarding their journal entries and thought process on those concepts. Based on the pre-test information, student two began the study with more background knowledge compared to their peers. The data demonstrated that all students benefited from writing strategies implemented through small group math instruction. Students' overall performance increased from the pre-test to the post-test. Students also demonstrated they were able to approach new mathematical concepts by transferring critical thinking strategies learned throughout the duration of the study.

Pre-Test and Post-Test Per Question

This chart shows the percentage of students who answered questions correctly. The pre-test data is shown in purple and the post-test data is shown in blue. The graph shows that more students were able to correctly answer on all questions except one. Question five was the only data point that did not show any growth. This may have been caused by student guessing. Questions fourteen through sixteen covered the standards that were taught in a new unit of district provided curriculum. Snow days and schedule interruptions led to less small group time. We were unable to get to all scheduled lessons and journal prompts. Though these topics were not all explicitly taught, there still was an increase in overall student performance. If students had received targeted writing instruction on those topics, there may have been a more significant increase.

T-Test Results

A paired-sample t-test was conducted to determine if the use of written communication strategies would have an effect on students achievement in number sense and overall mathematical reasoning. There was a significant difference in the scores prior to implementing the writing strategies (M=42.81, SD=9.85) and after implementing (M=82.86, SD=7.12) the written communication strategies; t(7)= 8.53, p =0.00007. The observed standardized effect size is large (3.22). That indicates that the magnitude of the difference between the average and μ0 is large. These results further prove that the use of written communication strategies in mathematics had a positive effect on student achievement. Specifically, the results suggest that the use of writing strategies in mathematics increase student number sense and mathematical reasoning abilities.

Math Journals

The left graph shows the journal responses that were scored by myself over the course of this research study. The graph on the right shows the journal responses that were scored by students over the course of the research study. Green represents students who scored as ‘on target’, yellow represents students who scored as ‘approaching target’ and red represents students who scored as ‘below target’. Each bar illustrates each graded journal entry and the number of students who scored on target, approaching target, and below target. The first journal entry labeled ‘baseline’ asked students which number would they add first in the equation 4+4+6. This prompt required students to have a fluid understanding of addition properties, number sense, and their ability to justify their choice. The journal entry labeled ‘final’ asked students which numbers they would add first in the equation 2+3+7. This prompt required students to have an understanding of addition properties, number sense, and students' ability to support their choices. The initial entry showed that most students understood the concept of addition strategies and how to find the correct solution, but they struggled with having a detailed enough explanation, using appropriate math vocabulary words to support their answer, and fluidity in number sense.

The baseline journal prompt was given to students before any written instruction. The students and I assessed their performance separately on rubrics. In the initial entry, most students graded themselves as ‘on target’ as shown in the graph on the right. When I graded the baseline, most students were in the ‘below target’ category. This was due to the students' lack of math vocabulary and processing abilities. This demonstrated that I needed to be explicit with my writing instruction and reteach the rubric so students could see an example of an ‘on target’ journal response. Journal entries were written to match each level of the rubric so students could have concrete examples when assessing themselves and their peers. After students were able to see these samples, there was more consistency between their self-assessments and the rubrics that I completed. While there were some discrepancies further along in their self-reflections, students demonstrated that they understood the expectations for their math journals

Each week, students were required to assess their own journal entry and create a goal for themselves moving forward. After three weeks of students completing these rubrics on their own, they were paired and asked to complete rubrics for their partner. After students scored their partners entry, they collaborated to come up with a goal for the following week. When looking through student goals there were a few common themes that arose. The pie chart illustrates the common themes students centered their goals around. The most significant theme was goals surrounding the use of more mathematical vocabulary in their entries. More than half of all goals written throughout the duration of this study focused on vocabulary. This was a major theme because the entirety of the study consisted of three different units representing a multitude of math concepts. The amount of new vocabulary students were exposed to in six weeks was substantial. It may be beneficial to examine one topic more in-depth over a period of time rather than multiple topics covering many concepts.

The second theme students centered their goals around was the need for a more detailed explanation. This accounted for roughly a quarter of all goals written throughout this research study. Again, over the course of this study, multiple concepts were taught. The short period of time allotted for each concept in the curriculum may have contributed to students inability to compose in-depth responses on a given topic.

Observational Notes

Observational notes were taken on one student at a time. These notes were taken during whole group, small group, and student conferences. The notes allowed me to see which students were able to correctly use math vocabulary, break down their thinking into smaller pieces, and transfer their knowledge from small group instruction into whole group lessons. At the beginning of the study, students struggled to incorporate the appropriate math vocabulary into their conversations about math. Most students would try to use math vocabulary, but they were not able to use them in the correct context. As students received written feedback and instruction strategies, they were able to have a more functional understanding of the vocabulary. I observed that students were more willing to attempt to use math vocabulary once they had been given feedback on how to accurately apply said terms. Over the course of this study, I was able to observe students increasingly participating in whole group discussions and their journal entries became more thoughtful. The pictures below show the notes taken throughout the study. Early in the study, this student struggled to use math vocabulary correctly, rarely shared in whole group lessons, and could not expand on their thought processes. The final time this student was observed, they increased the number of times they shared in whole group lessons from zero to four. When asked a question, this student used to sit quietly and was unable to express their knowledge. Towards the end of the study, this student was able to clearly express their thoughts during a conference in the final observation.

Likert Scale

Students were given a Likert Scale at both the beginning and end of the study. The aim of this Likert Scale was to assess how students' feelings about mathematics changed over the course of this study. Students were asked to assess themselves in four areas. These areas were: I like learning about math, I am good at math, I feel comfortable using math vocabulary, and I can explain my mathematical thinking clearly. Before implementation, 42% of students had stated that they did not enjoy learning about math and 42% stated that they sometimes liked learning about math. After implementation 42% of students stated that they sometimes liked learning about math and 28% of students always liked learning about math. There was an overall increase in students' attitudes about learning math. 57% of students responded that they were never good at math prior to the implementation of the study, 42% responded that they were sometimes good at math, and 0% of students responded that they were always good at math. This information indicated that my students had a negative self-image regarding their ability to succeed at math. After implementation, 14% of students responded that they were never good at math, 71% of students said that they were sometimes good at math, and 14% of students said that they were always good at math. Looking specifically at the student growth in their ability to succeed in math, all students changed their perspective except two. These two students missed three small group lessons. This may be a possible explanation as to why they continued to feel that they are never good at math. Implementing writing in mathematics increased most students' beliefs that they could be good at math.

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