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Data Analysis

Pre-test and Post-Test
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The pre-test (blue) was given prior to the beginning of the math action research and the post-test (purple) was given at the end of the study. In order to compare the how students performed on the pre-test and post-test, their scores were converted into their overall percentages.  Based on the data, 20/22 students improved their scores from pre-test to post-test, zero out of 22 students’ scores stayed the same and two out of 22 students’ scores decreased. The graph portrays that a majority of students improved based on the growth between pre-test and post-test. I wonder, however, why tw0 students did not improve their scores, but rather went down? This may be because as the unit progressed so did the rigor of the content and they did not have enough time to engage with and grasp the new content as strongly as I would have hoped during the study. This data explained that a majority of my students benefited from six weeks of utilizing intentional math communication strategies.
 
In addition, a paired-samples t-test was conducted to determine if the inclusion of verbal and written communication strategies will increase students’ ability to communicate their mathematical understanding. There was a significant difference in the scores prior to implementing verbal and written communication strategies (M=47.73, SD=21.53) and after implementing (M=76.59, SD=9.46) the verbal and written communication strategies; t(22)= 6.73, p = 0.000000590237. The observed standardized effect size is large (1.43). That indicates that the magnitude of the difference between the average and μ0 is large. These results suggest that the inclusion of verbal and written communication strategies had a positive effect on students’ ability to communicate their mathematical understanding. Specifically, the results suggest that the use of verbal and written communication strategies increased students’ mathematical understanding.
Math Journal Entries
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The baseline score of their written math communication was given to students before the study began and the end score for their written math communication was given to students at the end of the study. Students had to respond in writing about a question they had knowledge on for the baseline and ending unit question. The baseline writing question was: Explain how multiplication and division are related. The ending unit writing question was: Describe the relationship between multiplication and division. Give examples to support your reasoning.

According to the baseline writing entries, there were a few different themes presented. Zero students scored a four based on the response given the the question. Six students scored a three showing a solid understanding of the concept. Nine students scored a two with showing some understanding of the concept. Seven students received a score of one with showing little or no understanding of the concept. This communicated over half of my class could not describe or explain their answer with deep understanding. As the study progressed, I collected data on students writing entries in their math journals. Based on these entries, I selected three entries to be checkpoints to check where students were at in the writing process. For these three entries, I read through students' math journal entries and assigned them a score based on the same set of criteria that their baseline and final entries were scored on. As you can see based on the graph, as the study progressed several students moves from scoring a one or a two on their writing entries to scoring a three and even a four. This collection of data and information allowed me to see that students were making gradual progress in their abilities to write about math. From date one to date three on the graph, I can see that several students improved their writing by moving from a score of a one to a high scores such as a two or three. 

 

During the study I was able to observe how often students were using math vocabulary. For example, in the third math journal entry, students were explaining how multiplication and division were related. I had four students use the word inverse operations and the rest of the students used “opposite” 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 was able to adjust instruction by teaching the distributive property if students could not accurately explain how or why you use the distributive property. The math journals allowed me to adjust how to group students on a day by day basis. After reading students' writing entries, I was able to identify what students were still having trouble mastering concepts or skills and I would put them in a small group so I could support them. I used journal entries to adjust my teaching and create small groups during the entirety of my study. 

 

Sometimes when students were answering a question in their math journal, they would be writing down words or ideas to connect themselves or the teacher to their thinking. Some students would be honest in their answer and respond with “I do not know” or “I’m not sure.” These math journals allowed students to become more honest with their level of understanding. A conclusion I came to as reading students’ math journal entries was that students were writing down more about the answer than they would feel comfortable saying out loud in class. For example, one of my students who was reluctant to share her thinking out loud for fear or being wrong would not participate in class discussions, but would write down paragraphs in response to questions in her math journal. These math journals held each student accountable for their own learning and answers. 

 

There could be multiple reasons that could factor into why six students did not grow which include attendance, amount of support given, and the length of the study. I had outlined in my action plan the support I was going to give would be to students who were significantly below grade level. I did not account for students who are on grade level. The six 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.

Observational Notes
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Throughout my study, my CADRE associate came into my classroom and observed me interacting with my students during math. Specifically, she was observing and taking notes regarding the questions that I was asking students throughout math. From these notes, I was able to count the total number of questions I ask. After determining the total, I was able to select which questions were asking students to explain their thinking. Using these two numbers, I was able to calculate the percentage of the questions that I ask during a lesson or math talk that asked students to explain their thinking. By analyzing that graph, I came to the conclusion that as my study progressed, so did my ability to ask students to explain their thinking. This piece of data does not directly tie to student growth, but these observational notes had a clear impact on my teaching abilities. Specifically, I grew as an educator who was asking more challenging questions and open ended questions. These questions gave students more opportunities to practice and refine their mathematical understanding. Therefore, as I refined my teaching practice, it provided students with more opportunity to grow.

Triangulation

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Students were able to verbalize their thinking process and explain how to solve problems, which in turn lead to increased achievement on tests and students’ ability to communicate their mathematical understanding. I can come to the conclusion that the study was successful in increasing student achievement in math because it helped students create deeper understanding of the content. Such evidence was cited through a review of my data sources. Math journals helped challenge students to understanding how they got their answer in math by explaining their answer in writing. These journals also provided an opportunity to adjust instruction if there was a need, based on observation. Finally, the pre- and post-tests administered throughout the study demonstrated the growth students made. The growth from pre- and post-tests, students’ math journals, and use of observational notes to refine and adjust my own teaching practices revealed that students were able to comprehend and explain their thinking when solving math problems or concepts. The study was effective in allowing students to become engaged through math communication that in return increased their understanding of math concepts.

Lingering Questions

  • What impact would there have been on students if I had started my action research at the beginning of the school year?

  • How much of the growth was gradual typical growth acquired throughout a school year compared to utilizing intentional oral and written communication strategies?

  • What other instructional strategies could I pair with this instruction to have a greater impact on my students’ math communication skills?

  • Why did two of my students overall percentages drop from their pre-test to post-test?

  • How could I have ensured that I was being more intentional when teaching and providing feedback?

  • Would this study still be effective if it was implemented when my students held little to no background knowledge on what math communication was? Or was this background knowledge pivotal for the rapid growth that I saw?

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