Written Communication in Math
Data Collection Methods
Pre-tests and Post-tests
A piece of quantitative data collected throughout the study was unit/topic pre- and post- tests. These tests were curriculum based and showcased main ideas and concepts that were covered during the unit. The pretest was used created using the post - test as a guide, as pretests are not present in the curriculum. These tests were used because the question formatting, language, and illustrations matched those that the students were already familiar with. This pretest was especially helpful because students were able to practice skills daily and then be assessed in the same manner at the end of the unit using the posttest. I utilized both a pre and post test to showcase the growth from before the unit introduction through its duration. The pretest was also used for differentiating throughout the math topic. It helped define areas of need for individual students that would be addressed and practiced over the course of the unit. Initially, student groups were created based on specific data that was determined by the pretest. The pretest data also provided me with students who would need an extension of skills, as these students demonstrated mastery before instruction. This data was used because my goal was to improve overall math understanding by communicating about math and these tests showcased their improvement over the course of the study.
Pre-Test
Post-Test
Example of Cube Pattern Problem that Students Solved
Excel Spreadsheet of Collected Students Writing Scores
Example of Written Feedback that Students Received
Math Journal Entries
The next data collection method was math journal entries. This data collection method was informal. During this method, students would write a response to a question that was posed in their math journals. For example, if a lesson was focused on repeating colored cube patterns, students would receive a picture of a repeating cube pattern and explain how they use the cube train to help solve multiplication and division problems. Each day that students wrote in their journal, there was a group of six to seven students' math journal entries that I would read and provide written feedback to. I created a rotating schedule that ensured I was providing feedback to all students at least once a week. By dividing my students into small groups and creating a rotating schedule I was able to provide more meaningful feedback to each student. In order to ensure that I was providing feedback that was equitable, I was utilizing proficiency scales to help guide my feedback. Therefore, when I was looking at students journal entries, I was looking for the same indicators such as what vocabulary was being used. Additionally, even though I only collected a small group of journals each time they wrote, students received feedback on the same journal entry. This helped to ensure that students were getting feedback that was consistent yet individualized.
During the study, the math journals were graded on a proficiency scale based on the use of vocabulary and the level of understanding written. Before specific writing strategies in math were implemented and used, I used students communication score on their first math unit test as a baseline. I was then able to compare the baseline to the communication score on their math unit test that was given during the duration of the study to see growth of their mathematical communication and understanding. In order to help keep track of students entries throughout the study, each time that I provided feedback I collected data on the score that each student would have received. The scores that I collected were put into an excel spreadsheet so I could track how students were doing and the growth that was happening. However, students only received scores on their writing on their baseline and final writing entries. The scores that were collected based on their math journals was for myself to track the growth. Students were strictly receiving handwritten feedback within their journals.
Math journals were best chosen for my study's population because I knew my students had an interest in explaining their thoughts and ideas in math. During the school year my students had shown me that they enjoyed expressing their thoughts and ideas about math and understanding the why behind math concepts. I used math journals to hook their fascination of wanting to understand math at a deeper level. I was able to collect informal data about how students were doing in each lesson where the math journals were used. The writing communicated how students were showing their deep understanding of each topic. This was used to monitor how students were approaching their answer during the durations of the unit. I was able to understand how students came to an answer or how deeply they understood a topic or concepts by reading their journal entries. Additionally, I was able to clearly see what math vocabulary that students were understanding and able to use in their mathematical writing.
First Proficiency Scale Indicator
Student Example of a Score of Four on Post-Test
Score of Four Indicator on Proficiency Scale
The score of four is given when a student has gone above and beyond to demonstrate mastery of a skill. Specifically, the student demonstrates applications that go beyond what was taught in class.
Student Example of a Score of Three on Post-Test
Score of Three Indicator on Proficiency Scale
The score of a three is given when a student has demonstrated proficiency in the skill or standard. Specifically, it means that the student has met the standard to what was expected and taught in class.
Student Example of a Score of Two on Post-Test
Score of Two Indicator on Proficiency Scale
The score of a two is given when the student has gained an understanding of the vocabulary and simpler processes of the standard. However, the students has not yet met the standard.
Student Example of a Score of One on Post-Test
Score of One Indicator on Proficiency Scale
The score of a one is given when a student can achieve partial success in understanding the vocabulary and simpler processes involved in the standard with help.
Second Proficiency Scale Indicator
Student Example of a Score of Four on Post-Test
Score of Four Indicator on Proficiency Scale
The score of four is given when a student has gone above and beyond to demonstrate mastery of a skill. Specifically, the student demonstrates applications that go beyond what was taught in class.
Student Example of a Score of Three on Post-Test
Score of Three Indicator on Proficiency Scale
The score of a three is given when a student has demonstrated proficiency in the skill or standard. Specifically, it means that the student has met the standard to what was expected and taught in class.
Student Example of a Score of Two on Post-Test
Score of Two Indicator on Proficiency Scale
The score of a two is given when the student has gained an understanding of the vocabulary and simpler processes of the standard. However, the students has not yet met the standard.
Student Example of a Score of One on Post-Test
Score of One Indicator on Proficiency Scale
The score of a one is given when a student can achieve partial success in understanding the vocabulary and simpler processes involved in the standard with help.
Observational Notes
Observational Notes collected by CADRE Associate
Over the course of the study, observational notes were collected during verbal interactions that I had with students. This data was collected during math talks, student conferences, small group work, and feedback or share time at the end of a lesson. These observational notes were either completed by my CADRE associate or myself over the duration of the study. My CADRE associate came in once or twice a week over the course of the study to collect this data. Additionally, I collected data based on information that I was gathering about my students' level of understanding on specific skills or concepts. The data that my CADRE associate collected provided information in regards to the level of questions that I asked students, the wait time I provided, what students I called on, and the students' response. This data source was beneficial to my study because it provided insight into what students were given an opportunity to communicate about math verbally and if they were having to tap into a deeper level of thinking when responding to a question. The notes that I collected over the course of the study helped to inform the level of understanding that students had based on skills or concepts that we were learning that day. This data source helped me to have another data point to consider when creating homogeneous groups as we moved throughout the unit and onto to new skills or concepts.