Rationale
Math Talk Moves
Increasing Students' Number Sense
Purpose
Statement
The purpose of my study was to determine if using math talk moves would increase student achievement in their number sense skills​.
Rationale
History
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My research project was centered around my five freshman geometry classes that consisted of 124 students. I wanted to implement literacy across content by using math talk moves in order to build my students' number sense, so that their conceptual understanding increased. As of the 2019-2020 school year there were 1,878 students in the building where I taught which consisted of eighty-two percent minorities and eighty-six percent receiving free and reduced lunch. I was one of the twelve mathematics teachers and one out of almost one hundred teachers at my school. Also, eleven percent of my students had some kind of individualized education plan, and they were mostly in mathematics.
Need
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The data that I collected from my students at the beginning of the year showed that there was a need in my students' numeric relationships and in geometry. According to Fall 2019 MAP math data, 99 out 124 students were below the normal grade level mean Rasch Units (RIT), which tested students' growth from year to year. MAP math data also found that 78% of my students struggled with numeric relationship skills and 79% struggled with geometry skills. The average test scores for the first three summative tests showed that 42% of my students performed at the advance level, 17% were proficient, and 41% were at basic or below basic. This data showed me that there were varied levels of student ability in all of my classes that needed to be addressed. Also, through observations students showed deficiencies in applying their vocabulary terms. Finally, my students needed many reminders to stay on task and engaged in activities. This showed me that either students were not understanding the material or they just didn't care. All of these data points combined showed me that there was a need in additional support or change in instruction to help my students increase their number sense and geometry skills.
Importance
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In every job and everyday life, communication is important and when it comes to using communication in mathematics, it is even more important, especially in real life. Math discourse is important because it allows students to get their thoughts out and develop their communication skills. Math discourse is defined as when both teachers and students communicate through written or oral conversations, usually about their thinking processes. When it comes to mathematical discourse some teachers like to use a strategy called math talk moves.
Number sense is something that almost all students struggle with, ever since they were little and even high school students struggle with number sense skills. According to the National Council of Teachers of Mathematics (2000), number sense is a “foundational strand in early mathematics education and develops as children understand the size of numbers, develop multiple ways of thinking about and representing numbers, use numbers as referents and develop accurate perceptions about the effect of operations on numbers'” (p. 80).
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As freshman, students take the Measures of Academic Progress (MAP) test three times throughout the school year: Fall, Winter, and Spring. MAP testing was a computer adaptive achievement tests that tested over mathematics, reading, and science. On average, freshman in high school were supposed to score at or above 230 Rasch Units (RIT) in mathematics. During the Fall, 25 out of 124 of my students scored where they were expected to. That means 80% of my students were behind in their MAP growth in mathematics. My students also struggled with the subgroups of numerical relationships, also known as number sense, and their geometry skills.
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To learn more about math discourse and how important it is to get students to talk through their thoughts and building their number sense skills, I have provided my Literature Review
Action
Plan
What was implemented
During my research, I implemented mathematical discourse in order to increase my students’ number sense skills. I focused on three different Kagan strategies that helped my students talk more and stay on topic. Kagan strategies are instructional strategies that get students to cooperate and communicate in the classroom. One strategy that I tried was all record round robin. This strategy allowed for every student to share an idea that he/she had and then everyone wrote down the ideas. Not only did this get students talking who don’t normally talk, but it also allowed students to write down other students’ thoughts. It allowed students to see other students’ point of views that they possibly didn’t think about. Another strategy that I used was Jot Thoughts. In this strategy, I had my students write down anything and everything that they could remember from last semester. Then I had them talk through which ones they wrote down and then come up with the vocabulary words that they forgot to write down. The third math talk move that I used was Agree or Disagree. I used this more during their warm ups because it allowed students to talk through their thinking and work on communicating respectfully. This strategy also required them to use their vocabulary words to help develop their thoughts and be able to discuss it with their classmates. For more details on the strategies see the data collection tab below.
Why were these strategies chosen?
My students became disengaged when they do not understand what is being asked of them or when they don't understand the content. My students have asked for more group work because they said, “ I do better in group work because I am able to talk through my thoughts.” These strategies were also chosen because not only do I want my students to talk through things, but I also wanted to make sure that they can get their thoughts written down. Research states that mathematical discourse helps students increase their math vocabulary. When students increase their math vocabulary, they are then increasing their conceptual understanding as well (Montague, Krawec, & Sweeney, 2008). The research also states that it would increase students’ peer communication about mathematics and their performance on high stakes tests. There are also more research that supports my strategies in my literature review. I also sat down with my department head and she stated that in order for students to learn more about geometry they need the chance to talk. Teaching geometry should be about 10 to 15 minutes of lecture and the rest of the time should be spent on discussions and working on questions.
Why are these strategies best for the population outlined in the rationale?
My students needed time to talk, but they needed to do it in a productive matter. Math talk moves are good for this population because it allowed students to get their thoughts out on paper. When students can talk through thoughts, they are able to get more than one perspective and understand the material more fully. The strategies that I chose helped students get their thoughts on paper as well and gave them ample amount of think time. They were allowed to use their notes and worksheets on their test, but my students struggled with knowing how to actually use their notes. I hoped that if they took more time to discuss the material, they would better understand it and know where they can find the material and how to use it on their test. I also hoped that at some point they wouldn't need their notes that much because that would show that they fully understood the material.
When was this implemented?
My study was implemented in all of my classes from January 9 through February 20, 2020. I first explained to all of my students why it wass important to hear other students' thoughts and what was expected of them before we started anything. I then discussed with my students that if they couldn't stay on task and do what was being asked of them to do, then they would have an alternative assignment. Next, everyday I did about 15 to 20 minutes of instructional time and then an activity that required math discourse. This process allowed for students to walk through their questions with a partner or a small group. Finally, we would come back together, go over the activity and then do a formative check. The assessment allowed me to determine if students understood the material or if they didn't. It also helped me determine exactly what my students needed to be successful in the unit.
Action Plan
Calendar
Action Plan
Calendar
How were diverse learning needs addressed throughout the study?
In my study, I used my students' MAP data to set up grouping throughout the unit. Everyday, I would pull a small group of my lowest students together, so that they would get more of the one on one help. This grouping also allowed me to meet my higher ability students' learning. While my lower students were working together, I asked questions to further my higher ability students' thinking. For example, once my higher ability students were done I would ask them if they could come up with other ways of solving the questions or to see how many different ways they could think about a certain question. Another way that I differentiated instruction was giving fill in the blank notes. This strategy allowed the English Language Learners (ELL) or those who had an Individualized Education Plan (IEP) to follow along and to know exactly where their learning was going for the day. I gave all students fill in the blank notes, so that the students who actually needed them wouldn't get singled out. When doing activities, I would always have the instructions written on the board while discussing the instructions and the instructions were on their worksheets as well. This technique allowed all types of learners to be met, except for kinesthetic. My kinesthetic learners were met when we did our similar triangles and overlapping triangles activity. These were our hands on activities throughout the study, and inquiry based as well. Also, since students took a formative assessment every day, I was allowed to address all students' needs. I would talk about common misconceptions and how we as a class could fix those misconceptions, and address anything that my students were not understanding. During the whole study, I encouraged all students to discuss with each other their findings and how they got their answers. The math talk encouraged ELL students to practice their academic conversations through the modes of speaking, listening, reading, and writing. It also was a way to build community and develop relationships in the classroom.
What were the culturally responsive practices that positively impacted student learning?
My data helped support culturally responsive practices in many ways. I gave all students fill in the blank notes, so that it made it easier for students to follow along, but it also helped my English Language Learners (ELL) and my students who have an Individualized Education Plan (IEP) be more successful. This helped my students because it taught them what parts are important to take notes on and how to keep their notes organized. I also incorporated worksheets and activities that students were able to relate to. I did a sugar packet activity that discussed the importance of how many sugar packets go into a soda and how ratios can be found all over the world. Another thing that I discussed was when I talked about right triangles, I talked about driving and how it is important to know your angles when driving. I discussed this example because my students were starting to learn how to drive and I wanted them to see why it was important to know about right triangles and how this information related to the real world.
Stakeholders
My internal stakeholders have helped support my study through the whole process. My department head stated that she would like me to focus on getting my students to talk more, so that's why I chose to focus on math talk moves as my capstone project. Next, I was lost on which unit to do my project on, so I asked for input from the teachers who taught the same subject that I did. These three teachers stated that I should do it over ratios and similar triangles. The reason was that they were more prepared for that unit, then the next unit. When students didn't understand certain concepts, I asked my special education co-teacher if she knew of anything that would help out students.
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My external stakeholders included my cadre associate, a professor at the university, and my capstone professor. My cadre associate was someone that I leaned on for a great deal of help and inspiration throughout my whole project. She helped my students understand the importance of talking through their work and how to use their binders more. A university professor gave ideas about what to implement in the classroom and was also someone who I interviewed for my literature review. Finally, my capstone professor helped determine what data to use and how to use it to benefit my students.
Data
Collection
What data collection methods were selected
Pre-Test & Post-Tests
Formative Assessments
Observations
Showed student growth and understanding of ratios, scale factor, and similar figures. They also showed if students could use previous content to help them determine if they had similar figures.
Showed that if implementing the strategies were making a difference in my students' learning and to see if their conceptual understanding was increasing.
Showed how many reminders that my students needed to get back on task. It also showed if my students were understanding the material or not.
Prior to implementing my math talk moves, I looked at the last summative scores as my students' pre-test scores. The reason was that everything that my students learned during the last unit they were going to need for the next unit. I also noticed that their scores were very low last unit, so I needed to do something else so that their scores would improve. The pre-test scores that were collected gave me a baseline score which allowed me to see if what was implemented made a difference. Gathering the pre-test scores helped me realize that my students needed something different. Based off of that, I wanted to get my students to talk more in the classroom and discuss their learning and mathematical findings with their classmates. The pre-test and post-test scores were data points that informed if math talk moves were increasing my students' number sense skills. The pre-test and post-test scores were based on a 4 point scale as required by the district.
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The 4 point scale was as followed:
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A was from a 4 to a 3.26
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B was from a 3.25 to a 2.51
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C was from a 2.5 to a 1.76
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D was from a 1.75 to a 1.01
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F was from a 1.00 to a 0
Pre-Tests & Post-Tests
During the implementation process, the formative assessments helped inform me if my students were understanding the content. There were 4 main formatives that were given. The first one was over ratios and it was a scavenger hunt around the room to find all the different ratios. These scores should have been high because they had worked with ratios before, but if they weren't it would tell me if I needed to spend more time on ratios with certain students. The next formative was working with scale factor and this was a new concept to students. Students had to use a ruler and a compass to determine the side lengths and angles measurements of each. Then they had to compare each set of triangles with the other and determine the scale factor of each group. It was a new experience to my students because we were applying it to triangles and how we can use triangles to determine if 2 triangles were similar or not, on the next formative. The fourth formative was titled flipped family and it worked with dilations and how to use a scale factor to determine the dilation of a figure. All formatives have been attached below.
Formative Assessments
During class, I kept a roster of everyone's name and I would mark down every time that I would need to remind him/her to stay on task. I did this to see if students were getting off task because they weren't understanding what was being asked of them to do or if they didn't understand the material. Every day I would keep track of who was getting off task, why they were getting off task, and at what times were they getting off task. I determined why they were getting off task when I would go ask them if they needed help. If they said that they didn't understand what they needed to do, I knew that wasn't because of the content and it had something to do with my instructions. If the student said he/she was unsure of what to do for everything, then I knew it was because he/she didn't understand the content. As for time of day, I wanted to see if the off task behavior occurred in the beginning, middle, or end of the day, but that was just information for myself not for my research project.
Observations
What strategies were implemented?
Students completed the Jot Thoughts strategy above. They were asked to write down anything they knew about triangles. Next, they shared what they wrote down and why. Then, they categorized all of their thoughts. Finally, everyone went around to each table to see if they could add something that another group forgot. This activity allowed students to get their thoughts down and then they had time to share with their table mates and not in front of the entire class. Quite a few of my students do not like sharing out during whole group, but would share during small group activities.
All Record Round Robin
Students worked on a worksheet, but they each wrote down their ideas first. Next, they shared what they wrote down with their group. After each person shared, everyone wrote down that person's idea. When everyone shared, they moved onto the next section of the worksheet and did the same thing again. This activity allowed every student to be heard even if someone had the same idea. This enabled students who normally don't talk to talk and discuss with their table group.
Jot Thoughts
Agree or Disagree
In agree or disagree, students worked on their communication skills and built their vocabulary. During an around the classroom activity, students individually worked on the problem and then talked with their partners as to whether they agreed or disagreed with their answer and why. This activity allowed students to figure out where they made their mistakes and gave students time to work through their thinking.
Data
Analysis
On average, most students increased their grade by 1.01. Since the school where I worked was based on a 4 point scale, 62 students increased by at least one letter grade from their pre-test. Another big improvement was that my students went from getting 18 Fs and 20 Ds to 0 Fs and 5 Ds. From the pre-test to the post-test, the data suggested that the strategies that were implemented significantly made a positive difference in my students' learning. It showed that my students really understood the material and allowed for a lot of growth to happen from student to student. Based on the scores, it shows that my hypothesis was correct, that students need math discourse in order to increase their number sense skills and to develop their geometry skills.
Pre-Test & Post-Test
Daily Number of Reminders
Day One
80
Day Three
59
Day Six
38
Day Eight
16
During my research project, I focused on how many reminders my students needed to stay on task. I chose this focus because my students tended to veer off topic when they didn't understand the content or the instructions. On day one, 72 students needed around 80 reminders to stay on task, but by the end of the study, they only needed 16 reminders. The 4 shapes above show that the reminders go down daily. This data tells me that my students were increasing their number sense skills because they understood the material more fully. They were able to talk with their group and discuss their findings, which allowed them to fully understand the concept. When going around and making sure that students were staying on task, the ones that weren't staying on task was because they didn't understand the content. I knew this because of the questions that my students asked. Their questions informed me if they needed to join the small group for more instructional time and help with understanding the content. When the reminders started to go down it informed me that my students were understanding the material more and building their conceptual understanding.
Pre-Test and Post-Test
Formative Data Collection
During the implementation of the strategies, I relied strongly on the formative data. The data informed me what my students understood and with what specifically they struggled. It also told me which students I needed to add to my MAP data small group, so that I could go more into depth of what didn't make sense to them. For the first formative, 90 percent of my students received As, which I expected because this was review from previous years when they discussed ratios. Formative 2, or my introduction to scale factor formative, was new content and it required students to work in a group and complete a task. This formative told me if my students were understanding what scale factor was. So, the 12.5 percent of students that didn't understand it were placed in my small group instruction the next day. This allowed me to see what exact part with which they were struggling. Next, my formative 3 was the application of scale factor to similar triangles. The results told me that students could apply their knowledge about scale factor to determine if two triangles were similar or not. As for formative 4, the scores told me that my students could also apply their knowledge of scale to dilations. The three main
topics of ratios, scale factor, and dilations were the three mathematical standards that the students had to pass in order to be successful on their test. Their formatives would tell me which students needed more instruction and which students understood the material. It would also help me to determine which students would end up passing the test.
Triangulation
When looking at all the data above it is clear that implementing math talk moves increased my students' number sense skills. I used the pre-test scores to guide my instruction on what unit to do the research over and what exactly I needed to teach my students to be successful. I then implemented math talk moves, so that my students could talk through their findings and thoughts. This strategy helped them on their formatives and then during their activities I would observe if and when students would get off task, and then determine why. This helped me determine if some students needed to be added to my small group. Finally came their post-test, which helped me determine that implementing math talk moves increased my students' number sense and geometry . The variety of data collection methods created reliability to my study as I was able to see what students learned from different perspectives.
Reflection
Challenges
When I first started this research project I really just wanted to focus on my class periods at the end of the day. They were my classes that had the lowest MAP scores and were academically low in mathematics. I implemented everything the same in every class, but due to students not turning in their assignments and not being there I had to change my plans. So another challenge was block scheduling, which is where students have 4 classes on one day and 4 different classes the next day. I changed my research to include all of my geometry classes because when only focusing on a certain block it didn't support my research. Another challenge with block scheduling was that two snow days fell on the same block day and it was during MAP testing. I had to finish MAP testing, but then try and catch my A day back up because they were 2 days behind. I was stressing out, so I asked a fellow Geometry teacher how I could catch them back up and I never knew how much I could rely on fellow teachers until that moment. He was also one of my internal stakeholders that helped with my project.
Successes
Findings
One of the first successes that I felt during this project was before I even told my students what I planned on doing. I wanted to know what my students wanted in the classroom, so on the first day back from winter break we did an activity where they wrote down everything that they wanted in a classroom. In every single class, my students wanted more time to work on examples and work with their fellow classmates. Another success that I had was when I started implementing the new strategies. My students didn't do well with change and liked the set schedule of what I had done in the past, but when I started doing more group work my students were doing very well with it and actually enjoyed mathematics. Another success was that my data actually supported my purpose statement, which was that implementing math talk moves would increase my students' number sense skills. My final success was finding new ways to implement math discourse in my classroom. I had always wanted my students to do more of the learning, and when I got students to talk through the math they tended to learn more. I had also been told that teachers needed to make their students do more of the work than the because it allowed students to learn more and be more successful.
One of my first findings was that when I lectured for a large portion of the class my students wouldn't learn anything. A better way to teach a lesson was first do the following
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5 to 8 minute warm up
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10 to 15 minute lecture
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30 to 45 minute activity
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10 minutes to go over the activity and what it had to do with the learning goal and higher level question (HLQ).
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If time allowed another activity
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Come back together to discuss the activity
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Some kind of formative check
This type of gradual release lesson allowed students to do more of the learning. Another finding that I had was when I wanted students to talk about mathematics I had to teach them exactly what I was looking for and I also modeled what that looked like. I also noticed that once students started getting off task that was when I should move on. My final key finding was that students were more likely going to participate in something once they knew exactly why they were being asked to do it. During the implementation process, I made sure to always go back and state the learning goal and higher level question (HLQ) for the day. This allowed students to know exactly what they were learning for the day and made them accountable during their formative check.
Impact
This study has shown me what teachers do every year when things aren't going their way. They do research to find out what they need to do that might help things get better and change their routine. The research has also taught me why it is important to get your students to talk through their work more. It allows students to build their conceptual understanding and to build community in the classroom.
Changes
Something that I wish I could have changed about this study is that I wish I could have seen my students' MAP scores in April and use it for my data. The MAP data shows students' number sense skills, but since MAP testing happened during the beginning of April I was unable to use it. Another thing that I would change is implementing more math discourse.
Moving Forward
Next year, I plan on implementing math discourse from the beginning of the year. That way I can do some research to figure out how I can get my students to go through productive struggle. This year my students struggled with productive struggle and gave up once they didn't understand something. I plan on doing some research on how to start teaching students how to experience productive struggle so they can extend their thinking.
What I am still wondering
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How can I increase Bs and Cs, and decrease the number of Ds and Fs?
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What can I start implementing, so that I can take my students thinking to the next level?
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What other strategies will get students to think more?
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How can I get my students to be more accountable for their work?
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How do I implement these strategies in the beginning of the year?