Data Collection Methods:
- Aimsweb Math - Number Comparison Fluency-Triads (NCF-T) and Mental Computation Fluency (MCF)
- Timed Math Computation Assessments
- Student Interviews
Purpose:
I chose the data collection forms listed above because these methods were the best ways to see my students' growth over time in the area of number sense.
Aimsweb Math:
I chose to implement two different measures of Aimsweb Math because it was an assessment system that could be used for frequent progress monitoring. At the time my study was conducted, the Aimsweb program was the district’s benchmarking program used to monitor student progress in the areas of both math and reading. The Aimsweb Math system included assessments on different standardized measures that covered a range of topics. The measures I specifically used were Number Comparison Fluency-Triads (NCF-T) and Mental Computation Fluency (MCF). Such data facilitated progress monitoring in number sense, and helped me determine how to group students when working with them in small groups during guided math.
Math Computation Assessments:
I implemented three Math Computation assessments at the end of the third quarter. The Math Computation Assessments were three separate assessments which third grade teachers in the district are required to administer for five minutes at the end of each quarter. I used the collected data at the end of my study to determine growth in math computation in addition, subtraction and multiplication.
Student Interviews:
I conducted student interviews at the beginning and conclusion of implementation to give me insight into how familiar my students were with the area of number sense and to see what strategies they found beneficial to their learning in math.
Aimsweb Math:
I chose to implement two different measures of Aimsweb Math because it was an assessment system that could be used for frequent progress monitoring. At the time my study was conducted, the Aimsweb program was the district’s benchmarking program used to monitor student progress in the areas of both math and reading. The Aimsweb Math system included assessments on different standardized measures that covered a range of topics. The measures I specifically used were Number Comparison Fluency-Triads (NCF-T) and Mental Computation Fluency (MCF). Such data facilitated progress monitoring in number sense, and helped me determine how to group students when working with them in small groups during guided math.
Math Computation Assessments:
I implemented three Math Computation assessments at the end of the third quarter. The Math Computation Assessments were three separate assessments which third grade teachers in the district are required to administer for five minutes at the end of each quarter. I used the collected data at the end of my study to determine growth in math computation in addition, subtraction and multiplication.
Student Interviews:
I conducted student interviews at the beginning and conclusion of implementation to give me insight into how familiar my students were with the area of number sense and to see what strategies they found beneficial to their learning in math.
Analysis:
Aimsweb Math
After completing five Aimsweb probes, I saw growth overall, as depicted in the graph below. However, Probe 4 demonstrated a slight dip from Probe 3. I am uncertain as to why the dip occurred. I wonder what factor(s) interfered with the students’ output. As I reflected on the data, I noticed Probe 4 was administered the week prior to the students’ spring break in March. I question if the students’ anxiousness and excitement for spring break had an affect on their output. The Aimsweb math assessment system is a benchmarking program which I used to specifically measure Number Comparison Fluency-Triads (NCF-T) and Mental Computation Fluency (MCF). NCF-T and MCF are fluency measures that employ strict time limits designed to keep testing brief and to generate rate-based scores (e.g., number of items answered correctly per minute). Within each probe, the NCF-T score is combined with the MCF score and then reported as the Number Sense Fluency (NSF) score. The winter NSF benchmark for third grade is 23, and the spring benchmark is 31. When the students completed the first probe at the beginning of my study, only 12 out of 21 students had already met or exceeded the spring benchmark with a NSF score of 31 or higher. As a result of the outcomes from Probe 1, I extended learning by implementing the Xtra Math program to enhance computation fluency. I also created number comparison activities to incorporate into my math games station to improve my students' number comparison fluency. After my students completed the fifth and final probe in which data was collected, 19 out of 21 students had met or exceeded the spring benchmark with a NSF score of 31 or higher. Such data demonstrates the effectiveness that the strategies I implemented within the Math Workshop model had on student achievement in Number Sense Fluency.
Math Computation Assessments
The graph below shows the average score for the class of 21 students on each Math Computation Assessment at the end of the second and third quarters. The scores from the end of the second quarter are shown in pink, while the scores from the end of the third quarter are shown in green.
The Math Computation Assessments are considered district assessments, which requires third grade teachers to administer each assessment 4 times a year at the end of each quarter. The data shows that the average score of the class grew in each assessment from the end of the second quarter to the end of the third quarter. When reflecting on individual scores rather than the class average, all students made growth in at least two of the three Math Computation Assessments. Although the class grew in each Math Computation Assessment, one question I have is why the growth on the addition and multiplication assessments had greater gains than the subtraction assessment. I believe one possible explanation for this outcome is that a majority of the games I created for the games station involved the concepts of addition and multiplication. I wonder if incorporating more subtraction games, along with addition and multiplication, would enhance student achievement on the subtraction assessment.
The strategies used in this action research plan (e.g., Xtra Math) were extremely effective because not only did students grow in their math computation scores, they can all explain why and how to solve each type of problem. I observed the students ability to explain and solve each type of problem throughout the Math Workshop model. Specifically when working with students in skill groups, I witnessed the students “thinking aloud” to talk through the details of problems, the decisions they had to make as they tried to solve different problems, and the reasoning behind those decisions. Thinking aloud helped students, especially those who struggled with math, to clarify their ideas, identify what they did and did not understand, and to learn from others when they heard how their peers thought about and approached different problems. In addition, I heard students processing content together as they worked together at the game station. Throughout my study, students were using various techniques as they explained and solved different types of problems. Some students were using visual representations while other students were using manipulatives to express their thinking.
Students were also reflecting on the problem-solving process of different types of problems during the closure of the Math Workshop model. They were able to express their learning on a particular skill verbally and through writing. When students verbalized what they knew, it helped them reflect upon and clarify the problems they were trying to solve, and to focus on solving them one step at a time. During the closure of the math lessons, I was also able to formatively assess and monitor students’ progress, in order to adjust future instruction.
The Math Computation Assessments are considered district assessments, which requires third grade teachers to administer each assessment 4 times a year at the end of each quarter. The data shows that the average score of the class grew in each assessment from the end of the second quarter to the end of the third quarter. When reflecting on individual scores rather than the class average, all students made growth in at least two of the three Math Computation Assessments. Although the class grew in each Math Computation Assessment, one question I have is why the growth on the addition and multiplication assessments had greater gains than the subtraction assessment. I believe one possible explanation for this outcome is that a majority of the games I created for the games station involved the concepts of addition and multiplication. I wonder if incorporating more subtraction games, along with addition and multiplication, would enhance student achievement on the subtraction assessment.
The strategies used in this action research plan (e.g., Xtra Math) were extremely effective because not only did students grow in their math computation scores, they can all explain why and how to solve each type of problem. I observed the students ability to explain and solve each type of problem throughout the Math Workshop model. Specifically when working with students in skill groups, I witnessed the students “thinking aloud” to talk through the details of problems, the decisions they had to make as they tried to solve different problems, and the reasoning behind those decisions. Thinking aloud helped students, especially those who struggled with math, to clarify their ideas, identify what they did and did not understand, and to learn from others when they heard how their peers thought about and approached different problems. In addition, I heard students processing content together as they worked together at the game station. Throughout my study, students were using various techniques as they explained and solved different types of problems. Some students were using visual representations while other students were using manipulatives to express their thinking.
Students were also reflecting on the problem-solving process of different types of problems during the closure of the Math Workshop model. They were able to express their learning on a particular skill verbally and through writing. When students verbalized what they knew, it helped them reflect upon and clarify the problems they were trying to solve, and to focus on solving them one step at a time. During the closure of the math lessons, I was also able to formatively assess and monitor students’ progress, in order to adjust future instruction.
Student Interviews
Interviews were conducted at both the beginning and end of the action plan to 7 of 21 students. Students were asked to describe what strategies they had used to help them solve problems in mathematics. The same question was used in each interview, however, the responses I received at the end of the action plan had impressively transformed from the responses I received in the beginning.
The graph shows that at the beginning of the action plan, a majority of the students were capable of only explaining 1 to 2 strategies they used to solve math problems. In addition, I had one student who was unable to think of a specific strategy that was beneficial to learning math. The graph demonstrates the transformation in responses as all students were able to describe at least 1 or 2 strategies they used to be successful in solving different types of math problems. The majority of students interviewed made a change from describing 1 to 2 strategies, to communicating 3 or more strategies they were using such as mental math, drawing pictures, and using manipulatives. Throughout the action plan, students focused on the importance of making sense of numbers and were engaged in different activities to enhance their understanding of numbers. To see that 5 of the 7 students had shared multiple strategies that were implemented within the action plan means that the skill groups and math stations were effective.
The graph shows that at the beginning of the action plan, a majority of the students were capable of only explaining 1 to 2 strategies they used to solve math problems. In addition, I had one student who was unable to think of a specific strategy that was beneficial to learning math. The graph demonstrates the transformation in responses as all students were able to describe at least 1 or 2 strategies they used to be successful in solving different types of math problems. The majority of students interviewed made a change from describing 1 to 2 strategies, to communicating 3 or more strategies they were using such as mental math, drawing pictures, and using manipulatives. Throughout the action plan, students focused on the importance of making sense of numbers and were engaged in different activities to enhance their understanding of numbers. To see that 5 of the 7 students had shared multiple strategies that were implemented within the action plan means that the skill groups and math stations were effective.
Triangulation
When reflecting on my data collection, the Math Workshop model was proven to be effective in building students’ metacognition of math strategies. Students were able to identify and verbalize the strategies they utilized to guide them through the process of thinking and solving problems. Such evidence was cited through a thorough review of my data sources. Student interviews demonstrated that my students were able to communicate strategies they found beneficial in learning mathematics. In addition, the Aimsweb progress monitoring probes, as well as and the district Math Computation Assessments that were administered throughout my study demonstrated my students’ growth. The overall growth in student scores revealed my students’ abilities to implement the strategies they spoke about from the student interviews, to fully comprehend and compute math problems.