DATA COLLECTION METHODS
Qualitative and quantitative data were collected for my action research to show student growth in math achievement through the implementation of differentiated instruction. Data was monitored and collected over the course of a 6-week collection. Through this period of time, students covered two math topics: geometry (shapes and symmetry) and money (names, values, and counting). The four data points triangulated to represent this growth include Climate Surveys, Attitude Survey, Quick Checks, and Pre and Post Tests.
ATTITUDE SURVEY
I wanted to see how my students felt about math before the implementation of my differentiated math study. Students filled out a questionnaire about their attitude towards math in the classroom. Students marked yes, no, or I don’t know based on their feelings toward each statement about math.
During the course of the study, student progress was monitored by informal data collections of engagement and positive attitudes. After analyzing my practices and interactions, I noticed my students more engaged which caused a decrease in student behaviors. As my students gained stronger connections through the implementation of my research strategies which provided choice for how they best understood the geometry and money concepts. Through my observation, the use of BAWD engaged my students, which led to an increase in math enjoyment. Although “act” was apart of BAWD, my class did not use this strategy often. I wonder if this was caused due to my lack of "expressive acting" as a form of instruction. If I shared more excitement for acting out and set strong expectations, would my students use "act" from BAWD as a strategy to learn the math concept?
Reasoning
This math survey was selected for simplicity and clarity. it provided. I read aloud the statements to my students and answered any questions before the survey was taken independently at their desks to help retain focus and for students to work at their own pace. My students put a lot of thought and effort into their answers and I did not want to rush them. This math survey best fit the needs of my students because of the “I” statements. My students have used “I can…” statements for their learning goal.
Particularly, I cherished the statement “I like to work with a partner or small group during math” because of the insight I received. At first, I assumed all of my students enjoyed working together. This was due to the interactions with my students and the amount of group work incorporated through the day. Did my need for building a strong classroom community fuel the need I had for my students always working with a partner or group? With the information I received with 5 students who preferred to work alone, my instruction was altered to allow more independent work as a choice for my students. Another reason I chose this math survey was to monitor my students’ feedback on their math confidence throughout the study. I monitored their confidence, informally, through the strategy of Math Talks and conversations within the classroom.
ANALYSIS
OF ATTITUDE SURVEY
The qualitative data collected through this attitude survey enriched my students’ attitude towards math improved over the course of my action research. My class went from 45% of my students enjoying math to 77% enjoying math in only six weeks.
Through purposeful questioning, BAWD strategy, skill-ability math sheets, and engaging math games, students were taught to use these strategies to build knowledge and confidence in math. I met my students at their own learning level, through the differentiated style of teaching. This attitude survey showed me 24% of my students prefer to work by themselves. Being culturally responsive, I altered my instruction by allowing students to work independently, or with a partner, during math.
As you can see, this student preferred to work alone. To differentiate my instruction, I altered the layout of partner work and allowed this student to work independently. Through the use of Math Talk and being allowed to work alone, this student showcased positive attitude growth towards math.
By the end of my study, this student believed they were good at math, could work through challenging problems and would ask for help when confused. This data was monitored through informal classroom Math Talks and the amount of questions Student 1 asked. I wish I kept track of this data on a chart, rather than a post-it note. By the time I was able to reflect on the math lesson and Student 1, it was difficult to remember which type of question they asked. If I kept the data on a research-based form, it may have benefited the reflection and guidance for the next math lesson. With the increase of questions asked, so did the mathematical growth on the Pre and Post Tests. For Geometry, Student 1 improved by 33% and increased by 41% on the geometry unit.
"Math is now a fun challenge and I like it because I am good at it.” - Student 1
QUICK CHECKS
The Envision Math curriculum provided aligned formative assessments, Quick Checks, to access student understanding of the math lesson they received during whole group and guided instruction. After my students completed their math mat, they completed a Quick Check with 4-5 questions to show what they know on the newly learned math concept. These were chosen for formative assessments because they allowed quick, flexible grouping, to help plan my next step with instruction.
My instruction was altered through the math sheet the student completed next. I planned my instruction for flexible groups based on the daily math learning goal. Groups were based on the Quick Check score through the provided rubric. Students were given a prescription of differentiated instruction: Intervention, On-Level, or Advanced.
Student progress was monitored during the course of the study by data collection of the number of times a student received enrichment, extra practice, or intervention on a google document. I would collect the Quick Checks, mark their scores, and provide the differentiated instruction. The data collected during the course of the study was utilized to inform my instruction on the level of BAWD strategies, teacher guidance, and level of Envision math game to master the math concept.
Reasoning
The envisions math curriculum provided a score sheet with student examples as a baseline of scoring. The Quick Check prepared my students for the Post Test through the format of questioning with depth and complexity. Analyzing my interaction of depth and complexity within the same math lesson, allowed me to stretch my own thinking and planning to keep the learning goal active for all students. This was the best data method as a formative assessment because it occurred outside of the learning. If students completed the Quick Checks at the same time, would I receive more data from the amount of time the students spent on this assessment? My students completed their guided math practice at different times. Students were able to complete the Quick Check independently because of the student-friendly layout of the sheet. This allowed me to provide extra instruction to students in need. With only 3-4 multiple choice questions and 1 written response, scoring was quick and easy to provide the next step of instruction.
ANALYSIS
OF QUICK CHECKS
During the course of the study, student progress was monitored by scores on these formative assessments. I kept a Google Document to document the scores of eight students. These students were selected at random to gain a feel of the class as a whole. Within the six weeks of my study, nine Envision math lessons were taught which correlates to the nine Quick Checks given. Quick Checks were not given daily, due to my district’s two snow days, altered instruction for the break down of the first money lesson into four days, and two review days to prepare for the two testing days. Break downs of a lesson and review/testing days did not require Quick Checks but instead allowed more instruction for the previous math concepts.
Student progress was monitored by the score which led to the differentiated instruction for each student of interventions, extra practice or enrichment. This data was used for immediate planning of instruction for the next step of each student in the math lesson. Students received a score and grabbed the appropriate level of math sheet to begin the next step of instruction. I noticed, through my planning, students would be very excited when they were told to grab a blue sheet (enrichment). They would not be excited if I asked them to grab a green or yellow sheet (practice/intervention). How could I elevate the emotional connection to their score and the next step in their instruction? This may be done by having all sheets on white paper to share a sense of equality.
Quick Check scoring + graph: Students received a score of 3 (full bar) if they got 100% on the Quick Check. Students who missed 1 or 2 points, received a 2 (2/3 of a bar) and worked on a sheet that provided more practice. Students who missed more than 2 points received a 1 (1/3 bar) and worked on a Reteaching/Intervention sheet which broke down the learning goal step by step.
STUDENT C
Student C had 4 colors which means they have received scores for only 4 Quick Checks. I wonder why Student C was missing scores. This could be due to the fact of Student C was often late or absent three times throughout the week. Our math block is in the morning, which caused a lack of instructional time for Student C. I wonder if I were to switch our math time to the afternoon, if this student would make more achievement. The lack of instruction time during math confirms the missed Quick Check data points.
STUDENT H
This graph showcases the enriched data of Student H who, at the beginning of my study, performed markedly above grade-level expectations. To interpret the data from study H, they received the full three points on Quick Check #3, 4, 6, 7, 8, and 9. On Quick Check # 1, 2, and 5 they scored extra practice.
To ensure an active learning goal, this student was provided differentiated instruction through enrichment. I collaborated with the High Ability of Learning Education (HALE) teacher to align an enrichment tub filled with hands-on activities and math packets. This added depth and complexity to differentiate the instruction to receive purposeful instruction through all learning levels of the classroom.
Student H surveyed ‘yes’ they like school and ‘no’ to working in groups or partners on the Attitude Survey. Clearly, this student excels in mathematics which showcases their school enjoyment. The increase of scores and the 6/9 scores for enrichment explains the interest of working alone and excelling with the math concepts.
PRE TESTS + POST TESTS
Curriculum-based tests were given to the students as an opportunity to show what they knew within the upcoming math concept. The questions were closely correlated to the format in which the math assessment would be given. The Pre Test allowed me to gain an understanding of my students’ knowledge to introduce the new topic at appropriate skill levels. The Pre Tests provided a baseline which was used to see if the average scores collected from the Post Test increased throughout my action research. The groups for math instruction were guided by the Quick Checks. The Pre Tests allowed me to focus on the content which needed more practice, such as the names and values of coins. This lesson was broken down into four days of instruction to focus on the quarter, nickel, dime, and penny. Utilizing the Pre Tests, I noticed the students needed to work with hands-on materials and BAWD strategies to grasp the geometry and money concepts. Enrichment was influenced by having the advanced group use their mental math to solve the problems, before using materials or pencil and paper. This variety of instruction would give me insight if my differentiated math instruction had an effect on learning. This was chosen to see an overall effect of using BAWD strategies, mind maps, and purposeful questioning to guide learning through the two math concepts. Having a before and after view of the whole class during the study allowed me to see improvements through differentiated math instruction
Reasoning
This data method was best for this population of students because of the clarification needed and the direction of where to start the math lesson. My students were very excited to show me what they know before I taught them the math concepts of geometry and money. About 7 of my students want to be teachers who saw this as an opportunity to teach me what they know. This data was used to create a mind map to show what the class knows as a whole, what they will learn, and what they will know after the lesson. The Post Test was used to visually see the math achievement growth of each student. These were chosen because they aligned with a curriculum as a DCA and math topic test. Again, this population is very motivated and loved to be challenged. This fueled their motivation to learn more through the math lessons, in order to show more growth, after the math topic units.
ANALYSIS OF PRE TESTS + POST TESTS
For my action research, I averaged my students’ data from the Pre and Post-tests through the six weeks of action research. This graph shows my whole classes data points for topics of geometry and money.
Geometry, the first math topic in my study, clearly showed an increased of achievement from before to after my study. The class average before the study was 70% and a class average of 88% after my differentiated instruction. Confirming the 18% increase in geometry concepts, my students' math achievement increased because of the communicative community built through my math talks and purposeful questions. The research into the purposeful questions took a lot of time and effort. The collaboration with my CADRE Associate was beneficial with this strategy. I wonder if the increase in the Post Test would have been higher through the use of more hands-on materials. Finding 3D figures for students to work with was challenging, due to our misplaced materials during the school year. This caused a lack of preparation in my instruction which led to some frustration. I wondered what to do and decided to print 3D figures on cardstock and allow the students to fold and create various 3D figures. Did this cause the increase shown on the attitude survey of 12 % in using math tools?
Misconceptions were addressed, questions were answered, and voices were heard. 92% of my students surveyed ‘Strongly Agree or Agree’ to the climate survey statement “My teacher listens to my ideas”. This data confirms the strategy of mind maps, math talks, and purposeful questioning throughout our math units was effective. Using these strategies, students achieved through differentiated math instruction.
At the end of the money topic, my students’ scores increased by 27.6%. I conclude that my practices through action research of implementing differentiated instruction, hands-on materials, and math talks influenced this Post Test increase.
TRIANGULATION
Each piece of data supported the purpose of my study: differentiated instruction to improve my students’ mathematical achievement. Through the increase of achievement, connections were made through the implementation of differentiated groups, content, and hands-on activities. Enriched data through the Quick Checks guided successful differentiated math groups and instruction. For students who needed extra support and intervention, the use of BAWD and math talks increased the interest in these students.
This interest in working with hands-on materials and scaffold teacher instruction in a small group setting confirmed the 32% increase of math enjoyment on the Attitude Survey. Through the use of purposeful questioning, a comfortable environment was created. I noticed this through daily observation and communication with my students. This set the stage for my students to ask questions which cleared their confusion. The Quick Checks showed an increase of data throughout the study and the Attitude Survey had an increase of 23% after the study. Through this connection, it is confirmed that the purposeful questioning influenced the increase in confidence and mathematical achievement.
One question that arose from these connections comes from the data of Student C. If I were to change my math block from the morning to the afternoon, would his mathematical achievement increase? With the number of tardies to school, the lack of instruction had a strong impact on the absence of Quick Check data and instruction.
The explained data of 5 students who preferred to work alone, shined unexpected knowledge on the fact that some of my students enjoyed working alone. Knowing this data and altering my instruction, influenced the 32% of interest in math enjoyment. For Student H, when I provided him to work alone, his enjoyment increased. This was triangulated through the data collected from Quick Checks. Throughout the action research, Student H continuous scored enrichment. Based on my three data points, an execution was shown. By the utilization of data gathered to guide my differentiation instruction, all three data points showed an increase, which confirms the purpose of my study.