FINDINGS & CONCLUSIONS
Research has proven that math intervention has a “positive impact on students’ mathematics learning and achievement,” (Harbour, Adelson, Karp, Pittard, 2018). All students performing below grade level need intervention to promote individual growth and help students reach grade level standards. My school, a cyber school in Pennsylvania, has a large population of elementary school students performing below grade level in mathematics. The current math intervention program includes two math interventionists for about five hundred underperforming students. Since the need for intervention is so high, not all students are receiving intervention services.
As one of the math interventionists, I am responsible for improving mathematical understanding for tier 2 elementary students. Currently, I see a small group of students two times a week in 30 minute sessions, totaling 60 additional minutes of math instruction per week. There are many limitations and restrictions with the current model of math intervention. The students who enter the program remain in the program for the entire school year. The math interventionists decide which standards to focus on based on PSSA data. Students are invited to intervention based on their performance in three math content areas. Students are not grouped by needs, instead they are grouped scheduling conflicts. This study is intended to identify key components of successful math intervention programs that can be implemented in a cyber setting. The research was conducted through literature, professional surveys, and professional interviews with cyber teachers and brick-and-mortar teachers from local elementary schools.
DATA COLLECTION
SURVEY RESPONSES
My first collection of data includes survey responses from cyber school teachers. Participants completed an anonymous survey to share their experience with math intervention at brick-and-mortar schools. Two out of three teachers' experiences included pull-out models and all three teachers worked at a school with a push-in model. Question number 6 asks teachers to, “Describe any math intervention practices that have been most successful.” Teacher 1 responded to the question with a data driven focus, noting the use of pre-assessments to inform instruction, “Using data from pre-assessments has been helpful to determine which skills I should focus on during intervention. The data shows me what the students already know about a certain topic and what target skills they need more instruction on.” The other two responses note different practices, but they do not specifically name data that proves the practice is successful.
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Teacher 2: “I feel that the students who were pulled out did better in all of their classes. It is a way for them to learn in a different environment.”
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Teacher 3: “Keeping the group below 5 students. Establishing norms and a routine during the intervention time. Following a specific intervention program for at least 6 weeks before reviewing data and determining if it is an effective intervention.”
More information is needed to identify if the practices listed above improve mathematical understanding.
Click on each image to open the survey data in a new tab.
CYBER TEACHER INTERVIEWS
I interviewed three of my colleagues, who are elementary cyber school teachers, to identify their wants and needs for intervention. Each teacher was asked to respond to the following questions:
1. If there were no restrictions, what would a perfect math intervention program look like in a cyber school?
2. How can we implement your ideas within our current structure?
3. What actions can the school take to implement your ideas?
Several different ideas emerged relating to the structure of the program (push-in versus pull-out), flexible grouping by student performance of a skill, frequency of intervention, scheduling, assessments, and progress monitoring.
The most common idea was the need for flexible grouping. Participants responded to question one, “If there were no restrictions, what would a perfect math intervention program look like in a cyber school?” Teacher B shared, “I think it would be good to have it be more fluid…it would be beneficial in some way if it could be more on a basis of what the topic is that you are teaching and then the kids that need the support in that area.” Teacher C shared a similar idea, “[A common assessment] could be used to group the kids into what areas they need to work on.” Currently, the students who enter the math intervention program remain in the program year round. Students were invited to participate in math intervention based on PSSA data (if available) and iReady diagnostic data. The math interventionists use pretests and posttests, plus iReady diagnostic data, to analyze if the program has a positive effect on students' math ability. Additionally, the elementary school has a goal to increase math proficiency on the 2019-2020 PSSAs, assigned by the state’s School Improvement Plan (SIP), therefore, it was decided that the math interventionists work with tier 2 math students who were closest to proficiency. Furthermore, the school requires that all students receiving math intervention services be tracked in the Pennsylvania Value-Added Assessment System (PVAAS). If we were to adjust the program to a flexible grouping system the school may need to modify the requirements for tracking student data.
I asked teachers to respond to the next question, “How can we implement your ideas within our current structure?” Teacher B replied, “Parents would need to know ahead of time what that’s going to look like for the school year so that they will be prepared… if their kid needs to go work with the interventionists it’s because they might just be struggling with a certain skill that they need targeted support in, so having that plan in place at the beginning of the year would be helpful.” Similarly, Teacher C shared the need for clear communication to students, “For this to happen, the first thing we would need is a common assessment… that would have to be used to determine which students needed to meet with somebody from intervention. … Then of course teachers would need time to look at that and create groups. ... I think the big difficulty with us is the communication side of it, where students and learning coaches would need to know who they’re meeting with.” As a cyber school we allow students to create their own schedules. Students can work on the asynchronous lessons at any time of the day. Students are required to attend two synchronous lessons with their core teacher but the students get to pick their own lesson schedule. Typically, once a student picks their class schedule it remains the same for the year. This helps students stay organized at home while they are working independently and boosts attendance. Contrastingly, elective and support classes are assigned to each student, however, they are optional, meaning if the student is absent from the synchronous lesson it will not negatively impact their grade. If the math intervention program moves to flexible grouping all teachers, parents, and students must be informed at the beginning of the school year. Parental permission is required, so parents need to sign and return the math intervention form in a timely manner. Guidance counselors must enroll the student immediately after the parent permission form is returned. A communication system is required to inform students and parents about the additional class and lesson times. With all things considered, students still might not be able to attend the math intervention lessons if the assigned class times do not work with their personal schedule.
Cyber teacher interview transcripts
BRICK-AND-MORTAR INTERVIEWS
I interviewed three local brick-and-mortar elementary school teachers to find out how other school districts are implementing math intervention. Each participant shared information about student groups, assessments, instruction, and implementation. Significant findings from the interviews can be found within the next section: Key Components of Math Intervention.
FOCUS GROUP
At the conclusion of my data collection I invited three cyber school teachers to participate in a focus group. Each teacher was asked to read through the brick-and-mortar intervention models and bullet points from several pieces of literature. Participants shared their thoughts, including pros and cons, from each model.
In the end, the focus group decided that if the math intervention model changes, it should include:
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Flexible grouping
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Push-in support
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Pull-out support
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Concrete materials
Additional comments and findings from the focus group can be found within the next section: Key Components of Math Intervention.
KEY COMPONENTS OF MATH INTERVENTION
I. GROUP
SMALL GROUP INSTRUCTION
Through my research several key components of successful math intervention programs were identified. One of the most frequent themes was the use of small group instruction. Small group instruction may also include one on one instruction. Each brick-and-mortar interview identified the use of small group instruction. The literature also emphasized the importance of small group instruction. A complete list of the data can be found in tables 1 and 2. The current math intervention program is organized into small groups of tier 2 students, ranging from five to eight students in a group.
Table 1
Table 2
FREQUENCY OF INTERVENTION
Another emergent theme was the frequency of math intervention. A wide range of frequency of math intervention was identified in the literature and brick-and-mortar interviews. The brick-and-mortar interviews suggest that students should receive 90-150 minutes of math intervention per week. Based on the literature, students were pulled out of the classroom for 45 to 225 minutes per week. In both the literature and brick-and-mortar interviews, students received math intervention services three to five times per week (see tables 1 and 2). Currently, students meet with the math interventionist twice a week for 30 minutes, totalling 60 minutes a week. The intervention period (30 minutes) seems to be appropriate based on the findings, however, the frequency needs to increase from two days a week to at least three days a week.
FLEXIBLE GROUPING
The last reappearing theme of grouping is flexible grouping. Flexible grouping was not specifically identified in the literature, but one can assume the groups were flexible due to the duration of each study (see table 1). Even though flexible grouping was not present in the literature, each brick-and-mortar teacher specifically mentioned flexible grouping as a main component of the math intervention program at their school.
In Miss P.’s school, students are invited to math intervention based on their districtwide benchmark assessment along with previous PSSA data. If needed, students may complete the iReady diagnostic for an additional data point. Students may join intervention for just one skill if necessary. Student progress is monitored by their performance in the regular education classroom (unit tests) and by benchmark assessments.
Mrs. D. shared a similar situation, stating that the intervention program is flexible. If student performance improves during the year the student may exit the program. “If a student shows growth and scores proficient or above, they can be removed from the program, but it isn’t common,” she continues, “If they score 80s and 90s on unit tests throughout the year they can be removed.”
Miss S.’s school has a large caseload of students with mathematical difficulties, totalling about 80% of the student population. With such a large population of underperforming students, all teachers at Miss S.’s school are in charge of providing math intervention to their students. The intervention block is completed in centers: iReady (an adaptable online program), manipulatives, and small group instruction. Miss S. organizes her students into groups based on iReady diagnostic data. Student groups can change weekly depending on the upcoming skill.
During the concluding focus group the participants highlighted the idea of flexible grouping, something that is lacking in the math intervention model this year. The conclusion: 1) Students need to be able to enter and exit the math intervention program on an as needed basis, 2) The school needs to move away from grouping students by tier and instead group students by skill. As the discussion continued, the participants noted that to group students by skill, the entire program must change. The only logistical way flexible grouping can work in a cyber school is if each skill set had a common duration. Math interventionists and teachers would need to work closely together to identify students for intervention and progress monitor often. Lastly, parents would need to respond and accept the math intervention services in a timely manner in order to get the student enrolled into the course.
This may not sound like a lot, but it is a huge change for our cyber school. Currently all students have flexible classes. They get to choose their own schedule and are only required to attend two synchronous lessons a week. If students enter the math intervention program they must attend two additional synchronous lessons a week, but the lessons are nongraded so there is no penalty for being absent. If we move to a flexible grouping model students must become accountable for attending the lessons or the math intervention program may fail.
II. EFFECTIVE STRATEGIES
ASSESSMENT
In each math intervention model students were identified as having mathematical difficulties using a variety of assessments. It seems as though it is up to the institution to create guidelines for identifying students in need of intervention. In some instances benchmark assessments are used, in others diagnostics or screener tests are used. Student progress is monitored using benchmarks, diagnostics, and state assessments. The literature identified pretest and posttest as a data point as well. Correspondingly, in her interview Miss P. noted the use of pretest to group students by skill ability for the push-in model of intervention. However, Miss P. does not use posttest, instead she uses unit tests as a progress monitoring tool. In a cyber teacher interview, Teacher C brought up the idea of testing students using a pre- and post-assessments, “...So that would have to be based on an assessment... that could be given posted or virtual and that data could be used to group the kids into what areas they need to work on... Then kids would be assessed at the end of the week during an intervention block time to see if they had mastered that skill.”
This year, the math interventionists administer pre- and post-assessments to students enrolled in the program. The problem is that students in intervention remain in the program all year, so if the student scores high on a pre-assessment they will still participate in that unit of intervention. We can improve the program by administering the pre-assessment to all students in the regular education classroom. The data can be used to group students with common mathematical difficulties for intervention.
INSTRUCTION
The literature included a variety of effective instruction for tiered math intervention. Two specific strategies were found in multiple math intervention models, including Concrete-Representational-Abstract (CRA) and Schema Based Instruction.
Concrete math and the use of manipulatives ia also a common strategy found within the brick-and-mortar interviews. Miss S. is the only teacher who recognized drawing as one of the most successful strategies, however, she is the only brick-and-mortar teacher required to lead an intervention block at her school. Other successful strategies in the interviews and in the literature include explicit instruction, modeled thinking, verbalizing reasoning, clear and frequent feedback, playing games, and progress monitoring. These findings suggest that students with math difficulties learn best when they have access to concrete materials to understand and represent the problem. Our math interventionists have access to concrete materials, but not all students have the proper manipulatives to practice independently. Moving forward, the school will need to ship concrete math materials to all students enrolled in math intervention.
Focus group participants discussed effective strategies, like the use of concrete materials. In each brick-and-mortar model the math interventionist utilized manipulatives to teach math topics concretely before moving to the abstract model. Our students get math kits at the beginning of the school year, but students enrolled in math intervention need additional manipulatives. The participants discussed if students should receive an intervention kit once they are enrolled in the program or if all students should receive the manipulatives to use in the regular education classroom. Ultimately, administration will make the call. The school budget must be taken into consideration; it will come down to cost per math kit and shipping.
PUSH-IN SUPPORT
One recurring theme that was mentioned during the brick-and-mortar interviews and cyber teacher surveys, but was not present in the literature, was a push-in model of math intervention. A push-in model means the math interventionist joins a regular education math class and supports all students. Miss P. works directly with the math interventionist in this way. The math interventionist joins her math class daily and co teaches each lesson. They meet weekly to plan the instruction.There is no whole group instruction; students are placed into skill groups and work directly with Miss P., the interventionist, or work independently. Both the interventionist and Miss P. progress monitor every three days, so groups of students may change often. Miss P. noted that the push-in model was used in one classroom last year and was extended to a second classroom this year based on positive results.
Mrs. D. and Miss S. also noted a push-in model of intervention, though neither classroom is supported by the math interventionist. Mrs. D. shared that the math interventionist primarily pulls students out for support and only pushes into classrooms when there is time in her schedule. Miss. S.’s school does not currently have a math interventionist, though they are looking to hire one for the next school year. Last year, the math interventionist pushed into a select number of classrooms with an abundance of mathematical needs.
Similarly, all three focus group participants established that push-in support is essential to student success. The group talked about the logistics and decided it would be best if a push-in model was implemented in one grade level next year to 1) see how it works, and 2) see if it works. Ideally, the math interventionist would join a regular education math lesson and support any student in need. The participants talked about utilizing breakout rooms to group students by ability and work directly with the interventionist, this way more students will have access to math support. At the end of the focus group I asked participants to present their favorable model: push-in, pull-out, or both. Teacher A stated, “I like the push-in [model] with small group at the end of the lesson.” Likewise, Teacher C shared, “I think if we can do some kind of combination of the push-in and pull-out...we can test it out.”
While analyzing the data from the math intervention push-in models at brick-and-mortar schools I recognized that the math interventionist pushes into a small number of classrooms. Therefore, I believe perfecting the pull-out model should be a priority for next year. If the math intervention model includes push-in support it should only be in a few classrooms.
CONCLUSIONS
A successful math intervention program must include small group instruction at least three times a week. Students should be invited to participate based on a common assessment. Teachers and interventionists work together to group students by skill and ability. The instruction must target students' specific mathematical needs. Students have to master the concrete math model and represent the problem before they can work through and master the abstract concept.
IMPLICATIONS
I intend to present my findings to my colleagues and the administration along with an action plan for implementation. Groups will become flexible so that all students (from any tier) can enter and exit the program as needed. Teachers and math interventionists will work together to administer pretests to identify students with math difficulties before each unit. The pretest will also be used to group students when the math interventionists join synchronous lessons to support students during the regular education math lesson. Parents must return permission forms for the pull-out model within 48 hours and students will be enrolled in the intervention course with parental approval. Students will meet with the math interventionist more often, at least three days a week. A permanent schedule will be created, meaning no other classes are permitted to hold synchronous classes during the math intervention blocks. The school will communicate the new intervention model to parents and students to promote participation and attendance. The math interventionists will use CRA and Schema Based Instruction to support the mathematical understanding of each student. Math interventionists will progress monitor weekly and adjust instruction if needed. Success of the program will be measured by progress monitoring tools, quiz scores, unit test scores, and the iReady diagnostic. If a student does not make adequate progress the math interventionist, teacher, and data specialist will create a new support plan.
NEW QUESTIONS
Participants in the focus group determined that a push-in model of math intervention is vital to student success. While this may be true, the literature did not contain data pertaining to push-in models. Therefore, my new questions focus on push-in models of intervention. I would like to find out which model best supports student achievement in mathematics.
Questions
For Future Research
Do push-in models of intervention support student achievement in mathematics?
Do students with mathematical difficulties benefit more from a push-in model or a pull-out model of math intervention?
REFLECTION
I learned a considerable amount about math intervention from my research. The research will not only influence the structure of the program, but it will also influence my instruction in the classroom. I am more confident in my role as a math interventionist because I discovered the most successful strategies to help students succeed in mathematics.
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As a researcher I learned that it is important to record and transcribe interviews. When I listened to each interview I realized I shared my opinion and ideas with participants in response to their comments. At the time of the interview it seemed natural to conversate with the participant about the question at hand, but my comments were not beneficial to my research. I only transcribed original ideas from each participant because the purpose was to capture their experiences, opinions, wants, and needs. In the future, I will make sure to let the participant respond and only ask clarifying questions if needed.
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When I analyzed the qualitative data I acknowledged that not all of the data was necessary for my research project. The data collected from the survey was not as helpful as the data collected from the brick-and-mortar interviews. The survey responses were short, sharing little detail about math intervention models from previous experiences. Additionally, the cyber teacher participants shared their opinions and ideas during the focus group, so the individual interviews seemed unnecessary. If I could redo my research project I would eliminate the cyber teacher survey and cyber teacher interview for these reasons.
I also learned that literature is a driving force in research. I coded the literature to identify key components of successful math intervention programs. I then used the literature to code the transcripts from the interviews and focus group. I continuously referred back to the literature for the duration of the research project. I found similarities throughout the literature and I identified inconclusive information that will need to be researched further (push-in models). Overall, my research project was successful because I was able to answer the question: How can I improve the math intervention program so that it is more specific for individual students in cyber school?