Rationale
History
My capstone project was centered around two second-grade students who received special education services. Although I only implemented the strategies with two students, the instruction could be generalized to all students who have limited understanding of number sense. I had nine students on my caseload, seven of whom were in second grade. Two of those seven students were the ones who took part in my capstone project. Both of the students received support in all academic areas, as well as support for social and behavioral needs. These students have received special education services since kindergarten. One of the students received English Language Learning support once a week due to English not being his primary language at home. The other student struggled with maintaining attention, which impacted her academic achievement.
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Need
The data that I collected from my students indicated a need in mathematics, specifically in number sense. Based on the Measure of Academic Progress (MAP) math assessment taken in fall of 2018, the two students scored in the following percentiles: 21st and 28th. Both of them scored in the “low” range on number sense for this test. When given mental addition and subtraction fact fluency assessments, the students scored in the beginning level of the standard based on this assessment. Based on AimsWeb data, the students were below grade level for math fact fluency for addition and subtraction, math fact fluency with tens, and number comparison. These students needed direct instruction of weekly skills in order to show understanding of the material on weekly assessments. When receiving this direct instruction of skills, they were in an alternate small group setting. Even with an alternate setting and direct instruction, the students still struggled with understanding simple addition strategies and word problems, as well as the formative assessments taken during the lesson. These students had to work extremely hard during math and had a difficult time maintaining focus. Both students showed frustration to the point of tears when completing a math problem.
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Importance
These students needed to show growth in the area of number sense in order to bridge the gap from below grade-level ability to grade-level ability. Math was a very difficult time for these students and I hypothesized that if they had better number sense they would be able to perform better on grade-level weekly skills and concepts. I also hypothesized that it would help their confidence in mathematics heighten and lower their academic frustration. These students were important to me and I wanted to see them succeed. Having solid number sense was vital to these students’ futures as learners.
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When deciding what to do my capstone project on, I was torn between multiple areas. My students had a large spectrum of needs in a plethora of areas. I decided to choose number sense because I saw it as the area of most need. I also chose math because it was not one of my favorite subjects to teach, and I hoped that as I learned the many different evidence-based strategies and saw the growth in my students’ math abilities I would begin to gain confidence in my math instruction and start enjoying it more.
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Literature Review
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Introduction
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Mathematics is a multi-dimensional subject area that encompasses many complex ideas. It is built on a hierarchy of skills that begin to form at a very young age. One of the earliest forms of math understanding is the idea of number sense. Number sense is the understanding of numbers and their relationships between each other and the ability to use numbers and operations in flexible ways. To fully understand math concepts, number sense needs to be developed. Westenskow, Moyer-Packenham, and Child (2017) stated “mathematics is a discipline in which new concepts are built upon previously learned concepts; thus incorrect or insufficient knowledge of basic concepts limits future mathematical growth” (p. 1). When looking at school-aged children, 5 to 10 percent of students show signs of having a math disability. Students who do not exhibit signs of number sense have a more difficult time building higher-level math concepts, leading them to struggle in math.
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The purpose of my study was to determine if explicit math instruction in the area of number sense would increase student achievement. My capstone project was centered around two second-grade students who received special education services. The data that I collected from my students indicated a need in mathematics, specifically in number sense. Assessing number sense understanding and implementing appropriate interventions helped my students develop a deeper understanding of math concepts and make gains in their overall academic achievement. The literature I reviewed is organized thematically into two main topics: assessment and intervention. This research was intended to guide my number sense assessments and student-based interventions I used in my classroom.
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