Prospectus Task 1
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Western Governors University *
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C635
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Mathematics
Date
Feb 20, 2024
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docx
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Uploaded by kclinedinst
1
QYM1 Task 1: Prospectus
Kyle Clinedinst
Student ID-001029234
Western Governors University
Instructor: JeLena Fleming
July 7, 2022
2
Capstone Prospectus
A: Research Topic
The education related research topic that I will be researching and collecting data
on is number sense and fact fluency differentiated instruction focusing on multiplication and division among children ages 8-10. My current professional setting is a self-
contained third grade general education teacher. My degree program is Master of Arts degree in Mathematics Education (K-6). My research will be done through the “Mount Vernon Parks Summer Program” where teachers can volunteer to teach different lessons to students throughout the summer.
This topic relates to my degree program and professional setting because fact fluency is key to number sense and problem-solving skills. “Basic facts truly are the foundation on which all mathematical computation is based (larger numbers, rational numbers, operations with variables, and so on).” (Bay-Williams, Kling, 2019). Fact fluency not only is key for third graders in my school, but in the field of education. The ability to fluently add and subtract within 1,000 is a Ohio State Mathematic 2nd grade standard, and the ability to fluently multiply and divide within 100 is a Ohio State Mathematic 3rd grade standard. (
Ohio Learning Standards Mathematics
, 2017). Students that struggle with fact fluency also struggle with higher-level problem-solving skills and have continued difficulty with mathematics. (Hanich, Jordan, Kaplan, Dick, 2001).
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B1: Problem Statement
Students in my classroom and surrounding area struggle with number sense and fact fluency. Number sense and fact fluency difficulties lead to problem solving and critical thinking issues. Some possible causes to this problem may be the lack of fact fluency instructional time and the type of instruction.
B2: Problem Discussion
The instructional problem that my students face involves number sense and fact fluency. Many students struggle with fact fluency, which correlates to them struggling with word problems and problem-solving. Math instruction has placed an emphasis on real world problem solving which correlates to word problems. But these real-world problem-solving skills become more difficult for students who struggle with number sense and fact fluency at an early age. (
Sleeman, Friesen, Tyler-Merrick, Walker, 2021).
Some possible causes to this problem may be the lack of fact fluency instructional time and the type of instruction. Many teachers feel that there is not enough instructional time in a school day. Teachers often focus on problem solving and
critical thinking skills using manipulatives, which is great. But fact fluency gets put into centers in the form of online computer-based fluency practice. This form of instruction may not be efficient, especially for the children with disabilities and/or computer limitations. This is especially true for elementary students. (Cates, 2005)
C: Proposed Solution
The potential instructional unit that will be implemented is a peer/collaborative learning differentiated instruction. This instructional unit will be first modeled by the
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teacher, then practiced by the students, then be student led allowing the teacher to be the facilitator. The potential instructional unit will be 2 weeks in duration. The purpose of the instructional unit is to see if the instructional unit helps the participants improve their number sense and fact fluency skills according to the data collecting instrument. Day 1- (30 minutes) The first day of the instructional unit will be used to give the participants a pre-assessment, (seen in appendix A), to collect data and model the peer-lead instruction. The pre-assessment will assess the student’s prior knowledge and understanding of multiplication and division fact fluency and number sense. The data will be organized and used to make groups for the peer-lead instruction. The groups will be organized by common difficulties related to fact fluency and number sense which will begin on day 2. (Each group will be doing the same activities, but the flash cards will be differentiated according to the participants needs.) Next, the teacher
will model how to “play” the first type of fact fluency practice game with all 10 participants. The first flash card game will be called “Kings and Queens”. One player has a stack of pre-assigned flash cards and is the king or queen. (The king or queen sits in a chair while the others are in a half circle around them on the floor.) The king or queen will take turns showing each player flashcards. Each player has 5 seconds to answer the math fact. If the player does not get the answer in time, or says an incorrect
answer, the next player gets a chance to answer the flash card. At the end, the player with the most facts becomes the new king or queen. If there is a tie, a game of rock, paper, scissors will determine the winner. Days 2-5- (30 minutes per day) The teacher will start by reviewing the game “Kings and Queens”. Then, the teacher will provide the pre-assigned flash cards to
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each of the 3 groups of 3-4 participants. (Flashcards will be a mixture of previously known facts to build participants confidence, and unknown facts to build knowledge.) As the participants are playing, the teacher will walk around to each group and act as the facilitator using best practices. The teacher will work with groups on skip counting strategies at their level, multiplication and division tips, and ask open ended questions to expand on the student's thinking. Day 6- (30 minutes) The teacher will introduce a new fact fluency and number sense game, “Telephone Math.” Each group of students will have 2 dice with letters, a poster of the telephone (example below), and a simple game board. Each letter will correspond to a number and is designed like a telephone. example-
(Each group will have letters that correspond to numbers they need to work on.) The participants will take turns rolling the dice. They will make multiplication and division sentences for the 2 corresponding numbers. If done correctly, they will move their game piece on the game board. This will continue until one player reaches the finish line on their game board. Days 7-9- (30 minutes per day) The participants will play “Telephone Math” as the teacher acts as the facilitator.
Day 10- (30 minutes) The teacher will lead the participants in a “Around the World” fact fluency game. After the game, the teacher will provide the post-assessment
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to assess the student’s knowledge and understanding of multiplication and division fact fluency and number sense. D: Participants
The potential participants are currently involved in a (non-academic) summer program, which allows elementary age children the opportunity to participate in games and activities with lunches provided during the summer months. (Teachers are invited to teach mini lessons throughout the program.) These children are all enrolled in the same school district in which I teach with similar demographics as the students in my school. My school resides in an area of low income, 89% of the population classifies as low income. (GreatSchools.Org, 2022) The location of this program and my school district is a small urban community. There are 10 children aged 8-10, the same age group as my third-grade students, that are a part of this program. Among the 10 children, there are 7 boys and 3 girls. 80 percent of the potential participants are Caucasian, and 20 percent are African American. 6 of the children will be entering 3rd grade this coming school year, and the remaining 4 children will be entering 4th grade. E: Research Question
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1.
How are student’s fact fluency and number sense skills impacted by the implementation of peer-lead differentiated instruction in multiplication and division?
F1: Data Collection Instrument
The data collection instrument will be two identical math assessments to determine multiplication and division fact fluency. Both assessments will have 100 problems and be timed. The participants will have 5 minutes to complete as many multiplication and division facts as possible. (The timed aspect helps determine fluency.) The assessments will be used to collect quantitative data in the case study research setting. The data recorded will accurately depict the students’ base multiplication and division fact fluency knowledge and assess number sense skills. The assessments will be used to determine participant’s range of growth. The data collecting instrument directly aligns with multiplication and division fact fluency and number sense skills.
F2: Instrument This data collection instrument has 50 multiplication and 50 division fact fluency questions. Each question is worth 1 point for a total of 100 points. The columns are organized to help the researcher analyze fact fluency and number sense difficulties by factors for each participant. The first column focuses on multiplying and dividing by 2 and 4. The second column focuses on multiplying and dividing by 5 and 10. The third column focuses on multiplying and dividing by 3 and 6. The last 2 columns focus on multiplying and dividing by 7, 8, and 9. (See Appendix A)
F3: Research Method
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With my action research study, a quantitative research method will be used to collect and analyze data. 1.
Inform parents/guardians of the research purpose and research questions. 2.
Obtain informed consent from parents/guardians. Participants identities will remain anonymous.
3.
Distribute the pre-assessment to the participants. 4.
Organize and analyze data from the pre-assessment to group the participants. 5.
Perform the proposed solution. 6.
Distribute the post-assessment to the participants. 7.
Organize and analyze data from the post-assessment. G: Data Analysis The researcher will collect and organize the data using descriptive analysis. This
will be done in several ways. First, the researcher will find the mean score of the participants pre-assessment. Also, the quantitative data from the pre-assessment will be
used to determine the participants level of understanding of fact fluency and number sense. The researcher will find the median from the pre-assessment using the raw data from the pre-assessment.
After the instructional period, the researcher will collect and analyze data from the post-assessment. The researcher will again find the mean and median of the post-
assessment to compare with the data from the pre-assessment to see if the instructional
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unit
impacted the participants number sense and fact fluency skills. (Participants answers from the assessments and identity will be confidential.) References Bay-Williams, J., & Kling, G. (2019). Math Fact Fluency : 60+ Games and Assessment Tools to Support Learning and Retention
. ASCD. https://search.ebscohost.com/login.aspx?
direct=true&db=nlebk&AN=1999078&site=eds-live&scope=site
. Cates, G. L. (2005). Effects of peer versus computer-assisted drill on mathematics response rates. Psychology in the Schools
, 42
(6), 637–646. https://doi.org/10.1002/pits.20105
Dan Emmett Elementary School
. (2022). GreatSchools.Org. https://www.greatschools.org/ohio/mount-vernon/4760-Dan-Emmett-Elementary-
School/#Low-income_students
Hanich, L., Jordan, N. C., Kaplan, D., & Dick, J. (2001). Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology, 93(3), 615–626.
Ohio Learning Standards Mathematics
. (2017). Ohio Department of Education. https://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/Mathematics/
Ohio-s-Learning-Standards-in-Mathematics/MATH-Standards-2017.pdf.aspx?
lang=en-US
Sleeman, M., Friesen, M., Tyler-Merrick, G., & Walker, L. (2021). The Effects of Precision Teaching and Self-regulated Learning on Early Multiplication Fluency. Journal of Behavioral Education
, 30
(2), 149–177. https://doi.org/10.1007/s10864-
019-09360-7
Topping, K. J., & Ehly, S. W. (2001). Peer Assisted Learning: A Framework for Consultation. Journal of Educational & Psychological Consultation
, 12
(2), 113–
132. https://doi.org/10.1207/S1532768XJEPC1202_03
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Appendix A
Name: Answer as many questions as you can in 5 minutes. You may skip a question and go back to it at the end if you have time. Multiplication
2x8=
5x5=
2x3=
8x8=
9x8=
4x5=
10x10=
4x6=
7x5=
8x5=
7x2=
5x6=
7x6=
7x7=
7x8=
9x4=
10x3=
9x6=
9x3=
9x5=
6x2=
5x3=
3x5=
6x7=
8x2=
5x2=
6x10=
6x6=
5x7=
9x2=
3x2=
5x1=
6x0=
7x2=
3x7=
4x4=
8x5=
6x4=
8x4=
4x8=
2x0=
2x10=
2x3=
8x0=
9x0=
4x1=
5x9=
3x3=
9x1=
7x1=
Division
14÷2=
25÷5=
6÷3=
14÷2=
14÷7=
28÷4=
30÷10=
21÷7=
36÷9=
32÷4=
28÷7=
30÷5=
30÷6=
45÷5=
32÷8=
20÷5=
15÷5=
36÷6=
64÷8=
49÷7=
36÷4=
45÷5=
42÷6=
42÷7=
42÷6=
12÷2=
20÷2=
12÷3=
81÷9=
72÷9=
32÷4=
30÷6=
30÷3=
8÷8=
72÷8=
8÷2=
10÷10=
3÷3=
48÷6=
8÷1=
8÷4=
50÷5=
21÷3=
48÷8=
9÷0=
16÷4=
35÷7=
18÷6=
0÷9=
7÷7=
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