Task 3 Ch. 1-3 attempt 2
docx
keyboard_arrow_up
School
Western Governors University *
*We aren’t endorsed by this school
Course
C635
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
19
Uploaded by kclinedinst
QYM1 TASK 3: Capstone Written Project Chapters 1-3 Kyle Clinedinst
Student ID-001029234
Western Governors University
Instructor: JeLena Fleming
July 29, 2022
Table of Contents
Chapter 1: Introduction…………………………………………………………………3
Problem Statement …….…..………………………………………………….4
Problem Discussion ……………………………………………………………4
Research Question ........................................
……………………………….4
Conclusion……………………………………………………………………….5
Chapter 2: Literature Review ……..………………………………………………...5-9
Introduction ……………………………………………………………………5-6
Fact Fluency …………………………………………………………………..6-7
Collaborative learning ………………………………………………………..7-8
Conclusion ……………………………………………………………………...8-9
Chapter 3: Research Justification………………………………………………………….9-10
Research Question……………………………………………………………..10
Participants…………………………………………………………………….10
Methods and Procedures……………………………………………………10-13
Data Analysis ………………………………………………………………..…13-14
Data Collection and Instruments……………………………………………14-15
Ethical Issues and Concerns…………………………………………………15
Conclusion……………………………………………………………………15
Appendix………………………………………………………………………16-17
Reference……………………………………………………………………..17-19
Chapter 1: Introduction:
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).
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
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
critical thinking issues. Some possible causes to this problem may be the lack of fact fluency instructional time and the type of instruction.
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)
Research Question:
1.
How are student’s fact fluency and number sense skills impacted by the implementation of peer-lead differentiated instruction in multiplication and division?
Conclusion:
In conclusion, fact fluency and number sense skills are essential for K-6 students
to be successful in the future. We understand that these skills are being taught, but collaborative learning may be more effective as a form of differentiated instruction. This
will allow the students to take ownership of their own learning and allow the educator to act as the facilitator.
Chapter 2: Literature Review:
Introduction:
The purpose of this research study is to determine how collaborative learning strategies impact elementary aged students and their fact fluency and number sense abilities. This literature review will discuss how collaborative learning may improve students' multiplication and division number sense and fact fluency skills.
Many studies have been conducted determining that fact fluency is vital in solving more complex mathematical problems. (
Sleeman, Friesen, Tyler-Merrick, Walker, 2021 and Martin, Codding, Collier-Meek, Gould, DeFouw, Volpe, 2019
). “
Fluent recall of basic facts is essential to the development of more complex math skills.
Therefore, failure to develop fluency with basic facts may impede the development of these skills.” (
Sleeman, Friesen, Tyler-Merrick, Walker, 2021) More specifically, my research is focused on students' multiplication and division of fact fluency and number sense skills. The state of Ohio has determined that “fluently multiplying and dividing from 0-100 is a major cluster skill.” (Ohio Learning Standards/Mathematics Grade 3).
This means that third grade students need to master this skill by the end of the year to be successful not only in third grade mathematics but for their future learning. A simple definition of collaborative learning is working together to achieve a goal (Martinez-Moyano, 2006). This study will focus on collaborative learning for many reasons. Collaboration has shown to be more effective than “lecture or skill and drill”, helps motivate students, and increases active participation. Aslo, when the teacher acts
as the facilitator, this allows the students to take charge of their own learning and the teacher can focus on the individual needs of all students. Fact Fluency:
Fact fluency is critical for elementary students and an area in which my students could improve upon. In fact, the National Center for Educational Statistics, 2009, has shown that fact fluency skills among all students has decreased, with elementary students showing the greatest decrease. The lack of fact fluency among elementary students may be due to the form of instruction and the lack of practice outside of school.
Many students do not have the support at home to practice these skills. We as educators have to understand this and be willing to adapt. Though we may not have ample time to practice these skills as a whole group, these skills can be incorporated into centers and small groups where the teacher acts as the facilitator.
Many studies have shown that weak calculation skills lead to many other math difficulties. (Hanich, Jordan, Kaplan, Dick, 2001, Sleeman, Friesen, Tyler-Merrick, Walker, 2021 and Martin, Codding, Collier-Meek, Gould, DeFouw, Volpe, 2019). Jennifer Bay-Williams, & Gina Kling, 2019, state that basic facts truly are the foundation on which all mathematical computation is based (larger numbers, rational numbers,
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
operations with variables, and so on). My proposed study will focus on multiplication and division fact fluency practices. These skills are critical for 3rd grade students to not only be successful with the 3rd grade math curriculum, but also to be successful in the future. We understand that fact fluency is very important to deeper thinking and problem
solving skills. Fact fluency needs to be mastered in the elementary grades. “
In fact, one report suggests that students who do not achieve fact fluency by the end of fifth grade are unlikely to develop fluency and automaticity in later grades.” (Steel and Funnell 2001
). Many studies have been done on the importance and improvement of fact fluency skills. Most focus on teacher led or technology based instruction. (Musti-
Rao, Plati, 2015), found that technology based instruction is more effective than D-P-R (Detect, Practice, Repair) strategy that is teacher led. But very few studies have been done to determine how effective collaborative learning may be. Collaborative learning:
A common theme when students transition from 2nd grade to 3rd grade is comprehension. Whether this be reading comprehension or mathematics critical thinking, 3rd grade students are expected to understand and solve word problems. Many teachers find it difficult to work on these critical thinking skills and fact fluency. This often leads to teachers assigning fact fluency practice as homework. Instead of relying on elementary students and their parents to master these skills outside of school, this study is looking to see if collaborative learning strategies will impact students' number sense and fact fluency.
There are many different definitions of collaborative learning because collaborative learning can look different for all teachers and students. At its very core, collaborative learning is working together to achieve a goal (Martinez-Moyano, 2006). “Collaborative learning has the promise of active construction of knowledge, enhanced problem articulation and promotion for social interaction and has also been demonstrated to provide better outcomes than individual work in numerous studies.” (DiMarco, Luzzatto, 2010). In this study, students will work together and play different multiplication and division fact fluency games. The games are designed to simulate “center activities” where the students work together and the teacher acts as the facilitator. Not only are these instructional games meant to motivate the students, but collaborative learning has been known to improve student motivation. (Loes, 2022, Topping, Ehly, 2001, Harris, Meltzer, 2015, Arnold, 2012). Furthermore, collaborative learning requires students to take ownership of their learning versus receiving information from a teacher. "Collaborative learning is considered a more effective educational approach than passive forms of learning.” (Johnson, Johnson, and Smith 2007) Cates, 2005 also found that peer-learning or collaborative learning is more effective than computer based learning which is becoming more popular with teachers when teaching fact fluency and number sense. Conclusion:
In conclusion, fact fluency skills are critical for elementary students to be successful in mathematics. These skills will not only be used in the classroom, but also real world situations for the rest of their lives. To improve multiplication and division fact
fluency skills, my instructional unit will use collaborative learning strategies to help keep
students engaged and motivated. These strategies will also allow the teacher to act as the facilitator and hone in on individual student needs.
Chapter 3: Research Justification:
This study adheres to the action research approach because I first found a problem within my classroom. Many students struggle with fact fluency and number sense. Next, an instructional unit was created to help fix this problem. The instructional
unit will be used to find the effects that collaborative learning has on students number sense and fact fluency. Finally, data will be used to determine the effectiveness of the instructional unit and the results will drive my future instruction. I have chosen an action research approach using quantitative data to assess my instructional unit. I have chosen this approach for many reasons. First, it allows the participants to be familiar with their environment and these participants are of the same demographic as my students in the classroom. Next, with my action research study, a quantitative research method will be used to collect and analyze data using a pre and a post-test to determine growth. After the pre-assessment, students will begin the 10-day instructional unit where each lesson is 30 minutes. The teacher will teach and model how to play different types of fact fluency and number sense games/activities with the students. Then, the students will use collaborative learning and the teacher will act as the facilitator. The last day of the unit will consist of a whole group fact fluency and number sense game followed by the post assessment. The data will be collected and
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
organized by using descriptive analysis; finding the mean, median, and range of the pre and post test to determine growth. Research Question:
1.
How are student’s fact fluency and number sense skills impacted by the implementation of peer-lead differentiated instruction in multiplication and division?
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. These participants are the same age as the students that I teach in my 3
rd
grade classroom. My study covers K-6 Mathematics, and
these students fall under the K-6 range.
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.
Methods and Procedures
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. 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 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 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
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
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
to assess the student’s knowledge and understanding of multiplication and division fact fluency and number sense. 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
unit
impacted the participants number sense and fact fluency skills. (Participants answers from the assessments and identity will be confidential.) Data Collection and Instruments:
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.
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)
Ethical Issues and Concerns:
To ensure anonymity and confidentiality of the participants personal identities and information as well as data being collected, each student will be given a number 1-
10. They will use their given numbers when completing the pre and post-assessment and the same number system will be used when collecting and organizing data. All personal information will be kept in a secure/ locked file and will not be a part of the data. When the study is completed and the data have been analyzed, all personal information will be destroyed. Conclusion:
This action research study will use quantitative data to assess number sense and
fact fluency skills of 10 children ages 8-10. The data will measure the effectiveness of collaborative instruction with number sense and fact fluency. This will be done using an
identical pre, and pos-assessment with 100 multiplication and division facts 0-100. The data will be analyzed by using descriptive analysis. To do this, the researcher will find the mean score of the participants pre-assessment to determine the participants level of
understanding of fact fluency and number sense. The researcher will also find the median 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 unit
impacted the participants number sense and fact fluency skills.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
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=
Reference:
Arnold, K. (2012). Theoretical Frameworks for Math Fact Fluency. Journal of the American Academy of Special Education Professionals
, 28–33. https://search.ebscohost.com/login.aspx?
direct=true&db=eric&AN=EJ1135680&site=eds-live&scope=site
. 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
DiMarco, G., & Luzzatto, E. (2010). Collaborative Learning : Methodology, Types of Interactions and Techniques
. Nova Science Publishers, Inc.
https://search.ebscohost.com/login.aspx?
direct=true&db=nlebk&AN=369968&site=eds-live&scope=site
.
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.
Johnson, David W., Roger T. Johnson, and Karl Smith. 2007. “The State of Cooperative Learning in Postsecondary and Professional Settings.” Educational Psychology Review 19 (1): 15–29. https://doi.org/10.1007/s10648-006-9038-8
Karen R. Harris, & Lynn Meltzer. (2015). The Power of Peers in the Classroom : Enhancing Learning and Social Skills
. The Guilford Press.
https://search.ebscohost.com/login.aspx?
direct=true&db=nlebk&AN=1017586&site=eds-live&scope=site
. Loes, C. N. (2022). The Effect of Collaborative Learning on Academic Motivation.
Teaching & Learning Inquiry
, 10
(1), 1–17. https://search.ebscohost.com/login.aspx?
direct=true&db=eue&AN=155796767&site=eds-live&scope=site
Martin, R. J., Codding, R. S., Collier-Meek, M. A., Gould, K. M., DeFouw, E. R., &
Volpe, R. J. (2019). Examination of a Parent-Mediated Detect, Practice, and Repair Procedure to Improve Math Fact Fluency. School Psychology Review
, 48
(4), 293–308. https://search.ebscohost.com/login.aspx?
direct=true&db=eric&AN=EJ1234923&site=eds-live&scope=site
Martinez-Moyano, I.J. (2006). Exploring the dynamics of collaboration in interorganizational settings. In: Schuman (Ed.), Creating a Culture of Collaboration. Jossey-bass, San Francisco, pp. 69–85
Musti-Rao, S., & Plati, E. (2015). Comparing Two Classwide Interventions: Implications of Using Technology for Increasing Multiplication Fact Fluency. Journal of Behavioral Education
, 24
(4), 418–437.
https://search.ebscohost.com/login.aspx?
direct=true&db=eric&AN=EJ1082178&site=eds-live&scope=site
. National Center for Educational Statistics. (2009). National Assessment of Education Progress. Washington, DC: U.S. Department of Education.
Ohio Learning Standards Mathematics
. (2017). Ohio Department of Education. https://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/Ohio-s-
Learning-Standards-in-Mathematics/Model-Curricula-in-Mathematics/
Grade_3_Math_Model_Curriculum.pdf.aspx
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
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Steel, S., & Funnell, E. (2001). Learning multiplication facts: a study of children taught by discovery methods in England. Journal of Experimental Child Psychology,
79,
37–55.
https://doi.org/10.1006/jecp.2000.2579
.
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