QYM3 Task 3_ Ch 1-3

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[Fact Fluency: A Study in Growth] [Amy Sprague] Western Governors University [Matt Morgan]

Chapter 1 Topic The research topic I have picked to study is fifth graders' comprehension and fluency of basic math facts, including addition, subtraction, multiplication, and division. Fifth-grade students need help fluently solving basic fact problems and answering basic fact questions. Fluency is defined as answering correctly within 3 seconds. Students also need help to apply fact strategies when solving real-world problems. Math proficiency for students is critical for classroom success. Fact fluency also extends into the real world. Developing automaticity, which means to perform involuntarily or unconsciously, is vital for students’ success in mathematics (Baker & Cuevas, 2018). These essential fluency and math skills are vital to a student's successful future progress to more complex mathematical learning (McTiernan et al., 2016). Students who lack math proficiency are unable to quickly, within three seconds, answer the four basic operations. The lack of fluency starts with addition and subtraction in 1st-3rd grade. Interventions are required to help develop and improve their proficiency. Many students have yet to master the skills necessary to recall basic facts accurately and fluently, resulting in difficulty in math. Despite math being an essential component in the school curriculum, math fact fluency needs to be taught or given focus in many math curriculums used in schools today. These concepts align with the math Common Core standards of fifth grade.

As a current student in the WGU Master of Arts, Mathematics Education (K-6) program and a 5th-grade elementary teacher, this topic relates to my master’s program and professional setting. As a 5th-grade teacher, math is a subject I teach daily. Success in math is crucial for students as we see an increase in science and technology jobs. Students need a firm foundation of basic math facts to compute more complex math they will encounter in life and at higher grade levels. Problem Statement Students need help with fact fluency. The problem is teaching fact fluency to elementary students. When students cannot do basic math facts, they cannot understand and complete bigger math problems. Problem Discussion The Ma & Ma (2014) international comparative study shows that students have consistently shown that U.S. students are behind other students in developed countries. Students in different countries are advancing their mathematical skills, while U.S. students need to grow (Ma & Ma, 2014). Twenty-two percent of all adults have yet to master math skills, including fact fluency, past the eighth grade, which is essential for success in many jobs (Cozad & Riccomini, 2016). Because fact fluency is not part of most curricula, students lack fluency. They understand the principles of the operations, but the curriculum does not provide time to master the facts. This leads to students struggling later on in math as the numbers get more complex.

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Research Question 1. What is the effect of The Sprague Method on students' understanding of basic fact fluency? Conclusion The data surrounding the background of fact fluency shows that fact fluency is separate from most curricula and that students need more fluency. They understand the principles of the operations, but the curriculum does not provide time to master the facts. This leads to students struggling later on in math as the numbers get more complex. We need to support students in being fluent in math facts so they can have the confidence to solve more complicated math problems as they progress. Chapter 2 Literature Review After reviewing the relevant and necessary literature on basic math fact fluency, multiple themes were identified that support implementing our school improvement plan to help increase students’ basic math fact proficiency. These themes include purposeful interventions, fact fluency importance, and computer-based fluency practice. The proposed school improvement plan seeks to help students at Tambark Creek Elementary become automatic and fluent with their math facts to help increase proficiency levels. Importance Many studies on fact fluency in upper elementary grades show the importance of knowing your facts. Math proficiency for students is critical for classroom success. Fact fluency also extends into the real world. Developing automaticity, which means to perform involuntarily or unconsciously, is vital for students’ success in mathematics

(Baker and Cuevas, 2018). A peer-reviewed article by Caron, Thomas A. (2007) details the importance of helping students develop automaticity in multiplication. Automaticity will help students solve problems better later. Students who lack math proficiency are unable to quickly, within three seconds, answer the four basic operations. The lack of fluency starts with addition and subtraction in 1st-3rd grade. Interventions are required to help develop and improve their proficiency. Many students have yet to master the skills necessary to recall basic facts accurately and fluently, resulting in difficulty in math. Despite math being an essential component in the school curriculum, math fact fluency is not taught or given focus in many math curriculums used in schools today. One of the skills that help students reach mathematical proficiency is the ability to solve their basic math facts fluently (Conzad & Riccomini, 2016). Fact fluency is a fundamental skill that students need to learn early. Students must be able to solve problems accurately and quickly to be considered fluent. Fluent students can promptly, accurately, and effortlessly find, recall, and answer basic math facts. (Hawkins et al., 2017). The Ma & Ma (2014) international comparative study shows that students have consistently shown that U.S. students are behind other students in developed countries. Students in different countries are advancing their mathematical skills, while U.S. students need to grow (Ma & Ma, 2014). Twenty-two percent of all adults have yet to master math skills past the eighth grade, essential for success in many jobs (Cozad & Riccomini, 2016). Additionally, in the National Mathematics Advisory Panel report published by the U.S. Department of Education (2008), U.S. students showed a below-average achievement level compared to students worldwide (Rave & Golightly, 2014). In the

United States, mathematics is an area of concern and needs improvement in the educational system. The report concluded that there is a gap in skills and a need to develop the skills so students can add and subtract fluently by the time they reach the end of third grade. A peer-reviewed article by Caron, Thomas A. (2007) stresses the importance of helping students develop a sense of automaticity in multiplication. In doing this, they will be better equipped to solve problems later. The author states that students should have mastered multiplication facts by late elementary (5th grade). Nevertheless, many students entering 5th grade have not mastered these skills. Even more troubling is that 4th-grade students have not mastered multiplication and division facts by the end of fourth grade. These essential fluency and math skills are vital to a student's successful future progress to more complex mathematical learning (McTiernan et al., 2016). Knowles (2010) examined the benefits of drill practice. This 8- week quasi-experimental quantitative study, based on cognitive development and theories of the construction of memory, used an experimental design with 3-levels of independent variables to see if there was a relationship between how teachers’ implemented timed drill practices and the students’ level of automaticity with basic multiplication facts. The study focused on sixth-grade, regular education math classes. Knowles found significant increases in students' fact fluency. Knowles further says that students' fluency is necessary before reaching upper grades. Multi-Rao and Plati (2015) research shows the importance of teaching math fact fluency to students in elementary school. He explains the need to develop a solid foundation to transfer the skills to other settings and formats (Musti-Rao et al., 2015; McTiernan et al., 2016). McTiernan, Holloway, Healy, and Hogan (2016) conducted a

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randomized control trial by analyzing the impact of a frequency-building curriculum. The study worked to increase fluency with 28 males ages nine to eleven. McTiernan (2016) concluded that there is a correlation between students' math abilities and their fluency. Results from the study found a connection between the ability of a student to fluently be successful on one-digit addition and subtraction problems and their ability on assessments (McTiernan et al., 2016). Most of the students in the study demonstrated increased performance on fluency outcomes and could use these skills to succeed on standardized math assessments. These findings show how vital building math fluency skills are. Shockingly, in 2022, average scores in math declined across student groups in the U.S. After analyzing the data, we see that the average scores for students nine years old in 2022 decreased by seven points in math compared to 2020. This decrease is the first decline in math (The Nation's Report Card, 2023). The ability to proficiently compute with whole number operations is tied to reasonable and appropriate practice to develop instant recall of addition, subtraction, multiplication, and related division facts, says The National Mathematics Advisory Panel (The Final Report of the National Mathematics Advisory Panel - Ed, 2008, p. xix). Students need to become fluent with strategies for solving algorithms to improve addition, subtraction, multiplication, and division fluency. When students develop strong use of these strategies, it will help build the recall automaticity of basic math facts. Computer-based Instruction Researchers have concluded that foundational math fluency is vital in elementary grades (Musti-Rao& Plati, 2015). If the curricula teachers are using do not provide

adequate practice to master this basic math fluency, it will limit the chances for students to become fluent in their facts (Berrett & Carter, 2018). Using educational computer instruction programs with 63 third-grade students in three study groups, Berrett & Carter conducted a study (2018). They demonstrated improved fluency skills compared to their baseline. They continued demonstrating growth during the follow-up part of the study. Results from the study showed that teachers who use math curriculum and educational computer-assisted games effectively help develop and build math fact fluency in the classroom. Math curriculums used in elementary schools, especially those employed in the upper grades, assume that students have mastered fluency with their basic math facts and do not require time built in to focus on essential math fluency. Another researcher, Berger (2023), showed the benefits of using games in teaching fluency. This quantitative study compared two classwide approaches to promote fifth-grade multiplication fact fluency. Throughout the research section, a fifth-grade math class practiced multiplication facts for ten minutes daily. They used a game-based multiplication fact practice. The second fifth-grade math class practiced multiplication facts for ten minutes each day using computer multiplication fact practice. This researcher concluded that both showed growth, and neither was better. Further study is necessary to see if there is a way to combine these strategies to bring more beneficial growth. Purposeful Interventions Many techniques and strategies help students build fluency. Fluency building is built through flashcards, memorization, computer-assisted instruction (games, i-ready), and educational math games. Drill and practice activities such as memorizing and using flashcards can be more engaging and motivating for students. Drill and practice

activities and straight memorization are less effective than computer instruction and educational math games (Hawkin, 2017). When students reach 5th grade and beyond, the focus within math moves away from basic math fluency, even if students are not proficient, to instruction focused on concepts like three-digit multiplication and division. A qualitative research study by Baker & Cuevas (2018) had third--, fifth-, and 8th-grade students focusing on automaticity with basic math facts. Barker and Cuevas asked students fourteen questions. Half of the questions focused on allowing the time needed to produce answers for multiplication problems that were single digits. The second half of the questions asked the students to provide answers based on how they interpreted the problem. The study's results show that students need help with single-digit multiplication problems where they should be proficient. The data from this study also suggests a significant link between the automaticity of knowing basic math facts and the ability to solve more complex problems fluently (Baker & Cuevas, 2018). Since today's math curriculum lacks basic fact fluency, teachers must look for ways to supplement and build time for teaching these facts, focusing on fluency practice with targeted interventions and engaging activities. (Burns 2012) conducted an intervention study, a computer-based program to practice math facts thrice a week for eight to 15 weeks. The study involved 216 third- and fourth-grade students at a higher risk for math difficulties. The results showed that students who participated in the intervention had more substantial gains in their math scores than those students who did not partake in the intervention. Burns (2012) suggests that computer-aided instruction positively affects students' math fact fluency, leading to more meaningful core math instruction.

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Students are more likely to succeed in essential math fact fluency when actively engaged and motivated to learn. How can we get students motivated to learn and stay engaged? Spangenberg and Roberts (2020) say it is essential to encourage students to learn mathematics and stay motivated. One such way to motivate students is through computer-based instruction and games. Computer instruction is a way to give students an engaging and motivating tool to learn math facts. Computers have become prevalent in today’s classrooms for implementing academic intervention and practicing skills (Rich, 2017). Hawkins (2016) argues that there is a way for teachers to supplement their math curriculum with quick, easy, motivating, and engaging activities for students. Computer-based instruction programs, like i-Ready and XtraMath, are now a fun and effective way for teachers to support students with essential math fact fluency and lessons that directly target a specific student's need. Younger students are increasing their use of technology. So, traditional paper methods may become less appealing (Berrett & Carter (2017). Therefore, teachers must look for technology to increase students' desire to learn and engage. Computer-based games and computer-based instruction have changed dramatically in recent years. They are no longer just drill and practice activities. They are engaging and motivate students. According to Rich (2017) and Vanbevelaere (2019), computer instruction and computer-based games are excellent tools for building fluency because they are adaptive, engaging, and motivating. Rich (2017) conducted a research study examining the effectiveness of multiple computer-based math practices on paper-pencil performance. Fifty-seven second-grade students completed fluency tests with a computer, a mixture of computer and pencil-paper, or only paper-pencil. The study

showed the importance of analyzing all the parts when using and developing computer- based interventions. When making decisions, teachers must use computer interventions and progress-monitoring tools. These results indicate that practice effectively shows significant growth (Rich 2017). Rich (2017) also states that teachers should incorporate tried and true paper-pencil strategies and computer interventions to support all students in increasing math fact fluency. Using both forms, the data collected showed that students could connect the different modalities. Crawford, Higgins, Huscroft-D’Angelo, and Hall (2016) studied 3rd- 5th grade students, examining their math reasoning skills before and after using electronic support tools(ESTs), one computer learning component. Crawford (2016) concluded that ESTs are successful at increasing student success in math because they can prioritize the technology program to meet the individual students' needs. Students also improved reasoning skills during the program, which is also due to the use of the EST. Adaptive games are excellent for students because they always assess their performance and adapt the tasks to meet their needs. How can we incorporate all these methods into our teaching? Is there time to do so? More research is vital to find the most effective way to integrate fact fluency. Milton, Jessica H., Flores, Margaret M., Moore, Alexcia J., Taylor, Ja’ Lai J., Burton, Megan E (2019) used a mixed-methods research study to investigate the effects of concrete representational abstract (CRA) on multiplication and division facts. It focused on unknown facts and conceptual understanding for students with disabilities. This study saw student progress, but because it did not compare it to students learning by drills, they could not share the results of the better method.

Further research is needed to conclude which method will impact students the best. Researcher Valle-Lisboa (2017) conducted a qualitative study to see if a month- long game-based intervention can help. Valle-Lisaboa et al. (2017) selected schools with different socioeconomic backgrounds to participate in this study. A total of 454 first- grade girls participated. This study discovered a relationship between cognitive variables and SES. Additionally, it found that the intervention of games led to increased scores. An especially significant increase was found in students with a low SES status. The effect of this intervention positively impacts student math learning and achievement. Carver (2016) explored research on K-12 teachers’ beliefs about the benefits and hazards of educational technology when used by teachers or students in K-12 instruction. Data was collected using an open-ended qualitative survey format from a group of teachers enrolled in online classes in the education department. The study shows that teachers think students prefer technology because it is more engaging. Implementing computer games and learning strategies in the classrooms is a way to fix the gap in the math curriculum and provide individualized learning to meet the needs of all students. Another way to enhance a student's success with math procedures and reasoning is through technology, which is vital for overall math proficiency (Crawford et al., 2016). Math games are another effective, motivating, and engaging way for students to learn and practice math facts. Providing students with meaningful practice to help them master their basic math facts is an effective way to teach basic math facts. Bay-Williams and Kling (2014) state that meaningful practice can come in different forms, including, but not limited to, using story problems, games, and ten frames. When working with first

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and second-grade students, Bay-William & Kling (2014) found that students didn’t want to stop playing the games when it was time to quit. Math games can target fact practice based on a particular need that a group has. Bay-Williams & Kling (2014) state that the best time to make observations and interviews is while students play the math games. These interviews and monitoring are conducted to monitor their progress with their facts. Although games are engaging, they only sometimes do the job of teaching the students the facts so they can recall them quickly. Games are more productive in teaching students strategies to solve problems than they are at teaching fluency. Mass & Nyamsuren (2016) analyzed the strategies' performance in a math game and several tasks where students must have math fluency and mathematical creativity. The effectiveness of increasing math thinking is limited because it was not the focus of analysis in this study. Mass and Nyamsuren (2016) see a future for educational games as a study method in cognitive development for academic and scientific purposes. (Skarr et al., 2014) conducted a quantitative research study. This study found a relationship between using direct instruction flashcard procedures and a math racetrack game procedure and the mastery of basic math facts. The combined effect of tools proved highly effective for each student (Skarr et al., 2014). All the students in the study mastered all math facts across all three sets for at least three sessions. Developing mathematical learners requires teachers to think of new ways to provide students with activities to build fluency besides paper-pencil, drill, and practice. Educational games allow students to build fundamental math fluency through hands-on and interactive activities. According to Rai (2012), games can improve cognitive learning and enhance learning. Rai & Beck (2012) developed a framework for determining the effect of gamelike elements using a mixed-method approach. Rai &

Beck (2012) wanted to see the strengths of enhancing engagement and learning. They also wanted to cover the costs of distractions and working memory overload. In the study, 297 students were randomly assigned to four groups. The qualitative data in the research conducted by Rai & Beck (2012) supports the idea that students generally favored game-like aspects when learning. But is this because they are learning more or because it was simply fun? Unfortunately, the data collected on learning success resulted in no conclusive results or patterns. The brief intervention involved many skills (Rai & Beck, 2012). Conclusion Students today all learn differently and have a variety of learning needs. Building fact fluency at an early age may lead to more successful students. As math concepts deepen in later school years, students must rely on automaticity to solve problems. Incorporating educational games and activities motivates students to learn and practice their basic math fluency facts. Both traditional and computer-based games provided for students can engage them in learning. Nevertheless, are the strategies engaging the students and providing them with the academic growth necessary to be successful high school students and lifetime learners? Students will benefit significantly if we find a way to effectively engage and teach fact fluency. The Sprague Method combines technology use, games, rewards, and teaching students successful strategies. Each of these studies showed the importance of interventions for students with learning gaps that need to be addressed because core instruction is insufficient. These interventions include online tools and teacher-directed interventions and strategies. These studies show how targeted instruction and online tools will boost students'

knowledge or skills to succeed. Meeting the needs of all students is the responsibility of teachers and schools to ensure all students are successful in learning. All classrooms should have a time in their day when interventions can be implemented and regularly assessed to ensure they are working and meeting the needs of the students. Chapter 3 Methodology As the classroom teacher who will initiate the change, action research is an appropriate research approach to the research questions. I will use action research to determine problems or weaknesses of interventions, and I will use strategies of the Sprague Method for practical solutions to create greater student achievement on assessments. I will gather evidence of students' needs by evaluating the placement of students on the multiplication and division tests. From this, I will know how to change my interventions for specific students. By doing this, I hope students master their math facts fluently. Participants The participants of this study are 30 5th-grade students in Ms. Sprague’s class. The characteristics of the participants contain a large amount of diversity, including students from seven different nationalities. The participants include students above grade level, at grade level, and below grade level. The participants also include students who have ADD, ADHD, learning disabilities, and Autism. Students will receive the Sprague Method interventions, including XtraMath. Ms. Sprague is the teacher of the 30 students.

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Research Question 1. What is the effect of The Sprague Method on students' understanding of basic fact fluency? Data Collection and Instruments and Methods The data collection during this action research project will use quantitative data. The students will be tested on their previous knowledge of facts. This is quantitative data. I will give a pre-and post-test consisting of 100 multiplication questions and 100 division questions. These are aligned with 5th-grade Common Core Standards and are given with paper and pencil. Students will take the tests as pre-post-tests. This is a quantitative data collection. The pre- and post-assessments will be collected using paper and pencil, and their data will be entered into a spreadsheet. These assessments align with the research question because they will show whether students grew in math facts after receiving the Sprague teaching method. Data Analysis Data from the pre and post-test will be entered into a spreadsheet for statistical and quantitative analysis. It will show where students started with their understanding of math facts and what growth, if any, they achieved during the two weeks. This quantitative data will look at the descriptive statistics, comparing the averages of the pre and post-tests. I will look at all pre- and post-test scores when analyzing the data. I will see if student scores increased, decreased, or stayed the same after using The Sprague Method. The results from the data will address the following research question:

What is the effect of The Sprague Method on students' understanding of basic fact fluency? By looking at the data, I can determine if students' knowledge of fact fluency increased, decreased, or stayed the same, which will signify the effectiveness of the Sprague Methond on Fact Fluency. Ethical Issues and Considerations The ethical issues and considerations for this study would be explaining to the students that completing the instructional unit is voluntary and will not affect their grades. In addition, I would inform them that the instrument would only be used to gather data for my master’s program. To protect participants, all student names will be removed. Numbers will be assigned for any data that will be shared outside of instructor use. The instructor will secure all data collected in a locked file cabinet that is only accessible. After all data has been collected, assessments will be shredded. The final results of this study will be shared, but no student information will be included. This will prevent any possible ethical issues. Conclusion The instruction I will use to provide a solution for the participants in this action research project will take place during reteach math time, which is 20 minutes, five days a week. No regular instruction will be missed due to participation in this study. The research will be conducted in March inside the regular classroom. Data from the pre and post-test will be entered into a spreadsheet for statistical and quantitative analysis. It will show where students started with their understanding of math facts and what growth, if any, they achieved during the two weeks. This quantitative data will look at the descriptive statistics, comparing the averages of the pre and post-tests. I will look at all

pre- and post-test scores when analyzing the data. I will see if student scores increased, decreased, or stayed the same after using The Sprague Method. The results from the data will address the following research question: What is the effect of The Sprague Method on students' understanding of basic fact fluency? By looking at the data, I can determine if students' knowledge of fact fluency increased, decreased, or stayed the same, which will signify the effectiveness of the Sprague Methond on Fact Fluency. From the pretest, specific skills aiding in comprehension will be targeted. The comprehension skills will be scaffolded. Students will be instructed on strategies for solving multiplication facts, such as skip counting, close to 5, and one more than doubles. After the instruction and XtraMath practice, the post-test will be given, and the data will be analyzed. All students are expected to participate fully in all routine classroom activities. Students will voluntarily participate in intervention groups as needed. If a child chooses not to participate, he or she will participate in other intervention activities that will target his/her needs. Works Cited 1. Cozad, L.E., and Riccomini, P.J. (2016) ‘Effects of Digital-Based Math Fluency Interventions on Learners with Math Difficulties: A Review of the Literature, The

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Journal of Special Education Apprenticeship, 5(2), pp. 1–19. https://eric.ed.gov/? id=EJ1127743 2. Baker, A. T., & Cuevas, J. (2018). The importance of automaticity development in Mathematics. Georgia Educational Researcher, 14(2). https://doi.org/10.20429/ger.2018.140202 3. The nation’s report card. The Nation’s Report Card. (n.d.-a) https://www.nationsreportcard.gov/ 4. The final report of the National Mathematics Advisory Panel - Ed. (n.d.). https://files.eric.ed.gov/fulltext/ED500486.pdf 5. Knowles, P. (2010) The Relationship Between Timed Drill Practice and the Increase of Autmaticity of Basic Multiplication Facts for Regular Sixth Graders. Walden University https://scholarworks.waldenu.edu/cgi/viewcontent.cgi? referer=&httpsredir=1&article=1824&context=dissertations 6. Rave, K., and Golightly, A.F. (2014). The effectiveness of the rocket math program for improving basic multiplication fact fluency in fifth-grade students: a case study. Education, 134(4), 537-547. https://eric.ed.gov/?id=EJ1034993 7. Ma, V. J., and Ma, X. (2014). A comparative analysis of the relationship between learning styles and mathematics performance. International Journal of Stem Education, 1(1), 1-13 https://stemeducationjournal.springeropen.com/articles/10.1186/2196-7822-1-3 8. McTiernan, A. Holloway, J., Healy, O., and Hogan, M. (2016). A randomized controlled trial of the Morningside math facts curriculum on fluency, stability, endurance, and application outcomes. Journal of Behavioral Education, 25(1), 49-68. https://link.springer.com/article/10.1007/s10864-015-9227-y

9. Musti-Rao, S., Lynch, T.L., and Plati, E. (2015). Training for fluency and generalization of math facts using technology. Intervention in School and Clinic, 51(2), 112-117 https://journals.sagepub.com/doi/10.1177/1053451215579272 10. Musti-Rao, S., and Plati, E. (2015). Comparing two class-wide interventions: implications of using technology for increasing multiplication fact fluency. Journal of Behavioral Education . 24(4), 418-437. https://www.researchgate.net/publication/277934487_Comparing_Two_Classwid e_Interventions_Implications_of_Using_Technology_for_Increasing_Multiplicatio n_Fact_Fluency 11. Berrett, A.N., Carter, N.J. Imagine Math Facts Improves Multiplication Fact Fluency in Third-Grade Students. J Behav Educ 27 , 223–239 (2018). https://doi.org/10.1007/s10864-017-9288-1 12. Hawkins, R. O., Collins, T., Hernan, C., and Flowers, E. (2017). Using Computer-Assisted instruction to build math fact fluency: an implementation guide. Intervention in School and Clinic, 52(3), 141-147. https://eric.ed.gov/? id=EJ1122838 13. Milton, Jessica H., Flores, Margaret M., Moore, Alexcia J., Taylor, Ja’ Lai J., Burton, Megan E. (2019). Using Concrete-Representational-Abstract sequence to teach conceptual understanding of basic math multiplication and division. Learning Disability Quarterly, 42 (1) 32-45 https://journals.sagepub.com/doi/10.1177/0 14. Burns, M. K., Kanive, R., & DeGrande, M. (2012). Effect of a computer- delivered math fact intervention as a supplemental intervention for math in third

and fourth grades. Remedial and Special Education, 33(3), 184–191. https://doi.org/10.1177/0741932510381652 15. Spangenberg, E. D., and Roberts, A. K. (2020). Peer tutors’ views on their role in motivating learners to learn mathematics. Pythagoras, 41(1), 1-13 chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://files.eric.ed.gov/ fulltext/EJ1272027.pdf 16. Rich, S.E.H., Duhon, G.J. and Reynolds, J. (2017). Improving the generalization of computer-based math fluency building through sufficient stimulus exemplars. Journal of Behavioral Education, 26(2), 123-136. https://eric.ed.gov/?id=EJ1141247 17. Crawford, L., Higgins, K.N., Huscroft-D’Angelo, J.N., and Hall, L. (2016). Students’ use of electronic support tools in mathematics. Educational Technology Research and Development: AB 1- Monthly Publication of the Association for Educational Communications and Technology, 64(6), 1163-1182. https://experts.nebraska.edu/en/publications/students-use-of-electronic-support- tools-in-mathematics 18. Valle-Lisboa, J., Cabana, Á., Eisinger, R., Mailhos, Á., Luzardo, M., Halberda, J., & Maiche, A. (2017). Cognitive abilities that mediate SES’s effect on elementary mathematics learning: The Uruguayan tablet-based intervention. Prospects: Quarterly Review of Comparative Education , 46(2), 301–315. https://eric.ed.gov/?id=EJ1143729 19. Carver, L. B. (2016). Teacher perception of barriers and benefits in k-12 technology usage. Turkish Online Journal of Educational Technology - Tojet, 15(1), 110–116. https://eric.ed.gov/?id=EJ1086185

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20. Bay-Williams, J. M., & Kling, G. (2014). Enriching addition and subtraction fact mastery through games. Teaching Children Mathematics, 21(4), 238–247. https://doi.org/10.5951/teacchilmath.21.4.0238 21. Acrobatiq. (2015). Research Foundations. Online Courseware accessed through Western Governor’s University. 22. Common Core State Standards Initiative. (2002). http://www.corestandards.org/Math/ 23. Baker, A. T., & Cuevas, J. (2018). The importance of automaticity development in Mathematics. Georgia Educational Researcher, 14(2). https://doi.org/10.20429/ger.2018.140202 24. McTiernan, A. Holloway, J., Healy, O., & Hogan, M. (2016). A randomized controlled trial of the Morningside math facts curriculum on fluency, stability, endurance, and application outcomes. Journal of Behavioral Education, 25(1), 49–68. https://link.springer.com/article/10.1007/s10864-015-9227-y 25. Cozad, L.E., and Riccomini, P.J. (2016). ‘Effects of Digital-Based Math Fluency Interventions on Learners with Math Difficulties: A Review of the Literature, The Journal of Special Education Apprenticeship, 5(2), pp. 1–19. https://eric.ed.gov/?id=EJ1127743 26. Ma, V. J., & Ma, X. (2014). A comparative analysis of the relationship between learning styles and mathematics performance. International Journal of Stem Education, 1(1), 1-13 https://stemeducationjournal.springeropen.com/articles/10.1186/2196-7822-1-3

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27. Berger, Jordyn, "A Comparison of Two Approaches To Promote Multiplication Fact Fluency In Fifth Grade" (2023). Dissertations, Theses, and Projects. 776. https://red.mnstate.edu/thesis/776 28. Caron, Thomas, Learning Multiplication: The Easy Way, (2007). Clearing House: A Journal of Educational Strategies, Issues and Ideas. V80 p.278-282 https://eric.ed.gov/?id=EJ773613 29. Adam Skarr, Katie Zielinski, Kellen Ruwe, Hannah Sharp, Randy L. Williams, T. F. McLaughlin, (2014) The Effects of Direct Instruction Flashcard and Math Racetrack Procedures on Mastery of Basic Multiplication Facts by Three Elementary School Students. Education and Treatment of Children , Volume 37, Number 1, February 2014, pp. 77-93 (Article) Adam Skarr.Researchgaate 30. Maas, H. L. J., and Nyamsuren, E. (2017). Cognitive analysis of educational games: the number game. Topics in Cognitive Science, 9(2), 395-412. https://onlinelibrary.wiley.com/doi/10.1111/tops.12231 31. Rai, D., & Beck, J. E. (2012). Math learning environment with game-like elements. International Journal of Game-Based Learning, 2(2), 90–110. https://doi.org/10.4018/ijgbl.2012040106 32. Maas, H. L. J., and Nyamsuren, E. (2017). Cognitive analysis of educational games: the number game. Topics in Cognitive Science, 9(2), 395-412. https://pubmed.ncbi.nlm.nih.gov/27868349/

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QYM3 Task 3_ Ch 1-3

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