BASIC MATH FACT FLUENCY 2 Abstract Basic math fact fluency instruction has been altered in the last ten years. This alteration has led to the increase of students not being fluent in basic math facts and instruction in fifth-grade math has become difficult. This eight-week action project implemented a daily whole-class math routine for basic math fact fluency. A review of earlier projects showed that teachers are seeing problems with basic math fact fluency and implementing small group routines to mitigate the problem. The researchers did find success; however, the research was contained to small groups of students and not a class of 30 students. The project’s main goals were to increase fluency of students’ basic math facts, increase fluency and decrease the time for completion of students that are already proficient, and examine if the whole class approach would fill the need of at-risk students. Participants (N=30) fifth-grade students were assessed for their fluency, placed with a partner, and assigned games for fluency practice in one of the four basic math fact categories of addition, subtraction, multiplication, and division. At the end of the week, students were assessed for their knowledge of their category and possible advancement to the next area of concern in the basic math facts. Reflex Math, a computer basic math fact program, was also purchased by the school; this was used for practice for 20 minutes a day. Students did show success in most areas and the routine was changed to fit the needs of the students. Future study is needed to investigate the success of the computer game alone and the routine alone compared to the combination. BASIC MATH FACT FLUENCY 3 Acknowledgments Throughout this Master of Education program and action project, I have received a great deal of support and assistance. I would like to first thank my committee chair, Professor Sheryl J. Rushton, who helped with the implementation, writing, and analysis of student data. Your help was invaluable to the success of the project and the paper. I would like to thank my committee of Professor Sheryl J. Rushton, Professor Penée W. Stewart, and Principal Debra Marshall. Their kind words, editing, and encouragement to complete this project helped me to stay on track to complete it promptly. I would like to thank all the professors and teachers in the master’s program that helped me along the way to understand the process and encourage my research. In addition, I would like to thank my family, my husband, and children, that cooked, cleaned, and read every single one of my versions of this paper and all the homework needed to complete this degree. BASIC MATH FACT FLUENCY 4 Table of Contents Nature of the Problem…….……………………………………………………………………………………………..…………………….…6 Literature Review………………….……………………………...………………………………………………….….…………...……………7 The Ideal Mathematics Classroom……………….………………….………….………………...……….………………….7 Real-Life Struggles…………………….…………………………….……………………….…………...…………...………………9 A Case for a New Routine…………………………………………….…………………………………………….………….….11 Summary…………………………………………………………………………………………………………….…….………………12 Purpose……………………………………………………………………………………………………………………………………..………….13 Method………………………………………………………………………………………………………………………...….……………..……15 Participants……………………………………………………………………………………………………...……….……....…….15 Instruments ……….…………………………………………………………………………………………….………….....……….15 Procedures……………………………………………………………………………………………….………………..…....……...17 Data Analysis and Discussion………………………………………………………………………………………………….…….……….21 Question 1: Basic Math Facts Improvement Over Time…………………………………………….….….….……22 Question 2: Time Reduction Over Time While Retaining Proficiency………………….………….…..…….26 Question 3: Impact on At-Risk Students…………………………………………………………………………..……….29 Limitations………………………………………………………………………………………………………………..………………33 Recommendations and Future Research……………………………………………………………………..……………33 References………………………………………………………………………………………………….…………..………………..…...…….35 BASIC MATH FACT FLUENCY 5 Appendices…………………………………………………………………………………….……….………………….……...….……..…….38 Appendix A: Approval from International Review Board……………………………………...…..…...……….38 Appendix B: District Approval Letter………………………………………………………………………………..……….39 Appendix C: Administration Approval Letter ……………………………………………………………………..…….40 Appendix D: Explanation for Parents ..…………………………………………………………….………...……….……41 Appendix E: Pre/Post Tests…………………………………………………………………………………………………...….42 Appendix F: Weekly Tests………………………….………………………………………..………………….……….…...….50 Tables Table 1: Daily Routine times………………………………………………………………………….………………………..…20 Table 2: I-Ready Assessment Results…………………………………………………………………….……………..……24 Table 3: All Student Absences and Late Attendance………………………………………………..……..…………25 Table 4: Addition Practice……………………………………………………………………………………….………………..25 Table 5: At-risk Student Data……………………………………………………………………………………….…………….32 BASIC MATH FACT FLUENCY 6 Nature of the Problem Problem Statement Upper elementary students should be fluent (accurate, efficient, and flexible) with their basic math facts which will allow students to conceptualize problems. Being fluent with basic math facts (one-digit addition, subtraction, multiplication, and division) will allow students to understand the concepts of mathematics (Boaler, 2014). To become fluent, students need multiple representations (Rau et al., 2012) and ways to learn the facts that are engaging (Boaler, 2015). Engaging mathematics includes real-life mathematics problems (Seely & Burns, 2015), repetition for practice (Boaler, 2015), and a deep understanding of number sense (Russell, 2000). Students in Utah are learning to conceptualize mathematics but are struggling due to a lack of math fluency with basic math facts. Students need a foundation of basic math facts (Chiesa & Robertson, 2000) to succeed with upper elementary mathematics problems. Schools are either implementing computer programs to increase basic math fact fluency (Rau et al., 2012), Cover-Copy-Compare methods (Codding et al. 2007), or precision teaching of the basic math facts to fill in learning gaps of students who are struggling with mathematics (Chiesa &Robertson, 2000). Teaching basic math facts daily will increase the abilities of students’ mathematics understanding in upper elementary and into future learning. Students need time and practice for mastery of basic math facts (Boaler, 2015; Seeley & Burns, 2015; Russell, 2000). That practice can take the form of mathematical games (Boaler, 2015), Math Talks (Seeley & Burns, 2015), and rich engaging problems that promote deeper thinking (Boaler, 2014; Boaler, 2015; Seeley & Burns, 2015). These concrete games and engaging problems, with manipulatives, develop math fact fluency to the extent of abstract thinking (Boaler, 2015; Seeley & Burns, 2015). This abstract thinking of basic math facts allows students to concentrate on the harder problems and not on the precursory skills (Seeley & Burns, 2015). BASIC MATH FACT FLUENCY 7 Literature Review The Ideal Mathematics Classroom Mathematical success and understanding of mathematical processes in upper elementary classrooms are connected to the mastery of basic math facts. In the textbook for Utah’s Elementary Mathematics Endorsement, Van de Walle et al. (2013) state “Mastery of a basic fact means that a student can give a quick response (in about 3 seconds) without resorting to inefficient means” (p. 171). Addition and subtraction recall should be learned in first grade and mastered by second grade. Mastery, in this case, is answering in 3 seconds or less. Jo Boaler, a leader in mathematics instruction, claims that students will commit basic math facts to heart when they have meaningful number activities and then will have a deeper understanding of mathematics and numbers (2015). Common Core State Standards for Mathematics (CCSSM) 2nd grade states that students will “Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction” (National Governors Association, 2021). There are no fluency guidelines in CCSSM on basic multiplication or division facts, only for multidigit multiplication in 5th grade. This implies that they will be fluent in their basic multiplication facts, but the implications are misinterpreted. Misinterpretations of the meaning of fluency in the common core are commonplace and publishers continue to emphasize rote memorization (Boaler, 2015). Russel (2000) explains fluency as efficient, accurate, and flexible. Fluency in basic math facts will increase student understanding and flexibility in mathematics. However, rote memorization is not the best method of instruction (Boaler, 2015). Memorizing multiplication tables, timed tests, and some practices are damaging to students and cause mathematics anxiety. Boaler explained in her 2014 article that timed tests and rote memorization are calculated into a student’s grade and that have the students compete against each other is stressful and will cause math anxiety in students. Number sense, the flexible thinking of numbers, is more important for students’ deeper understanding of numbers and their relationships; inferring students will become BASIC MATH FACT FLUENCY 8 proficient in basic math facts if they have number sense. In the same article, Boaler found that less successful students did not have number sense and more successful students did (2014). Proficiency in basic math facts and skills, along with good pedagogy, will contribute to better mathematical understanding and less stress for students (Seeley & Burns, 2015). Mathematical pedagogy has changed over the years, there are multiple strategies to achieve mastery of basic math facts. With multiple representations and multiple pedagogical strategies for mastery of basic math facts, there are multiple ways to solve simple and complex problems in mathematics (Boaler, 2015; Van de Walle et al., 2013). Including real-life mathematics problems to engage students in mathematics will increase the student’s abilities (Seeley & Burns, 2015). Math Talks and Number Talks expand student knowledge of mathematics and numbers by changing instruction in the classroom. Instruction changes by having the teacher as the facilitator, not the lecturer, of the conversation of students who are doing the thinking and sharing (Humphreys & Parker, 2015). The teacher asks a student to explain their thinking as they solve a problem. The teacher will write exactly what the student says whether it is right or wrong. This allows the student and their peers to have discussions about the strategies used to solve the problem and clarify misconceptions. Students in the conversation and classroom will learn from each other. Math Talks, Number Talks, number sense, practice, repetition, and engaging activities consistently performed can be used to promote fluency and increase students’ abilities in understanding mathematics (Boaler, 2015). There are studies that demonstrate the necessity of mastery of basic math facts to increase student understanding of mathematical processes in upper elementary mathematics (Chen, 2018; Chiesa &Robertson, 2000; Codding et al., 2007; Garnaas-Halvorson, 2014; Hoelscher, 2016; Russell, 2000). BASIC MATH FACT FLUENCY 9 Real-life Struggles Before and after the adoption of CCSSM and a change in the pedagogy for mathematics instruction in lower and upper elementary classrooms, students are and were struggling with basic math facts, the process of computation, and a deeper understanding of mathematics (Chen, 2018; Chiesa & Robertson, 2000; Coding et al., 2007; Garnaas-Halvorson, 2014; Ginsburg & Leinwand, 2005; Hoelscher, 2016; Rau et al., 2012). Teachers were concerned with students falling behind their peers because of their lack of mastery of basic math facts (Chiesa & Robertson, 2000). Several different studies were conducted using models from other countries to increase mathematics comprehension because of the need for basic math fact fluency for American students (Chen, 2018; Ginsburg & Leinwand, 2005; Samuelsson, 2010; Stigler & Perry, 1988). The use of timed testing causes anxiety in students and the fear, dislike, and avoidance of mathematics as a subject in upper elementary students (Boaler, 2014; Seeley & Burns, 2015). Seeley and Burns (2015) found that students were nervous about timed tests and did not perform to their abilities because of the time constraint and fear of failure. This nervousness highly contributed to their low achievement, mathematics avoidance, and negative experiences with mathematics. Mathematic anxiety was the rationale for discontinuing the rote memorization and timed testing of basic facts. Seeley and Burns suggest using timing sheets to show student growth and not calculated in the grade book as an acceptable use for timed tests (2015). Many teachers have found a struggling student’s lack of basic math facts an issue and tried several strategies to increase student basic math fact knowledge (Garnaas-Halvorson; 2014; Hoelscher, 2016; Russell, 2000). Computer games are a popular strategy for increasing basic math facts. Rau et al. (2012) used 3 different computer programs for increasing fraction knowledge. The program, Fraction Tutor, included Sense-making with worked-out problems, auto-linked representations, or no Sense-making; each program either had basic math fact fluency or no basic math fact fluency. Students who BASIC MATH FACT FLUENCY 10 had worked on examples and fluency practice showed the most increase in the post-test. The study showed that Sense-making alone was not enough, students needed basic math fact fluency for comprehension. Codding et al. in 2007 tried using the Cover, Copy, Compare (CCC) strategy to increase student fluency in basic math facts. This strategy was scripted with a small pull-out group. The teacher wrote the basic fact on the board, the students copied it on their paper, and they compared to make sure the two matched. This was repeated many times to ensure students did not forget the facts. The strategy was repeated for less basic mathematical problems as well. The study did show improvement for the students who were included. Garnaas-Halvorson (2014) used multiple addition strategies and timed addition and subtraction tests to prove mastery and progression to the next step in basic math facts. The parents signed a document to practice with their students at home regularly. Twenty-five students from third to fifth grade spent after-school time with the teacher for 8 months. A timed pre-test determined the starting point for each student in the program and a survey was given to each student to uncover the student’s thinking. This information directed the next strategies for the teacher to address to the students. The strategies included adding on, making 10, doubles, doubles plus one, adding zero, and adding one. The students took a test and survey each week as they entered the classroom to assess progress. When the student achieved mastery (completion of the timed test in 5 minutes or less) they were able to move on to subtraction. In this study, all students showed improvement. Hoelscher (2016) worked with at-risk Title 1 second and third-grade students in a pull-out setting for twelve weeks on basic math fact fluency. The students were given a self-evaluation on their feelings about mathematics and a timed test to determine placement. The intervention of playing fluency games and introducing strategies lasted 30 minutes each day during the students’ intervention time. At the end of the twelve-week program, students were given another timed test and a survey BASIC MATH FACT FLUENCY 11 about how they felt about mathematics. All students commented they felt better about mathematics and increased their basic math fact fluency. Precision teaching was the strategy used by Chiesa and Robertson in 2000 to increase students’ ability for basic math fact fluency. Out of a class of 25, five students were perceived as at-risk for failure. These five students were given precision instruction, direct instruction in another classroom, to increase their basic math facts. Students were given weekly timed tests to prove mastery to move to the next set of math facts. At the end of the twelve weeks, the five students outscored all but one of the other students in the class on an assessment. These researchers found that practice with basic math facts and introducing math fact strategies helped students to increase their fluency and understanding of upper elementary mathematic concepts. A Case for a New Routine The routine of daily basic math facts practice will increase the abilities and understanding of mathematical processes in upper elementary students and increase their future learning in mathematics (Seeley & Burns, 2015). Riccomini et al. concluded that as more research shows that basic math fact fluency is important for students the standard practice, or routine, is crucial for effective and efficient in K-8 classrooms (2017). Achievement of mastery of basic math facts takes time, preparation, and daily repetition through many strategies. Mastery can be achieved through time and practice with basic math facts using multiple strategies (Boaler, 2015; Russell, 2000; Seeley & Burns, 2015). Mastery of basic math facts is not to be achieved by rote pedagogy, but instead, instruction should include Number Talks, Math Talks, and games that promote number sense (Boaler, 2015; Seeley & Burns, 2015). Increasing the number sense by instructing from concrete items to the abstract and by providing multiple exposures will increase students’ knowledge. This exposure should be routine in a classroom setting. BASIC MATH FACT FLUENCY 12 The mastery of basic math facts allows students to move from simple to more complex problems with less difficulty (Seeley & Burns, 2015). This explanation is imperative for lower elementary teachers to understand so their students can succeed in upper elementary and later mathematics classes. Mastery of basic math facts through number sense will bring about deeper thinking about mathematics and the ability to complete more complex mathematics tasks (Boaler, 2014; 2015). Deeper thinking, or the ability to persevere and conceptually understand, is the process we need our students to be able to achieve (Seeley & Burns, 2015). These articles and books in this literature review all coincide with the need for mastery of basic math facts for future mathematical success and enjoyment of students’ mathematical knowledge (Seeley & Burns, 2015). Summary In an ideal upper elementary classroom, all students should be ready for the mathematical concepts taught at their grade level. Students should have a conceptual understanding of basic mathematical processes and basic math facts. With these basic understandings in place, students will be able to think abstractly and have a deeper understanding of mathematical processes and procedures (Boaler, 2015; Seeley & Burns, 2015). Students will be able to complete real-life problems with multiple strategies in an acceptable amount of time. Students are currently struggling to understand and conceptualize upper elementary mathematics (Chen, 2018; Chiesa & Robertson, 2000; Coding et al., 2007; Garnaas-Halvorson, 2014; Ginsburg & Leinwand, 2005; Hoelscher, 2016; Rau et al., 2012). Anxiety and mathematical phobias are showing up in classrooms (Boaler, 2014). These phobias are leading to a deficit in mathematics in upper elementary classrooms. Teachers are being creative in their solutions by trying new strategies for teaching basic math facts with computer games and reteaching mathematics strategies that should have been mastered in second and third grade (Coding et al., 2007, Rau et al., 2012, Van De Walle et al., 2013). New pedagogy and curriculum have been developed to decrease the gap between proficient BASIC MATH FACT FLUENCY 13 students and those who are at-risk with basic math facts (Boaler, 2014; Seeley & Burnes, 2015). These practices are designed for daily practice and take extensive time in the classroom. Many teachers are struggling with being able to include these practices in their daily schedules. The solution is to make time for the practice with daily routines that will promote mastery of basic math facts and upkeep practice of those learned facts. These daily routines will help to promote deeper learning in mathematics by having conversations about mathematics and number sense (Boaler, 2015). With the routine, the students will be able to complete more complex problems with less difficulty because of their fluency with the basic math facts (Seeley & Burns, 2015). Purpose With the increased need for students to conceptually understand mathematic concepts, the need for fluency in basic math facts is imperative (Seeley & Burns, 2015). Curriculum has been developed to help students conceptualize mathematics, however, the practice of basic math facts has declined and in some areas is non-existent (Chen, 2018; Ginsburg & Leinwand, 2005; Samuelsson, 2010). Teachers, including the author, have found that students are taking longer to complete tasks due to the inability to recall basic math facts (Seeley & Burns, 2015). This extending of time on tasks is limiting teachers’ ability to include more complex and real-world problems into the mathematics instruction time. There is a problem with misinterpreting leaders in the mathematics society (Boaler,2015). The interpretation is that students do not need to be fluent in basic math facts and that “drill and kill” routines are causing anxiety in students and so they should not be implemented (Boaler, 2014). The leaders have said that the basic math facts need to be practiced so that the student will become fluent in a way that is not stressful (Boaler, 2015; Russell, 2000; Seeley & Burns, 2015). The problem is that the routine for practice and upkeep of basic math facts has not been fully developed and implemented in a whole class setting. BASIC MATH FACT FLUENCY 14 The purpose of this eight-week quantitative action project is to implement a basic math fact fluency routine to increase the student’s mastery of basic math facts. This routine is different than other studies in the literature review in that this will be whole class and not done in a pull-out or afterschool program. This routine will hopefully increase the ability of students to recall basic math facts that allow for a more conceptual understanding of fifth-grade mathematics. The questions to answer for this study are: 1. Do students improve over time in their mastery of basic math facts? 2. Do proficient students reduce the time needed for completion of the basic math fact assessments throughout the study while retaining accuracy? 3. How does the practice routine impact the basic math fact fluency of the at-risk students? BASIC MATH FACT FLUENCY 15 Methods In this eight-week quantitative action project, a basic math fact fluency routine was developed and implemented. This routine allowed students to start where they have gaps in their basic math facts. Filling the gaps allowed students to better understand the basics of mathematics and increase their ability to complete tasks. Daily practice of basic math facts through games with a partner increased the use of the basic math facts. Participants Thirty students aged 10-11 years old in one fifth-grade classroom participated in this study. The class was chosen by the administration and consisted of students of differing abilities and socioeconomic statuses. The class consisted of 16 boys and 14 girls in a suburban/urban area school. There were students included who have Individualized Education Plans (IEPs) for learning disabilities, 504 plans for anxiety and ADHD, and some with issues that have not been evaluated and documented. Instruments The instruments used for this study included basic math facts and mathematic timing sheets, fluency games, Reflex Math, and I-Ready computer assessment tools. The mathematic timing sheets were published by Shoecraft and Clukey (1981) in their book “The Mad Minute”. These mathematic timing sheets allowed assessment of students’ abilities, the grouping of students with similar needs, instructional differentiating, and a starting point for the routine. Problems on addition, subtraction, multiplication, and division facts (sixty of each) were used for the pre-tests and post-tests. The same book supplied the weekly assessments with thirty problems on each page. Students used the games for fluency produced by J. Petersen (2013) in her book Math Games for Number and Operations and Algebraic Thinking. The games promoted the upkeep of basic math fact fluency by dealing with only one of the four basic math facts at a time. The teacher selected a few games for the students to choose from as they practiced their basic math facts. Games included Missing BASIC MATH FACT FLUENCY 16 Addend or Factor, roll to $1.00, Build 10, Anything but 10, Addition Table Trail, Addition Tic-Tac-Toe, Cross Out Sums, Finding Factors, Hit the Target (mental multiplication), Spinning Sums and Differences, and many others. The math games were not sufficient or supportive of students learning basic math facts and replaced with math games with dice and Uno cards that increase the practice of basic math facts. The author decided that the number of basic math facts needed for proficiency needed more practice for learning the basic math facts. Students were given a base number to work with for the day and 0-9 dice to roll and add, subtract, or multiply to the base number depending on their placement in the basic math fact category. The division category multiplied the number and then wrote the two-division problems. The Uno cards were used for addition, subtraction, or multiplication “war.” Uno Cards were also used for a division game that involved 3 students. Two students would put a card on their forehead the other student would multiply the numbers and the goal was to figure out the number on their head. Students used the computer program Reflex Math. This computer program allowed the students to practice their basic math fact fluency using computer games. To start the program the author placed all the students in the addition and subtraction 0-10 program. When a student showed completion of the addition and subtraction 0-10 in the computer program, the author changed the computer setting for that student to multiply and divide 0-10. The program was used four days a week during computer learning time in the classroom. Each session took up to twenty minutes to complete. I-Ready is a computer math intervention and instructional tool. The program does have initial, intermediate, and final placement tests to assess student knowledge in grade-level mathematics. The placements allow students to use the program to increase their math knowledge at their current placement. The placements also allow teachers to provide interventions for students. BASIC MATH FACT FLUENCY 17 Procedures Preparation Permissions. Permission to conduct the action research was first obtained from the author’s university’s IRB (Institutional Review Board) to allow for the action project (see Appendix A) and then the district (see Appendix B). The third permission was from the administration at the school. The principal and assistant principal each received a copy of the research to review. When the project was approved by the administration written acknowledgment was obtained (see Appendix C). Parental consent from all thirty students was obtained. The consent letter outlined the purpose, need, and how student information was used. The parents were allowed to know their student’s progress toward mastery of their basic math facts, however, the names of the students or any other identifying markers were removed before insertion in the completed document. The letter was sent to parents both digitally and in paper form one week before the commencement of the action project. Parents had the option of denying consent. Their students would still have participated in the procedure because this was a daily mathematic routine in the classroom, however, their results would not have been published in this paper (see Appendix D). Pre/post and weekly assessment tests. At the beginning of the study, students took all four pre-tests on the same day with small breaks in between that allowed students to relax and reduce anxiety. The tests were graded by the teacher and analyzed to find gaps in the fluency of the four categories of basic math facts (addition, subtraction, multiplication, and division). The measure of fluency was determined with 95% accuracy on each test. If a student tests at 95% for all four basic math facts, that student still participated in the weekly practices to upkeep their skills. The teacher determined which category of basic math facts to have these students help other students who may need peer interventions. All students were given a different set of the four post-tests at the end of the BASIC MATH FACT FLUENCY 18 eight weeks. The post-test was of the same nature as the pre-test and did not increase in difficulty (see Appendix E). Students were notified that the results of the tests are not figured into their grades. Weekly tests were given in the student’s designated category of need starting with addition, then subtraction, then multiplication, and finally ending with division. Each weekly test had thirty facts with a time of three seconds per question. When the student achieved proficiency with 95% or higher on the weekly test, the student was moved to the next category of concern in the four categories of basic math facts (see Appendix F). Students who showed proficiency with all categories of basic math facts in the pre-test still participated and were tested in their assigned practice category for the week to help with the upkeep of skills. Fluency routine games. The practice part of the routine included many games the students participated in to obtain fluency. The games were from the book: Math Games for Number and Operations and Algebraic Thinking. The games in the book were copied, laminated, placed in a large-sized envelope with the instructions, and placed in the room close to the manipulatives needed for the games. The students were assigned a partner and a choice of two or three games to play that allowed them to practice their basic math fact category and increase their recall ability. After day two of the action project, the games were changed to reflect the needs of the students that had not achieved fluency in basic math facts. The new games supported the learning of basic math facts and conversations that promoted proficiency. Routine To begin the study, students were encouraged to understand the need for fluency in the basic math facts. Students were first asked what they feel and think about mathematics. Students were asked to write down their answers; pictures were encouraged. Students were then asked to share their pictures or words with their table groups, and then finally with the teacher. The teacher then asked if they knew of a way to make mathematics easier and what advantages each of their ideas might have. BASIC MATH FACT FLUENCY 19 Luckily, a student did mention that mathematics is easier with the fluency of basic math facts. If that did not occur, the teacher would have brought up the topic of fluency in basic math facts and asked the students who feel confident with mathematics if they are fluent with their basic math facts. The students were then instructed about the program from start to finish. The first of the four pre-tests, addition, was given. The students were allowed to see the timer on the board that was set for three minutes. This allows three seconds for each problem, the amount of time used for fluency for sight words, and the time expected by Vander Walle et al. (2013). The students were told that the required percent correct for each test will be 95%, so they can miss up to three problems and still be considered fluent. Students wrote down the time on the timer at the top of their paper to show how much time remained when they completed the test. The remaining three tests were administered with the same instructions and expectations. The tests were collected after each category. Students who showed proficiency in all categories during the pre-test still took the assessments to improve their time for completion and help with the upkeep of their skills. The teacher then corrected each test and recorded the data in excel, assigned each student a number from one to thirty (the amount in the classroom with parental permission). Each test was placed in separate excel spreadsheets to simplify analysis and placement. Weekly routine. Each Monday through Thursday students participated in ten minutes of practice with their targeted category of basic math facts with a partner who had been chosen by the teacher. The partnership was given a target number to learn the basic math facts. Students who showed proficiency in all basic math facts were partnered with a student to become peer instructors and give strategies to help increase the skill of their partner. Table 1 shows the times needed for instruction and implementation. BASIC MATH FACT FLUENCY 20 Table 1 Daily Routine Times Time of Day Time for Completion Fluency Games Beginning of the Day 10 minutes Strategy Conversation Beginning of the Day 2-3 minutes Math and Number Talks Imbedded in Math Instruction 10-15 minutes Journaling Imbedded in Math Instruction 2-3 minutes Reflex Math After Lunch Recess a9-20 minutes Note. a Students can achieve the completion of a day’s assignment in Reflex math in as low as 9 minutes, however, some students with low focus often complete the assignment in 20 minutes. On Friday, each student took a timed test. The students were reminded of the 95% accuracy and wrote their time left over at the top of their paper. The results were used to analyze growth and determine potential advancement to the next targeted category. Students who had previously shown proficiency tried to beat their own time on the assessment. The teacher initially analyzed the pre-test and placed students into partnerships, after the first week the teacher analyzed the weekly tests for placement and updating partnerships. Students were placed in categories of the need for basic math facts and then partnered with a student with similar needs to allow for practice. The categories had students close to or who showed proficiency partnered with one with less proficiency. Students with 50% proficiency or less were not partnered with another student with 50% proficiency or less to ensure that one of the partners was sharing correct strategies with the other. Daily the teacher observed and analyzed the progression of the partnership to check to see that the practice happened, and fluency was increasing. If needed, partnerships were altered to ensure productive work. BASIC MATH FACT FLUENCY 21 After the ten-minute practice, students were allowed to reflect on their practice. The class had an open ten-minute Math and Number Talk. Math Talks and Number Talks increased students’ knowledge of different ways of solving basic math facts. Students were able to share ways they had learned to solve basic math facts to help other students. Those strategies, such as adding on or decomposing numbers, which were shared were discussed for their usefulness and effectiveness. Students were able to write them down in their mathematics journals to implement them in their next day’s mathematics routine. On Fridays, students were given a weekly assessment of thirty problems for one and a half minutes (three seconds per question) in their category of practice for the week. Students wrote down their time left over at the top of their paper. Students were reminded of the required 95% proficiency and the ability to move to another basic math fact category of need. The teacher graded, collected the data, placed the data in excel, and determined placement and partnerships for the next week. After the action project, students were given the post-test of sixty problems of each category of basic math facts and corrected for the 95% accuracy and decrease in time needed for completion. After the program was done, the teacher discussed the program with the administration at the school and then in the grade level meeting with colleagues. The program in its entirety with the accompanying data was analyzed for possible implementation in other classrooms or changes that would make implementation recommended. Data Analysis and Discussion Thirty students’ (N =30) pre-test/post-test and weekly tests were graded. The number correct and time for each student were placed into an excel worksheet with each student being assigned a number to remove any identifiable marker. The excel worksheet was analyzed after the process using Paired Sample T-tests to statistically examine the differences between all the means of the variable used in the experiment. The dependent variables are the improvement between the pre-and post-test scores BASIC MATH FACT FLUENCY 22 and the change in the completion times while maintaining accuracy. The independent variables are the treatment of practice routine games and Math and Number talks. A linear regression model will be used to analyze the effectiveness of at-risk students compared to other students in the classroom. After answering the questions of the study, the analysis determined changes that needed to be made to the routine, or suggestions for differentiation. The growth of all students’ knowledge is the primary goal, and the project is successful if any student increases their knowledge. Question 1: Basic Math Facts Improvement Over Time Addition The initial pre-test on addition showed 11 students proficient, the post-test showed 18 students proficient. The descriptive data results from the scores of the addition basic math fact fluency pre-test (M=45.47, SD= 19.07) were lower than the post-test (M=47.13, SD= 15.39). The results of an independent t-test showed that this difference was statistically significant, t (29) = 3.43, p<.001. This suggests the routine was successful in increasing student proficiency in addition basic math facts. Subtraction The initial pre-test on subtraction showed 11 students proficient, the post-test showed 14 students proficient. The descriptive data results from the scores of the subtraction basic math fact fluency pre-test (M=38.27, SD= 15.77) were lower than the post-test (M=52.07, SD= 11.54). The results of an independent t-test showed that this difference was statistically significant, t (29) = 4.93, p<.001. This suggests the routine was successful in increasing student proficiency in subtraction basic math facts. BASIC MATH FACT FLUENCY 23 Multiplication The initial pre-test on multiplication showed 7 students proficient, the post-test showed 15 students proficient. The descriptive data results from the scores of the multiplication basic math fact fluency pre-test (M=31.33, SD= 18.73) were lower than the post-test (M=47.81, SD= 15.58). The results of an independent t-test showed that this difference was statistically significant, t (29) = 7.37, p<.001. This suggests the routine was successful in increasing student proficiency in multiplication basic math facts. Division The initial pre-test on division showed 9 students proficient, the post-test showed 14 students proficient. The descriptive data results from the scores of the division basic math fact fluency pre-test (M=33.53, SD= 20.02) were lower than the post-test (M=41.97, SD= 20.33). The results of an independent t-test showed that this difference was statistically significant, t (29) = 3.90, p<.001. This suggests the routine was successful in increasing student proficiency in division basic math facts. General Like many of the other researchers quoted in the literature review, the author did find some problems with students not being fluent in basic math facts. At the initiation of the project student data did show that there were gaps in mathematical learning shown by IReady placement testing (see Table 2). This initial low placement of IReady could be due to many factors including the COVID-19 pandemic, soft closures, hybrid learning, test anxiety, online learning, and the misinterpretation of Boaler with lack of number sense (Boaler, 2015). While the Math and Number Talks were happening during class, the Math and Number Talks were not productive due to the inability to focus on just one category of basic math fact fluency. If all the students were in one category, the Math and Number Talks would be more consequential. BASIC MATH FACT FLUENCY 24 Table 2 I-Ready Assessment Results Assessment Results Beginning of the year Middle of the Year 5th-grade level 10 16 4th-grade level 16 10 3rd-grade level 3 2 2nd-grade level 1st-grade level 1 Assessment Results for Number and Operations Beginning of the year Middle of the Year 5th-grade level 10 15 4th-grade level 17 11 3rd-grade level 2 2 2nd-grade level 1st-grade level 1 Note. Two students moved, the beginning of the year has 30 students, middle of the year has 28 students. The results varied due to student absences during the week and on the weekly test days. Nine students were at all eight of the end-of-week tests. Four students were quarantined for two weeks due to Covid-19 protocols. Table 3 shows the absences of students and late attendance along with the justifications. Students who were late to school missed the routine and were included in the table. During the routine, the weekly tests showed the need for more practice for addition (Table 4). Nine students tested completely proficient and were assigned to support those not proficient. Overall, the students did increase their basic math fact fluency. The author attributes the multiplication math fact fluency increase due to the content area of multiplying double-digit numbers at the time of the project. BASIC MATH FACT FLUENCY 25 Table 3 All Student Absences and Late Attendance Reasons for Absences and Late Attendance COVID Parent Cleared Out of Town Late Week 1 7 3 5 Week 2 2 7 9 4 Week 3 11 3 Week 4 5 10 3 Week 5 7 14 8 Week 6 4 12 10 Week 7 8 20 5 Week 8 2 14 11 Total missed 28 95 12 49 Note. These data are for all 30 students in the class for example during week one there were a total of 10 absences and 5 late entries into class. Table 4 Addition Practice Number of Students Working on Fluency in Addition Week 1 19 Week 2 10 Week 3 7 Week 4 7 Week 5 6 Week 6 4 Week 7 1 Week 8 0 BASIC MATH FACT FLUENCY 26 Question 2: Time Reduction Over Time While Retaining Proficiency Addition Eleven students were identified as being proficient in addition basic math facts at the beginning of the project. The descriptive data results from the scores of the proficient students (achieving 95% or higher) in the addition basic math fact fluency pre-test (M=59.73, SD= 0.47) was slightly higher than the post-test scores (M=59.09, SD= 1.38). The results of an independent t-test showed that this difference was not statistically significant, t (10) = -1.75, p= 0.111. The results show that the students did not improve on their 95% correct but maintained their proficiency shown by the mean (M) score of 59.09 out of 60. The results from the descriptive data for the remaining time on the addition basic math fact fluency pre-test (M=47.00, SD= 30.47) were lower than the post-test (M=49.55, SD= 21.64). The results of an independent t-test showed that this difference was not statistically significant, t (10) = 0.46, p= 0.657. This suggests the routine was not successful in decreasing the students’ remaining time after completing the addition basic math facts post-test. This data does show that they increased their remaining time, however, the time was not statistically significant. Subtraction Eleven students were identified as being proficient in subtraction basic math facts at the beginning of the project. The descriptive data results from the scores of the proficient students (achieving 95% or higher) in the subtraction basic math fact fluency pre-test (M=59.00, SD= 0.89) were lower than the post-test (M=59.18, SD= 0.98). The results of an independent t-test showed that this difference was not statistically significant, t (10) = 0.48, p= .640. This suggests the routine was not statistically successful in retaining the student’s proficiency. The mean (M) did improve from the pre-test to the post-test showing that students did not decrease their proficiency and had a slight increase in proficiency. BASIC MATH FACT FLUENCY 27 The descriptive data for the remaining time on the subtraction basic math fact fluency pre-test (M=40.18, SD= 29.74) were lower than the post-test (M=49.18, SD= 22.35). The results of an independent t-test showed that this difference was not statistically significant, t (10) = 1.549, p=.152. This suggests the routine was not statistically successful in decreasing the students’ remaining time after completing the subtraction basic math facts post-test. The mean (M) scores do show an increase in the time remaining from the pre-test to the post-test showing there was a slight increase in practical significance. Multiplication Seven students were identified as being proficient in multiplication basic math facts at the beginning of the project. The descriptive data results from the scores of the proficient students (achieving 95% or higher) in the multiplication basic math fact fluency pre-test (M=59.14, SD= 21.00) were lower than the post-test (M=60.00, SD= 0.00). The results of an independent t-test showed that this difference was not statistically significant, t (6) = 2.52, p=.45. This suggests the routine was not statistically successful in retaining the student’s proficiency in the multiplication basic math facts. The mean (M) does show that students did improve in their scores and did not reduce their proficiency. The results from the descriptive data for the remaining time on the multiplication of basic math fact fluency pre-test (M=24.71, SD= 21.00) was lower than the post-test (M=81.00, SD= 21.43). The results of an independent t-test showed that this difference was statistically significant, t (6) = 4.46, p<.004. This suggests the routine was statistically successful in decreasing the students’ remaining time after completing the multiplication basic math facts post-test. The mean (M) shows that the time left over was significant to show an increase in both statistical and practical significance. BASIC MATH FACT FLUENCY 28 Division Nine students were identified as being proficient in division basic math facts at the beginning of the project. The descriptive data results from the scores of the proficient students (achieving 95% or higher) in the division basic math fact fluency pre-test (M=59.33, SD= 0.71) were higher than the post-test (M=59.22, SD= 2.00). The results of an independent t-test showed that this difference was not statistically significant, t (8) = -0.15, p=.886. This suggests the routine was not statistically successful in retaining the student’s proficiency in the division basic math facts. The mean (M) score does show a slight decrease in student proficiency but only by .11, this shows that proficiency was maintained. The descriptive data for the remaining time on the addition basic math fact fluency pre-test (M=22.11, SD= 12.59) was lower than the post-test (M=65.22, SD= 21.67). The results of an independent t-test showed that this difference was statistically significant, t (8) = 5.62, p<.001. This suggests the routine was successful in decreasing the students’ remaining time after completing the division basic math facts post-test. The mean (M) score does show both practical and statistical significance. General The data did not show statistical significance growth in all areas and did show a very slight decrease in some concept areas. The author acknowledges that the proficient students scored in the 95% range in three minutes. The ability to increase the percentage and increase time left over is very small. The data did show that there was not enough change for a significant improvement. Seven students showed proficiency in all four mathematical categories. Two more students showed proficiency in all but multiplication. Those nine students had minimal absences and late attendance except student 7 who was quarantined due to COVID. The proficient students did become peer mentors for those less proficient and they shared strategies not only for basic math facts but also for test-taking strategies. The author saw two mentors cheering for their peers when they completed their tests and encouraged improvement. BASIC MATH FACT FLUENCY 29 Question 3: Impact on At-Risk Students Addition The descriptive data results for the at-risk students for the scores of the addition basic math fact fluency pre-test (M=33.40, SD= 19.48) were lower than the post-test (M=39.20, SD= 16.02). The results of an independent t-test showed that this difference was not statistically significant, t (4) = 2.70, p=.055. This suggests the routine was not successful in increasing at-risk student proficiency in addition basic math facts. Students at this level of at-risk struggle with increasing their abilities. The mean (M) scores do show an increase in the number of questions correct. The descriptive data of the at-risk students for the remaining time on the addition basic math fact fluency pre-test (M=7.60, SD= 12.59) was higher than the post-test (M=4.60, SD= 7.06). The results of an independent t-test showed that this difference was not statistically significant, t (4) = 3.00, p=.701. This suggests the routine was not statistically successful in decreasing the at-risk students’ remaining time after completing the addition basic math facts post-test. The mean (M) does show that there was less time left over at the end of the post-test. All but one of the students decreased their number of incorrect answers on the post-test which explains the lack of time remaining. Subtraction The descriptive data results for the at-risk students for the scores of the subtraction basic math fact fluency pre-test (M=20.20, SD= 12.83) were lower than the post-test (M=33.80, SD= 22.19). The results of an independent t-test showed that this difference was statistically significant, t (4) = 2.70, p<.041. This suggests the routine was successful in increasing at-risk student proficiency in subtraction basic math facts. The descriptive data results for the at-risk students for the remaining time on the subtraction basic math fact fluency pre-test (M=0.00, SD= 0.00) were lower than the post-test (M=6.40, SD= 14.31). The results of an independent t-test showed that this difference was not statistically significant, t (4) = BASIC MATH FACT FLUENCY 30 3.00, p=.374. This suggests the routine was not statistically successful in decreasing the at-risk students’ remaining time after completing the subtraction basic math facts post-test. When looking at the mean (M) you can see that there was no time remaining for the pre-test, and 6.40 seconds was remaining for the post-test. This signifies that none of the students completed the subtraction at the pre-test, but some completed the post-test. Multiplication The descriptive data results for the at-risk students for the scores of the multiplication basic math fact fluency pre-test (M=15.20. SD= 5.85) were lower than the post-test (M=30.40, SD= 11.82). The results of an independent t-test showed that this difference was statistically significant, t (4) = 3.34, p<.029. This suggests the routine was successful in increasing at-risk student proficiency in multiplication basic math facts. The author acknowledges that the math concept of double-digit multiplication in the classroom helped improve the students’ increase in multiplication. Because none of the five at-risk students finished the test in the three-minute assessment for the pre-test or post-test the independent t-test was not conducted. Division The descriptive data results for the at-risk students for the scores of the division math fact fluency pre-test (M=15.60, SD= 4.62) were lower than the post-test (M=16.80, SD= 9.09). The results of an independent t-test showed that this difference was not statistically significant, t (4) = 0.33, p=.755. This suggests the routine was not statistically successful in increasing at-risk student proficiency in division basic math facts. The students did show a slight improvement in their mean (M) scores. Because none of the five at-risk students finished the test in the three-minute assessment the independent t-test was not conducted. BASIC MATH FACT FLUENCY 31 General Although the paired sample t-tests did not show significant improvement for the five at-risk students and the project was considered not statistically significant or not successful for these students, the author did see a practical difference in the five students identified as at-risk. The author noticed a difference in the students’ I-Ready scores and noted a correspondence between absences and success with the routine (see Table 5). This study focused on improving fifth-grade level basic math fact scores. Students in this grade are expected to be able to add, subtract, multiply and divide with little difficulty. Those struggling with these basic math facts have been able to compensate for these shortcomings and find ways to complete tasks without having proficiency. The result usually is a lower performance on unit tests, end-of-level tests, and placement tests. In the literature review, the author mentioned that practice is needed for proficiency (Seeley & Burns, 2015). Along with the need for basic math fact knowledge, practice for fluency retention is also needed. BASIC MATH FACT FLUENCY 32 Table 5 At-risk Student Data Absences and Late Attendance Student 1 Student 2 Student 3 Student 4 Student 5 Week1 Week 2 2 2 1 3 Week 3 Week 4 3 1 Week 5 2 2 Week 6 2 3 1 2 Week 7 3 2 5 Week 8 2 1 2 1 Total Missed 9 9 2 15 5 I-Ready Results Before and After Initial Placement Grade 3 Grade 3 Grade 1 Grade 4 Grade 3 Ending Placement Grade 4 Moved Grade 3 Grade 4 Grade 5 I-Ready Results in Number and Operations Initial Placement Grade 4 Grade 4 Grade 1 Grade 3 Grade 4 Ending Placement Grade 4 Moved Grade 4 Grade 3 Grade 4 Note. Student numbers are random BASIC MATH FACT FLUENCY 33 Limitations This project was conducted at the beginning of the school year. COVID caused several issues with this study. Twenty-eight students who were quarantined missed ten days of school or were exposed to COVID missed up to five days of school. This was a significant factor in determining the amount of practice the students had for their basic math facts. Other student absences, 95 parent cleared and 12 out of town, also impacted the project. Students were taking more days off for illnesses, anxiety, vacations, and overall days off this year than in past years. Late attendance, 49, impacted the research due to the main practice was done before 9:30 in the morning. There were 184 absences and late attendance for the whole class. This is 15% of the days of the project that were missed by students. The amount of time allowed in the school schedule for basic math facts practice was also a factor in the success or failure of the routine. The author felt pressured by herself to decrease time in the routine to be synchronous with the other classes in the grade level. The time that was spent with the basic math facts did, however, help increase the knowledge of the students and decrease the time needed for completing assignments. The author’s misunderstanding of the purpose of the math games in the book by J. Petersen (2013) for the routine complicated the project for a few days. Within two days of the fluency practice, the author noticed the need for students to obtain mastery of basic math facts that the games did not provide. The games provided for the upkeep of students’ current mastery but did not increase mastery of unknown basic math facts and so the games failed in their purpose. The author changed the practice to mastery-building games to increase students’ mastery of basic math facts. Recommendations and Future Research Basic math fact fluency is important for fifth-grade mathematics. The need for fluency and mastery needs to start at a lower grade level. The author recognizes the district’s increased awareness and testing in younger grades with Acadience Math, a new testing program implemented this year to BASIC MATH FACT FLUENCY 34 test grades kindergarten through second grade on basic math facts. This program should increase students’ mastery of basic math facts if used to its fullest potential of informing teachers of instruction needed for mastery of basic math facts. The author will still stress basic math fact fluency and test students at the beginning of the year and work on mastery throughout the school year. The routine will be altered by not doing the Math and Number Talks as a whole group, but with small groups of students working on the same basic math fact component. The math games in the book by J. Petersen (2013) will only be used by students who already show proficiency and not the non-proficient students. Future research could include determining the impact of Reflex Math with or without the routine. The computer program may have impacted the success of the program. Future research on attendance and its impact on basic math fact fluency learning in the COVID pandemic and after would be suggested. The author recommends that the district’s mathematics instruction include basic math fact fluency routines for fluency and the upkeep of the student’s knowledge of basic math facts. The author recommends a study from the district on the impact of COVID, attendance, and student learning of not only basic math fact fluency but of overall learning of all students. BASIC MATH FACT FLUENCY 35 References Boaler, J. (2014). Research suggests that timed tests cause math anxiety. Teaching Children Mathematics, 20(8), 469-474. Boaler, J. (2015). Fluency without fear: Research evidence on the best ways to learn math facts. Reflections, 40(2), 7-12. Chen, J. (2018). Using an adapted cover-copy-compare math intervention in China: A Pilot study. Journal of Human Services: Training, Research, and Practice, 3(1), 4. https://scholarworks.sfasu.edu/cgi/viewcontent.cgi?article=1046&context=jhstrp Chiesa, M., & Robertson, A. (2000). Precision teaching and fluency training: Making maths easier for pupils and teachers. Educational Psychology in Practice, 16(3), 297-310. Codding, R. S., Eckert, T. L., Fanning, E., Shiyko, M., & Solomon, E. (2007). Comparing mathematics interventions: The effects of cover-copy-compare alone and combined with performance feedback on digits correct and incorrect. Journal of Behavioral Education, 16(2), 125-141. Garnaas-Halvorson, A. (2014). The Impact of weekly math tests and strategy instruction on math fluency. https://sophia.stkate.edu/maed/92 Ginsburg, A., & Leinwand, S. (2005, November). Singapore math: Can it help close the US mathematics learning gap [Conference presentation]. In CSMC’s First International Conference on Mathematics Curriculum, November (pp. 11-13). Hoelscher, L. (2016). Effective strategies for increasing basic math fact fluency. BASIC MATH FACT FLUENCY 36 https://sophia.stkate.edu/maed/190 Humphreys, C., & Parker, R. E. (2015). Making number talks matter: Developing mathematical practices and deepening understanding, grades 4-10. Moorabin: Hawker Brownlow Education. National Governors Association (2021) Common core state standards initiative. http://www.corestandards.org/read-the-standards Petersen, J. (2013). Math games for number and operations and algebraic thinking. Sausalito, CA: Math Solutions. Riccomini, P. J., Stocker, J. D., & Morano, S. (2017). Implementing an effective mathematics fact fluency practice activity. TEACHING Exceptional Children, 49(5), 318–327. https://doi.org/10.1177/0040059916685053 Russell, S. J. (2000). Developing computational fluency with whole numbers in the elementary grades. The New England Math Journal, 32(2), 40-54. Rau, M. A., Aleven, V., Rummel, N., & Rohrbach, S. (2012, June). Sense making alone doesn’t do it: Fluency matters too! ITS support for robust learning with multiple representations [Conference presentation]. In International conference on intelligent tutoring systems (pp. 174-184). Springer, Berlin, Heidelberg. Samuelsson, J. (2010). The impact of teaching approaches on students’ mathematical proficiency in Sweden. International Electronic Journal of Mathematics Education, 5(2), 61-78. Seeley, C. L., & Burns, M. (2015). Faster isn’t smarter: Messages about math, teaching, and learning in the 21st century: A resource for teachers, leaders, policy makers, and families. Sausalito, CA: Math Solutions. BASIC MATH FACT FLUENCY 37 Shoecraft, P. J., & Clukey, T. J. (1981) The mad minute: A race to master the number facts. Addison-Wesley Stigler, J. W., & Perry, M. (1988). Mathematics learning in Japanese, Chinese, and American classrooms. New Directions for Child and Adolescent Development, 1988(41), 27-54. Van de Walle, J. A., & Karp, K. S. & Bay-Williams, J. M. (2013) Elementary and middle school mathematics teaching developmentally. Pearson. BASIC MATH FACT FLUENCY 38 Appendix A September 18, 2021 Sheryl Rushton Linda Hunzeker Students, Teacher Education Re: Exempt - Initial - IRB-AY21-22-25 Basic Math Facts Hunzeker Dear Sheryl Rushton: The Weber State University Institutional Review Board has rendered the decision below for Basic Math Facts Hunzeker. Decision: Approved Approval: September 18, 2021 Selected Category: 4. Collection of data through noninvasive procedures (not involving general anesthesia or sedation) routinely employed in clinical practice, excluding procedures involving x-rays or microwaves. Where medical devices are employed, they must be cleared/approved for marketing. (Studies intended to evaluate the safety and effectiveness of the medical device are not generally eligible for expedited review, including studies of cleared medical devices for new indications.) 6. Collection of data from voice, video, digital, or image recordings made for research purposes. Findings: Research Notes: Subjects are considered adults, signatures/consent are required, and they may choose not to participate. Anonymity and confidentiality are addressed appropriately, and the type of information gathered could not "reasonably place the subjects at risk of criminal or civil liability or be damaging to the subjects' financial standing, employability, or reputation" (Code of Federal Regulations 45 CFR 46, Subpart D). You may proceed at this time; you have one year to complete the study. Please remember that any anticipated changes to the project and approved procedures must be submitted to the IRB prior to implementation. Any unanticipated problems that arise during any stage of the project require a written report to the IRB and possible suspension of the project. If you have any question please contact your review committee chair or irb@weber.edu. Sincerely, Dr.s Hubler, Meerts-Brandsma & Williams College of Education IRB Sub-committee Weber State Institutional Review Board BASIC MATH FACT FLUENCY 39 Appendix B Approved verbally on August 23, 2021 BASIC MATH FACT FLUENCY 40 Appendix C BASIC MATH FACT FLUENCY 41 Appendix D Parental Consent August 23, 2021 Dear Parents and Families, Hello, I am Linda Hunzeker your child’s 5th-grade teacher. In a desire to increase my abilities as a teacher, I am currently a student in the Master of Education in Curriculum and Instruction at Weber State University. As a student, I am asking for your help with my master’s Action Project. This Action Project focuses on the need for basic math fact fluency. Fluency does not mean rote memorization, but the ability to produce an answer in three seconds or less. This type of fluency can be achieved by practicing the facts daily and learning new strategies for solving basic math facts. My project will involve students taking timed tests to assess their current needs. The tests will be graded and analyzed to determine placement with one of the four basic math facts: addition, subtraction, multiplication, and division. Weekly tests will be taken in their category of need and analyzed for advancement or further instruction. In addition to the timed tests, students will participate in ten minutes of daily practice with their assigned category of need. Each student will be paired with another student to play a mathematic game to increase their basic math fact understanding. After the practice, the class will engage in a class discussion on what strategies were used and what strategies could increase fluency. This discussion will ask all students to share what is going on in their heads to solve the problems. I would ask for your help at home as well. Any practice at home with games, flashcards, or talking with your child about strategies that you use will help increase their knowledge. I will be sharing your student’s findings with you weekly. I want you to know your student’s progress and where their need for support lies. As I am presenting information to the university, no names, photographs, or any other personal information about your student will be disclosed. I will only be using the data collected to inform my conclusions and findings of practice with basic math facts. I do need your permission to use your child’s data for this action project. The attached permission slip from Weber State University needs to be signed with permission for using your student’s data or refusal of the use of your student’s data. If you have concerns about the project, please contact me for further information. Thanks, Linda Hunzeker BASIC MATH FACT FLUENCY 42 Appendix E Placement tests Addition pre-test BASIC MATH FACT FLUENCY 43 Addition post-test BASIC MATH FACT FLUENCY 44 Subtraction pre-test BASIC MATH FACT FLUENCY 45 Subtraction post-test BASIC MATH FACT FLUENCY 46 Multiplication pre-test BASIC MATH FACT FLUENCY 47 Multiplication post-test BASIC MATH FACT FLUENCY 48 Division pre-test BASIC MATH FACT FLUENCY 49 Division post-test BASIC MATH FACT FLUENCY 50 Appendix F Addition weekly tests BASIC MATH FACT FLUENCY 51 BASIC MATH FACT FLUENCY 52 BASIC MATH FACT FLUENCY 53 BASIC MATH FACT FLUENCY 54 Subtraction weekly testsBASIC MATH FACT FLUENCY 55 BASIC MATH FACT FLUENCY 56 BASIC MATH FACT FLUENCY 57 BASIC MATH FACT FLUENCY 58 Multiplication weekly testsBASIC MATH FACT FLUENCY 59 BASIC MATH FACT FLUENCY 60 BASIC MATH FACT FLUENCY 61 BASIC MATH FACT FLUENCY 62 Division weekly testsBASIC MATH FACT FLUENCY 63 BASIC MATH FACT FLUENCY 64 BASIC MATH FACT FLUENCY 65