Mastering Basic Facts through the Reflex Program (Grantee Research Outcome)

By Barbara Dotson

    Mastering Basic Facts through the Reflex Program (Grantee Research Outcome)

    About the Author

    Barbara Dotson
    La Presa, CA
    1 Article Published
    Barbara Dotson

    I graduated from San Diego State University, California, USA, with a Liberal Arts Degree and earned my teaching credential and Master’s degree through Chapman University, California. In addition to my Elementary Education Credential, I have a supplemental credential in math for Grades 7-9. This is my 24th year in the La Mesa Spring Valley School District. I have taught math all 23 years, as well as other subjects for multiple years. I have taught 6th and 7th grades in three different schools and various math classes, including Intensive math classes in which students are multiple years below grade level, Common Core 7th grade math class, and 7th grade Intervention math class.

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    Project Summary

    Most of the students in my intensive math class are multiple years below grade level and struggle with basic math facts. To help students recall the basic facts with automaticity so they can solve more advanced math problems without being hindered by their lack of basic skill, I implemented the Reflex program, a game-based computer program that was developed for such purposes. Seventh grade students (N = 70) from Individualized Education Programs and Intensive math classes participated in this research project. The purpose of this teacher-research was to determine the effect of the Reflex program on students’ abilities to master basic math facts to the level of automaticity and math performance on multiplication and division.  My research showed that the Reflex program did increase the students’ fluency speed on multiplication and division basic facts indicated by their performance on multiplication and division.

    Project Context

    This project took place at STEAM Academy in La Presa, California. STEAM Academy serves 4th through 8th grade students. The teachers who teach math in the upper grades, and also teachers in the lower grades, used the Reflex program to help students develop the level of automaticity in processing basic math facts. This project was relevant to my school site because we have a significant amount of students who are academically below grade level in math. Mastery of basic math facts with automaticity will help students go beyond the basics and access higher-level problems. Working through a structured process that has a high interest level for students, the mastery of basic facts will allow students to be more confident, more willing to persevere through higher level problems, and have more success in their mathematical futures. It is difficult to teach the math standards for 7th grade when students become stuck on a simple math fact and cannot proceed through the problem due to this lack of basic knowledge and skills. In this practitioner research, I examined whether a game-based computer program, Reflex, is effective for our students in this school in helping them develop fluency with math facts to the mastery level, which will then enable students to access higher level math with greater confidence and perseverance.

    Research Goal, Method, and Outcome

    Project Goal and Significance

    When students in my intensive class enter 7th grade, most, if not all, do not have their basic math facts mastered and this slows down their math fluency, which frustrates them while trying to learn a new math concept.  When students become fluent at their basic skills, they become more confident in math as a whole, and they can complete problems in a fluid manner. A significant amount of research has been conducted on the importance of basic math facts mastery with automaticity to access higher-level mathematical problems. In “Learning multiplication: The easy way,” Caron (2007) stated that when automaticity of math facts is reached by students, it opens up space in their working memory which allows students to execute more advanced mathematical concepts. This research project was designed to help 7th-grade students master their basic math facts which will give them the opportunity to then access the 7th-grade level math concepts with less frustration. Since basic facts are typically mastered no later than 5th-grade, 7th-grade students who have not mastered basic facts tend to give up on math due to a high level of frustration. Caron (2007) also confirmed that students who fail to memorize basic math facts for several years may begin to avoid the task altogether. I see this occurrence every year with math students who are performing below grade level.

    In “The relationship among working memory, math anxiety, and performance,” Ashcraft and Kirk (2001) stated that over time this may cause students to develop an anxiety towards math, which may negatively affect and decrease their working memory. In addition, in “Why can’t Johnny remember his basic facts,” Baroody, Bajwa, and Eiland (2009) stated that memorizing the basic combination math facts must be done in a well structured and connected body of knowledge involving number sense. There is a need in 7th grade to provide students who are performing below grade level the opportunity to practice and ultimately master their basic math facts in a structured, constructive, and high interest way, so these students can find success in math. In this research, I applied the Reflex program to help my students recall the basic facts with automaticity so they have more cognitive space available for solving more difficult problems successfully without being hindered by the lack of basic skills. The purpose of this teacher-research was to determine the effect of the Reflex program on students’ abilities to master basic facts to the level of automaticity manifested in math performance on multiplication and division.


    Participating Students

    My research was focused on 70 seventh grade students. Students in three math classes taught by three teachers participated in this research. Class 1, 7th grade intensive math class, taught by the author included 18 girls, 2 on Individualized Education Programs (IEPs), and 22 boys, 13 with IEPs, with the rest of my students being general education students. Class 2 was taught by a teacher participating in this research who had a 7th-grade Specialized Academic Instruction (SAI) class with 5 girls and 11 boys who are all on IEPs. Class 3 was taught by another participating teacher who had 7th/8th grade SAI classes with 4 girls and 10 boys, all on IEPs. All three teachers used the same program. The demographics of my school at the time of this research were 68% Hispanic, 11% African American, 11% Caucasian, 4% Filipino, 4% two or more races, and 2% other, with 82% of the students socioeconomically disadvantaged. 

    Overview of the Reflex program

    Reflex (Cholmsky, n.d.) is a computer-based math skill program designed to help students of all school ages. The program includes activities and games for addition and subtraction and for multiplication and division, for students from Grades 2 to 12. The addition and subtraction facts go from levels “0 to 10” and the multiplication and division facts go from levels “0 to 10” (multiplication) and levels “0 to 12” (division). In the program, students play games with fact families. They can reach milestones, see the facts on which they are fluent, the facts on which they are not fluent, which facts have not yet been assessed, earn points, unlock new games as they advance, and even shop for their Avatar with their earned points. The students can monitor their own progress each session by trying to fill the “green light” located in the upper corner of the computer screen. This “light” indicates if they have met the expectation for the day. The teacher can monitor group or individual progress in the program in many different ways. A report is available that tells the fluency gained, time usage on the program, milestones met, and other customizable information. This program is of high interest for students, with up to date graphics and sound features. As in most video games of today, users must continue to play to unlock the next game and/or to be able to “buy” their avatar accessories. 

    Reflex is a research-based program (Cholmsky, 2011). Research to date includes the effects of flashcards versus the Reflex program on student learning, with the latter demonstrating 3 times more significant gains during the school year than a traditional flashcard method (Cole, 2017). Case studies on the impact of the Reflex program on standardized test scores showed significant growth in standardized scores for students who used Reflex on a regular basis (Reflex and Grade 6 Standardized Test Results, n.d.). More research studies are included on the homepage of the Reflex website (


    Every Monday, Wednesday, and Friday, students entered the classroom and retrieved their iPads. They logged in to Reflex and worked for a 20-minute session.  The introduction to Reflex includes an initial assessment. This allowed students to begin the program at their own appropriate level. During each session, students worked to fill the “green light.” This is a circle that fills with green as the students work during a session. The teacher monitored the progress of students and encouraged those students whose green light was lacking. Students wore ear buds, as the program has continuous sound. Earbuds also helped students focus on the task at hand with less distraction from others. In addition to daily monitoring, the teacher monitored the students’ fact fluency gains weekly. Students also had the opportunity to work on Reflex at home to help increase their skills.

    After the 20-minute warm up session, the class focused on note taking and the lesson for the day. Strategies during these lessons included but were not limited to think-pair-share, white board reviews, working on example problems through guided practice, practice with scaffolds, and independent practice. On the days Reflex was not used, students worked on a warm-up consisting of 5 problems based on 7th-grade standards.


    All students involved in this study took an individual pre-assessment of multiplication and division on an iPad at the start of the school year. It consisted of 54 problems.  Examples of the problems include 5×8, 9×3, and 6×7 for multiplication, and 6÷2, 81÷9, and 27÷3 for division. The students were given 5 minutes to complete as many problems as possible. At the end of the school year, students took a final post-assessment. The assessment data were analyzed to examine the growth in fact fluency throughout the school year. Reflex also has an initial assessment built into the system to show each student’s starting point and assessments of growth of the students in the program. The pattern of growth in the Reflex program was analyzed to determine whether the Reflex program was effective for student learning of math facts.

    All data are kept confidential and the results of the study are shared in this report by focusing on the pattern of progress with groups of students (pre-assessment and post-assessment), not individual students.  The permission for this research was obtained from the site principal.

    Results and Discussion

    The average scores of all students are broken into several categories in the following results.  Keep in mind that there were different numbers of boys and girls, therefore the overall average will not be the average of the boys’ average and the girls’ average. It is the average of all students in that category. Presented below are the multiplication (54 problems) and division (54 problems) pre-assessment and post-assessment score breakdowns by type of students.

    All Participating Students


    • Pre-Assessment:  Average score – 49%; Boys – 49%; Girls – 50%
    • Post-Assessment: Average score – 70%; Boys – 71%; Girls – 68%


    • Pre-Assessment: Average score – 52%; Boys – 52%; Girls – 52%
    • Post-Assessment: Average score – 71%; Boys – 70%; Girls – 68%

    General Education Classroom: All Students including 15 students on IEPs


    • Pre-Assessment: Average score – 60%; Boys – 64%; Girls – 55%
    • Post-Assessment: Average score – 77%; Boys – 81%; Girls – 71%


    • Pre-Assessment: Average score – 62%; Boys – 66%; Girls – 56%
    • Post-Assessment: Average score – 75%; Boys – 77%; Girls – 72%

    General Education Classroom: 25 General Education Students Only


    • Pre-Assessment: Average score – 62%; Boys – 64%; Girls – 60%
    • Post-Assessment: Average score – 77%; Boys – 85%; Girls – 73%


    • Pre-Assessment: Average score – 63%; Boys – 69%; Girls – 59%
    • Post-Assessment: Average score – 77%; Boys – 82%; Girls – 74%

    General Education Classroom: 15 IEP Students Only


    • Pre-Assessment: Average score – 58%; Boys – 62%; Girls – 22%
    • Post-Assessment: Average score – 76%; Boys – 79%; Girls – 54%


    • Pre-Assessment: Average score – 62%; Boys – 66%; Girls – 33%
    • Post-Assessment: Average score – 74%; Boys – 76%; Girls – 56%

    SAI Special Education Classroom (All IEP Students)


    • Pre-Assessment: Average scores – 32%; Boys – 30%; Girls – 34%
    • Post-Assessment: Average score – 55%; Boys – 56%; Girls – 54%


    • Pre-Assessment: Average score – 15%; Boys – 16%; Girls – 12%
    • Post-Assessment: Average score – 40%; Boys – 46%; Girls – 25%

    All Students on IEPs


    • Pre-Assessment: Average score – 42%; Boys – 45%; Girls – 32%
    • Post-Assessment: Average score – 63%; Boys – 67%; Girls – 54%


    • Pre-Assessment: Average score – 46%; Boys – 50%; Girls – 20%
    • Post-Assessment: Average score – 63%; Boys – 66%; Girls – 38%

    Summary of Improvement from Pre- to Post-Assessment by Student Types in Multiplication and Division

    All Participating Students

            Multiplication = 21%; Division = 19%

    General Education Classroom: All Students

            Multiplication = 17%; Division = 13%

    General Education Classroom: General Education Students Only

           Multiplication = 15%; Division = 14%

    General Education Classroom (IEP Students Only)

            Multiplication = 18%; Division = 12%

    SAI Special Education Classroom (All IEP Students)

            Multiplication = 23%; Division = 25%

    All Students On IEPs

            Multiplication = 21%; Division = 17%

    As can be seen in the percentages of improvement, every category showed an improvement in the multiplication and division skill levels. The student group that showed the highest gains was in the SAI special education math class. In particular, the boys in SAI made the highest gains of all groups. Although the SAI students made the highest gains, there needs to be continued efforts to master the math facts to reach the mastery level. With the success shown from the current research, a continued use of the program might help these students reach the mastery level. The second group of students who made significant gains was students on an IEP, no matter the classes in which they were placed.  Similar to the SAI group, students on IEPs might benefit from continuing with this program to help them reach the mastery level. Both groups showed the potential to do so in this research. The results also showed that overall, boys outperformed girls in most categories on both pre and post assessment. Finding when this pattern begins to surface may be helpful to begin addressing the reasons behind the discrepancy and the best ways to strengthen math instruction to close the gap between boys and girls. A worthwhile future research project would be investigating the reasons behind the pattern at this school site.    

    Based on the data pattern, I find that the Reflex program:  (a) showed growth potential for students who are not fluent in their multiplication and division facts; (b) is beneficial for students in all classroom placements; (c) shows a positive impact on student’s math fluency in multiplication and division; and (d) is significantly beneficial for the SAI classroom. The pattern of growth indicated that if students use the Reflex program consistently, most students will benefit, but not all at the same rate. Therefore, an alternative program may be necessary for those students who progress at a slower rate. 

    In summary, through working with Reflex, the 7th-grade math curriculum became more accessible for participating students due to their learning basic facts and achieving a greater amount of working memory to learn new math skills, albeit some students will need more time to reach mastery level of basic facts.

          Limitations and Future Research. In this research, there was no comparison group of students who studied multiplication and division in classrooms taught by teachers without the Reflex program. However, based on my years of teaching math, I drew these conclusions that the program was effective. Further studies that compare teaching approaches would shed more light. The SAI student group and students on IEPs made good progress using the Reflex program. This pattern of improvement is quite desirable. It would be important to understand what makes this program successful for these groups of students, requiring continued research on this topic.


    Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and math performance. Journal of Experimental Psychology, 130(2), 224-237.

    Baroody, A. J., Bajwa, N. P., & Eiland, M. (2009). Why can’t Johnny remember the basic facts. Developmental Disabilities Research Reviews, 15, 69-79.

    Caron, T. A. (2007). Learning multiplication the easy way. The Clearing House, 80(6), 278-282.

    Cholmsky, P. (n.d.). ExploreLearning.

    Cholmsky, P. (2011, March). Reflex from acquisition to automaticity: The Reflex solution for math fact mastery.  Retrieved from

    Cole, M. (2007, December). Math fact fluency study in Houston, Texas elementary schools. Retrieved from

    Reflex and Grade 6 Standardized Test Results. (n.d.). Retrieved September 9, 2018, from

    To cite this work, please use the following reference:

    Dotson, B. (2019, November 16). Mastering basis facts through the reflex program. Social Publishers Foundation.

    Copyrighted by Creative Commons BY-NC-SA

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