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

By Barbara Dotson

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

    About the Practitioner-Researcher

    Barbara Dotson
    La Presa, CA
    Barbara Dotson

    My name is Barbara Dotson. I graduated from San Diego State University with a Liberal Arts Degree and earned my teaching credential and Master’s degree through Chapman University. In addition to my Elementary Education Credential, I have a supplemental credential in math for Grades 7-9. This is my 23rd 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 grade in two other schools and 7th grade in the school where I now teach. Currently, fall 2018, I teach two Intensive math classes in which the students are multiple years below grade level, one Common Core 7th grade math class, and one 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. Through the Reflex Program, I would like my students to be able to recall the basic facts with automaticity so they can solve more advanced math problems without being hindered by their lack of basic skills. Seventh and eighth-grade students (N = 112) from Individualized Education Programs and Intensive math classes will participate in this research project. The purpose of this teacher-research is to determine the effect of the Reflex program on students’ abilities to master basic facts to the level of automaticity and math performance on multiplication and division.

    Project Context

    This project will take place at STEAM Academy at 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, will use this program to help students develop the level of automaticity in processing basic math facts. This project is relevant to my school site because we have a significant amount of students who are academically below grade level in math. Mastery of basic 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. I anticipate the research showing the importance of having fluency in basic math facts. In the research, I will examine 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.

    Project Significance and Method

    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 concept.  When students become fluent at their basic skills, they become more confident in math as a whole and they are able to 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 project will 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 weak mastery tend to give up on math due to a high level of frustration. Caron (2007) also confirms this fact, stating 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) state 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) state 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 give 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. Through the Reflex Program, I would like my students to be able to 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 is to determine the effect of the Reflex program on students’ abilities to master basic facts to the level of automaticity and math performance on multiplication and division.


    Participating Students

    My research will be focused on 112 seventh and eighth-grade students. There are 23 girls, 5 on Individualized Education Programs (IEPs), and 31 boys, 17 with IEPs, in my 7th grade intensive math classes. In my 7th grade intervention class there are 5 girls, one on an IEP, and 9 boys, one on an IEP.  The rest of my students are general education students. A second participating teacher has a 7th grade Specialized Academic Instruction (SAI) class with 7 girls and12 boys who are all on IEPs. A third teacher participating in this research has 7th/8th grade SAI classes. In the seventh-grade class there are 2 girls and 10 boys, all on IEPs. In eighth grade, there are 8 girls and 15 boys, also all on IEPs. The demographics of my school are 68% Hispanic, 11% African American, 11% Caucasian, 4% Filipino, 4% two or more races, and 2% other. In my school, 82% of the students are 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 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) or 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 they 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 traditional flashcard method (Cole, 2017). Case studies on the impact of the Reflex program on standardized tests 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 will enter the classroom and retrieve their iPads. They will log in to Reflex and work for a 20-minute session.   The introduction to Reflex includes an initial assessment. This allows students to begin the program at their appropriate level. During each session, students will be working to fill the “green light.” This is a circle that fills with green as the students work during a session. The teacher will monitor the progress of students and encourage those whose green light is lacking. Students will wear ear buds, as the program has continuous sound. Earbuds also help students focus on the task at hand with less distraction from others. In addition to daily monitoring, the teacher will monitor the students’ fact fluency gains weekly. Students also have the opportunity to work on Reflex at home to help increase their skills.

    After the 20-minute warm up session, the class will focus on note taking and the lesson for the day. Strategies during these lessons include but are not limited to think-pair-share, white board reviews, working on example problems through guided practice, practice with scaffolds, and independence practice. On the days Reflex is not being used, students will work on a warm-up consisting of 5 problems based on 7th grade standards. Through working with Reflex, the 7th-grade math curriculum should become more accessible for the students due to mastery of basic facts and a greater amount of working memory to learn new math skills.


    All students involved in this study will take an independent pre-assessment of multiplication and division on an iPad. It will consist 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 will be given 5 minutes to complete as many problems as possible. Every 8 weeks the students will take the independent assessment. At the end of the year, students will take a final post-assessment. The assessment data will be 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 shown in the independent assessments and the pattern of growth in the Reflex program will be analyzed to determine whether the Reflex program was effective on student learning of math facts. All data will be kept confidential and the results of the study will be shared by focusing on the pattern of progress with groups of students, not individual students.

    Anticipated Research Results

    I anticipate that the results will show consistent gains in fact fluency throughout the school year. By the end of the year, I anticipate most students will obtain mastery level of basic math facts up to level 10 (addition, subtraction and multiplication) and level 12 (division). With a positive outcome, I will continue using the Reflex program and analyze the growth patterns in other groups of students.


    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 

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