**Author: Laquita Bolden, Cleveland State University**

**Abstract**

Lack of fluency in math facts is a common deficit in American elementary classrooms. Students struggled with quick computations of multiplication facts. Fluency in basic math facts is important because math facts are the pre-requisites for elementary school math standards. According to Musti-Rao et al. (2015), The Nation Mathematics Advisory Panel is finding that students in America are struggling with basic mathematic and computation skills.

This study incorporated daily practice of multiplication facts and weekly assessments. Students were given a set of time tables, and students could not move on until they mastered the set. The data suggested that students were mastering basic multiplication facts, and improving achievement in other related standards. This topic is useful in Mathematics because it focuses on improving a common deficiency in urban education.

**Introduction**

I decided to become an elementary school teacher when I noticed my passion for assisting others with processing and learning different concepts. Teaching has been a passion of mine since I was a little girl. My mother knew I would be a teacher when she saw me teaching my brother how to add and subtract using M&Ms. I attended and graduated from a public urban school district. I did not understand the impact of the achievement gap until I became an adult. Daily practice at school and home is the reason why I was successful throughout my academic career. Fluency in basic math facts was a part of daily practice when I was in school. As a current educator, I noticed the lack of focus on fluency in basic math facts in daily in classroom routines. The lack of daily practice closely correlated to the lack of fluency I observed in my students. Seeing my students struggle with simple multiplication problems inspired me to shift my focus. Math standards build over time. The skills acquired the prior year are the basic building blocks for the current school year to come. The gap in fluency sets a weak foundation for mastery of other mathematical skills. Before I could expect my students to master current grade level standards, I had to find a way to close the gap in fluency.

I created an intervention for my current students in an urban school district to improve fluency in basic multiplication facts. Mastering Math is the name I created for this intervention. Practice in basic multiplication facts was incorporated in our daily routine. Students were given a set amount of time to practice multiplication facts. Weekly assessments were given in order to track mastery of each set. On Fluency Friday students would practice and quiz each other on their multiplication sets. Also, we would watch Flocabulary videos for different multiplication sets. After practicing and watching Flocabulary students would be given their weekly assessment. Students who mastered their multiplication facts would move on to the next set of facts. If you did not master your set you continued to practice until mastery was achieved. The students who mastered their multiplication up to the 12s would receive an ice cream party at the end of the school year.

From this intervention my students advanced in multiplication and other related standards. Seeing and practicing multiplication daily made it easier for students to memorize their multiplication facts. Students mastered other standards due to an increase in fluency. Relating division to multiplication became easier for my students because they started mastering basic facts and could identify the relationships between the numbers. I also saw improvement in classroom culture. Students wanted to help other students achieve their goals. They would work together during anytime they had to practice and work with classmates who struggled with advancing to the next set. Students became more confident and participation during class increased.

As an educator this intervention helped me grow as a professional. Lack of fluency was a major road block for the academic success I wanted to see for my students. I had to find time to re- teach skills that were not outlined in my required standards for the year. It was challenging meeting the needs of all my students with so many varying ability levels. I had to find ways to challenge my students who were rapidly advancing but also teach the students who were severely behind. Finding ways to differentiate and meeting the needs of all of my students helped me grow as an educator. My research question for this study is: Does testing students’ fluency on basic multiplication facts each Friday increase achievement on multiplication post assessments and other math standards?

**Literature Review**

A current issue in education is the lack of math literacy in American students. The United States ranks low in math proficiency compared to other countries. According to Musti-Rao, Lynch and Plati (2015) the United States is ranked 24th out of 57 countries in Mathematics. Research shows that low proficiency rates in math strongly correlate with American students struggle with basic math facts (Musti-Rao et al., 2015). Only 50% of school-aged students master multiplication (Reisener, Dufrene, Clark & Tingstrom, 2016). Fluency in basic math facts is important because math facts are the pre-requisites for most math standards. Fluency in basic math skills are pre-requisite skills required to master other composite skills. Fluency in basic math facts can predict math ability (McTiernan, Holloway, Healy & Hogan, 2015). Math literacy is a key element in other fields of study and can impact student success in other areas of life. McTiernan et al. (2015) talks about mathematics being key in everyday life and curriculum. Basic literacy in math is a building block for other areas of expertise such as engineering, medicine and business.

Fluency can be defined in different ways. Musti-Rao et al. (2015) and Reisener et al. (2016) define fluency as quick and correct responses. McTiernan et al. (2015) describe fluency as students being able to apply pre-requisite skills to achieve more complex skills. Math and other fields of study start with component skills that build into more complex skills over time. Fluency is maintained over time with repetition and feedback (McTiernan et al., 2015). In this study a sample size of 28 males were evaluated to identify the impact of building fluency in math facts. Endurance, stability and application were all observed in relation to fluency. All of these components played a major role in students attaining fluency in basic math facts. 20 out of 28 students achieved their fluency aims. Stability and endurance were higher during weekly post assessments than weekly pre-assessments. Overall there was a steady increase of fluency, endurance and stability over the duration of this study. Reisener et al. (2016) also observed that modeling, prompting and providing feedback built fluency in students, and fluency was maintained through drill and practice. In both studies the interventions that included practice and feedback yielded high results.

In a study by Berrett and Carter (2017), it was stated that math proficiency seems to decline as students advance from grade to grade. Improving proficiency in the early grades is important because it provides the basis for students to be proficient later on in math. In this study, a computer-based intervention was used to improve math fact fluency in third grade students over a 12 week period. The mean scores of the groups increased from 13.0 to 18.8 when the computer based intervention was implemented. Even after removing the intervention students’ math fact fluency remained high, averaging a score of 23.1. Implementing daily practice improved fluency in basic math facts. In support of this study, Poncy, Fontenelle and Skinner (2013) saw improvements in math fluency by incorporating computer based interventions in a 3rd grade classroom. A 12.8 increase was seen in the digits correct per minute (Poncy et al., 2013). A class wide intervention was used to remedy math fact discrepancies. A computer based program was used to detect the equations that students could not immediately respond to. Students would practice these problems using a re member and recall strategy. Then, students would repair problems by solving them with a time restraint.

Interventions are required to improve math fluency deficits in American students. Reisener et al. (2016) did a study on the effects of multiple interventions for building math fact fluency. A group of elementary students practiced fluency using a variety of interventions three times a week. The results of this study showed some interventions improved math fluency more than others, but overall interventions in general resulted in higher math fact fluency. This study shows that the type of intervention is insignificant compared to the action to improve the deficit.

In support of this study Schutte et al. (2015) did a study that saw improvement in math fact fluency based on the amount of time students engaged in practice. This study included forty-eight third graders who were placed in three groups. Each group was given a different amount of practice time. Students who had more practice exhibited higher fluency growth rates. The two groups of students that received practice multiple times per day improved more than the group of students who only practiced once a day.

The focus of this study is to determine if improving math fact fluency can impact student achievement in other related standards. Fluency in basic math facts is important because math facts are the pre-requisites for majority of elementary school math standards. These studies have shown that fluency in math facts is closely related to improving math literacy in American students. In this study a math intervention was implemented in an urban 3rd grade classroom. This intervention was implemented to see if building fluency in math facts could improve student achievement in other math content. The question imposed by the researcher was: Does testing students’ fluency on basic multiplication facts each Friday increase achievement on multiplication post assessments and other math standards?

**Methodology **

The focus of this study is to provide students with an intervention to improve fluency in multiplication facts. Participants were 14 third grade students between the ages of 9 and 11 years old. There were a total of six males and eight females. All of the students were African American. 21% of the population were on an Individualized Education Plan and received services from an intervention specialist. All participants attended the same Title 1 elementary school. This elementary school is a part of a public school district. The district population is 64.5% Black, 15.8% Hispanic, 15.7% White and 4% other nationalities (Cleveland Metropolitan School District, 2015). 100% of the student population receive free or reduced lunch.

Students received the intervention as a part of their daily instruction during math class over a 12 week period. Students receiving special services had a modified version of the intervention. These students were given extended time and scrap paper to use other strategies to solve multiplication problems during weekly assessments. Extended study time was also given to special needs students. Study time was completed with the general education teacher, and the weekly post assessments were given by the intervention specialist. All treatment conditions were conducted by the general education teacher and the intervention specialist.

Materials used in this study included paper and pencil, multiplication charts, digital timer, and the Flocabulary website. Paper and pencil were used during practice and to record answers on weekly assessments. Multiplication charts were used to monitor accuracy during practice, and to grade weekly post assessments. Students and teacher monitor time using a digital timer. The timer was displayed in the front of the classroom for easy monitoring. The Flocabulary website provided songs to aid in memorization of math facts and engagement. Students studied sets of multiplication facts daily to increase fluency in math facts. Each multiplication set focuses on one factor multiplied by integers 1 to 12 (2s, 3s, 4s etc.). Students were given a pre-assessment that contained a combination of 80 problems from all multiplication sets (1-12s) randomly selected by an online worksheet generator. Two minutes were given to complete the assessment. Every student started on their one times tables and progressed based on weekly mastery. During bell work students would drill and memorize their set of multiplication facts for fifteen minutes. Drilling to memorize and study with a partner were the two techniques used during this intervention. The drilling to memorize involved teaching students to identify patterns in the different multiplication sets and skip counting. Studying with a partner involved teaching students a practice and repair strategy (Poncy et al., 2013). Together students would practice multiplication problems, identify the incorrect problems and repair by increasing practice and review. Students were given weekly post assessments. At the end of each week students would study with a partner, then the class would watch Flocabulary multiplication videos. A total of three videos were picked based on the multiplication sets that most of the students were currently studying. After the video students would remove everything from their desk except a pencil. Each student was given a post assessment that contained twenty-one problems from their current multiplication set. Students were given two minutes to complete the post assessment. Once the assessment was completed the papers were collected then distributed to peers for grading. To ensure validity in this study students graded papers of classmates who sat at different tables and they used pens and multiplication charts to avoid discrepancies. The general education teacher monitored and corrected assessments during this time. After assessments were graded, students passed back papers and provided feedback. Based on assessment scores students would either move to the next multiplication set or continue to practice the current set.

To improve intrinsic motivation two rewards were provided. Students were able to track their own progress on a chart displayed in the classroom. A sticker was earned for every multiplication set complete. At the end of this intervention the students who mastered all multiplication sets (2s-12s) would receive a certificate of completion and an ice cream party.

Quantitative and qualitative data were collected during this study. Student assessment scores and standardized test scores are the quantitative data sources, and the qualitative data source was a questionnaire. Excel was used to collect weekly assessment data. The multiplication set and student scores were recorded in a table to track mastery and progression. Individual progress overall progress, and average scores are all analyzed from the post assessment data. The Northwest Evaluation Association (NWEA) scores were used to measure the impact of building fluency on other related math standards. Fall to winter and winter to spring NWEA scores were used to analyze individual student scores, student growth and proficiency. A questionnaire (See Appendix A for more information on the questionnaire) was given at the end of the study to analyze the impact building math fluency had on each student. The questions focused on challenges students faced and how much building fluency impacted their learning process. Positive vs Negative responses, motivation and feelings were all analyzed from the questionnaire.

** Data and Findings **

The data collected was used to analyze if testing students’ fluency on basic multiplication facts each Friday increased achievement on multiplication post assessments and other math standards. NWEA fall scores and a pre-assessment were used for baseline data. For this study 80% or higher (B or higher) is considered mastery of a skill. NWEA scores are analyzed based on Cleveland Metropolitan School District (CMSD) NWEA 3rd grade Math cut scores. Students scoring a 189 in the fall, 197 in the winter and 202 in the spring are considered proficient (Cleveland Metropolitan School District, 2018). NWEA provides each student with a projected growth score to measure growth. This score is calculated based on student’s start score and grade level proficient score. Students who meet their projected growth scores are on track to being proficient. In this study student scores that increase by one point or more are categorized as showing growth.

The NWEA fall data showed that 12 students were non-proficient, and 2 students were proficient. Majority of the population were functioning at a 1st and 2nd grade ability level. 3 students of the studied population completed all the problems on the pre-assessment in two minutes. 11 students did not complete the pre-assessment. No students showed mastery on the pre-assessment (80% or higher).

Multiplication sets and post-assessment scores were documented for 12 weeks. Out of the 14 students 10 mastered all multiplication sets (1s-12s). Two students mastered multiplication sets up to the 12s (reached 12s but did not master), which is considered near mastery. One student mastered multiplication sets up to the 8s, and one student mastered multiplication sets up to the 4s. 14 students mastered the first set of multiplication facts (1s) with a 90% or higher. All students except for one scored 90% or higher on the 2, 5 and 10 multiplication sets. 89% is the overall average post assessment score. Nine students had an average score of 90% or higher. Four students had an average score of 80% or higher, and one student’s average score was 52%.

NWEA winter and spring scores are analyzed to determine if the intervention impacted students mastery of other math standards. The achievement and growth summary report was used to analyze NWEA fall 2017 to winter 2018 scores. This report showed achievement status and growth between two testing periods. Two students did not have a valid growth summary report, because they transferred into the school after the fall 2017 NWEA testing window. There are no NWEA fall scores to compare to winter scores, so analysis for these two students was not complete for NWEA fall 2017 to winter 2018. No students were proficient according to the CMSD NWEA 3rd grade winter 2018 cut scores. Five students met their projected growth score. Five students showed growth (scores increased by one point or more), and one student showed no growth. One student’s score declined by two points.

NWEA winter 2018 to spring 2018 scores were analyzed to determine the impact of the intervention for the remainder of the school year. The entire study population had a valid growth summary report for winter 2018 to spring 2018. Eight students met their projected growth score, and four students showed growth. One student declined by two points, and another student’s score declined by seven points. Out of the eight students that met their projected growth score one student was proficient according to CMSD NWEA cut scores.

The questionnaire contained six questions about what the students liked/disliked about the intervention and how it made them feel. The first question asked students what they thought about the intervention. Ten students thought the intervention was fun or amazing because it helped them learn their multiplication facts. One student thought the intervention was a great challenge. Two students found the intervention hard, and one student said it was a great way to learn multiplication. Question two asked what students liked about the intervention. According to question two, 13 students liked immediate feedback after taking the post assessments and the Flocabulary videos. The third question asked how students felt when they passed their assessment. 12 students felt excited or happy when they passed their post assessments, and two students felt smart. Question four asked students how they felt if they failed or scored below 100% on post assessments. Seven students felt sad or mad. Three students said they would study more, and four students said they would do better the following week. The fifth question on the questionnaire asked students what they did not like about the intervention. Six students disliked the time constraint of the test and the number of problems. Two students disliked failing and repeating multiplication sets. Five students reported no complaints about the intervention. The last question asked students how this intervention impacted other math standards learned this school year. Responses to this question varied from “it helped with learning division” to “I can solve multiplication problems faster”. Students reported being able to solve division and other math standards because they knew their multiplication facts. Some students just mentioned how easy multiplication was by the end of the school year.

**Discussion**

The research question for this study was: Does testing students’ fluency on basic multiplication facts each Friday increase achievement on multiplication post assessments and other math standards? The current study demonstrated positive outcomes associated with the intervention. Baseline data NWEA test scores showed that majority of the studied population were functioning below grade level at the beginning of this intervention. No students mastered the pre-assessment that contained a mixture of multiplication sets. Some students finished the test, but did not answer 80% of the questions correctly. Other students were unable to complete all 80 problems in two minutes. From this pre-assessment misconceptions were identified. Some students solved the problems using addition which aligns with the ability levels identified in the NWEA fall scores. Students had only mastered up to 1st grade standards. By the end of the 12 week intervention an increase in standardized test scores and weekly post assessments were observed. Most of the studied population completed the intervention and demonstrated enhanced performance on NWEA assessments and mastering multiplication sets.

According to the weekly post-assessment data most of participants mastered all 12 multiplication sets. Students progressed weekly in learning multiplication sets. With daily practice an increase in fluency of math facts occurred. Students were able to complete 21 problems in two minutes. Just like the study done by McTiernan et al. (2015) there was a steady increase of fluency over the duration of the study. Researchers suggested that implementing daily practice can improve fluency in basic math facts (Berrett and Carter, 2017). The results from this study align with previous research showing daily practice increases fluency.

Building fluency in basic math facts impacted NWEA spring test scores. Most of the 3rd grade standards are derivatives of basic multiplication. Area, missing factors, fact families and other math concepts all require fluency in basic multiplication facts. Fluency is defined as applying pre-requisite skills to more complex skills (McTiernan et al., 2015). This intervention focused on mastery of pre-requisites to increase mastery of other complex math skills. By spring students were tested on 3rd grade standards required for the entire school year. Most of the population showed growth or met their projected growth score on the NWEA spring assessment. This data indicates that building fluency in math facts impacted other math standards. Poncy et al. (2013) observed the long term effects of fluency in math facts. In this study after the intervention was removed student achievement continued to increase. In this current study results also showed long term effects. By the end of the school year one student was proficient and 11 others were on track to reaching proficiency.

The two students in the studied population who rarely mastered multiplication sets also did not grow or declined on their NWEA spring assessment. The students who did not master all sets remained on multiplication sets for multiple weeks or scored below 80% on post assessments. Some factors that impacted these results were engagement and attendance. Practice yields positive results when students are engaged. McTiernan et al. (2015) identified the importance of students being engaged with practice. Students who were highly engaged during practice times also showed an increase in fluency. The two students who did not master their multiplication sets rarely completed activities during practice time. Attendance was the biggest factor that impacted the results of these two participants. Each student missed over 30 days of school during the intervention period. Missing days of practice and post assessments negatively impacted their final results.

The data from the questionnaire inferred that students had a positive response to the intervention. Most of the studied population felt that the intervention helped them learn their times tables and other math standards. Students personally observed their ability to master more complex skills after mastering multiplication sets. According to the questionnaire building fluency in math facts helped them learn other math standards and feel more confident.

**Limitations and Recommendations for Future Research **

Overall this study showed an increase in fluency of math facts and mastery of other related math standards. There are a few factors that may have influenced the process of this current study. This intervention was only for 12 weeks. An increase in fluency and success was observed, but a longer implementation period may enhance results. There are a total of 36 weeks in a school year. 12 out of 36 weeks is not a sufficient time to implement an intervention. Based on the results of this intervention a longer implementation period would result in higher student success. The studied population was also a factor. 14 students is a small population. Small populations may increase the margin of error, and may reduce the power of the study. Attendance and other factors had a greater impact on this study due to a small study population. Other testing occurred during the implementation of this intervention and may have indirectly impacted the final results of this study. Three other assessments were conducted during the NWEA spring assessment. Students took three ELA assessments, one science and one social studies assessment. The science and social studies assessments were conducted the week prior to NWEA spring testing and ELA testing was conducted in the same week. Many researchers have commented on the impact of over testing students (Poncy et al., 2013). Stress brought on from testing can result in students rushing through tests and a lack of engagement.

Winter break is another factor that may have influenced the process of this study. Shortly after the NWEA winter assessments students went on winter break. This two week break may have impacted the NWEA spring scores. A two week period of no practice could have impacted the process of students mastering multiplication sets.

Overall the impact of fluency in math facts on other math standards were not addressed sufficiently. So many other standards and topics are assessed in the NWEA spring test. Test scores are based on the mastery of a variety of other standards that do not directly correlate to multiplication. So many other factors can influence results of the NWEA assessment. Other assessments that evaluate math standards related to multiplication would directly show the impact of an increase in fluency of basic math facts.

Incorporating daily practice of basic math facts benefited the studied population. After implementing daily practice students mastered post assessments weekly and improved standardized test scores. Student confidence and ability levels increased due to the implementation of this intervention. Data confirmed that learning other math standards related to multiplication became easier and students felt more confident to attempt more challenging concepts. An increase in student success was observed overall. Future studies should increase study population and use different post assessments to ensure data accuracy and reliability.

**References **

[1] Berrett, A. N., & Carter, N. J. (2017). Imagine Math Facts Improves Multiplication Fact Fluency in Third-Grade Students. *Journal of Behavioral Education,* *27*(2), 223-239. doi:10.1007/s10864-017-9288-1

[2] Mctiernan, A., Holloway, J., Healy, O., & Hogan, M. (2015). A Randomized Controlled Trial of the Morningside Math Facts Curriculum on Fluency, Stability, Endurance and Application Outcomes. *Journal of Behavioral Education,* *25*(1), 49-68. doi:10.1007/s10864-015-9227-y

[3] Musti-Rao, S., Lynch, T. L., & Plati, E. (2015). Training for Fluency and Generalization of Math Facts Using Technology. *Intervention in School and Clinic,* *51*(2), 112-117. doi:10.1177/1053451215579272

[4] News and Events. (n.d.). Retrieved June 11, 2018, from http://clevelandmetroschools.org/

[5] Poncy, B. C., Fontenelle, S. F., & Skinner, C. H. (2013). Using Detect, Practice, and Repair (DPR) to Differentiate and Individualize Math Fact Instruction in a Class-Wide

[6] Setting. *Journal of Behavioral Education,* *22*(3), 211-228. doi:10.1007/s10864-013-917-1

[7] Reisener, C. D., Dufrene, B. A., Clark, C. R., Olmi, D. J., & Tingstrom, D. H. (2015). Selecting Effective Interventions To Increase Math Computation Fluency Via Brief Experimental Analyses. *Psychology in the Schools,* *53*(1), 39-57. doi:10.1002/pits.21887

[8] Reisener, C. D., Dufrene, B. A., Clark, C. R., Olmi, D. J., & Tingstrom, D. H. (2015). Selecting

[9] Effective Interventions To Increase Math Computation Fluency Via Brief Experimental Analyses. *Psychology in the Schools,* *53*(1), 39-57. doi:10.1002/pits.21887

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