The Impact of Daily Multiplication Fact Review

The Impact of Daily Multiplication Fact Review

Amy Bystrom
Omaha, Nebraska

Math In the Middle Institute Partnership
Action Research Project Report

in partial fulfillment of the MAT Degree
Department of Mathematics

University of Nebraska-Lincoln
July 2010

Abstract
Many students enter fifth grade lacking the basic fluency skills needed to solve complex
math concepts, and the struggle to solve these problems may restrict students from enjoying
mathematics. Recent studies indicate that students might perform at higher levels and enjoy
solving more complex math if they are fluent in their basic math facts. This action research
study shows the impact of implementing daily fact review into math class in order to increase
student performance and confidence in this subject area. The daily fact review was presented
through various methods: timed tests, games and flash-card practice. I discovered that while
implementing the daily fact review did increase fact fluency among the five target students, it did
not increase their confidence in math nor their attitude toward long division. As a result of this
research, I plan to continue the daily fact review with my current class and future classes.

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Introduction
Every year, some students enter fifth grade not having mastered their multiplication facts.
Multiplication facts are introduced in third grade, yet for some reason, the majority of the
students lack the fluency needed to be successful for more complex mathematical concepts
introduced within the fifth grade math curriculum. After discussing this dissatisfaction with
sixth grade teachers from my school and middle school teachers in my district, this area of
concern stretches through sixth and eighth grades as well. Mastery of basic multiplication facts is
crucial when performing fifth grade math operations including identifying factors and multiples,
long division, problem solving and basic algebra. Since the beginning of the year during math
class, students depended on the multiplication table I have on my math wall as well as in their
assignment notebook where they can find a copy of the multiplication table. When asked to find
the product of two numbers, the majority of my students turned to look at the back wall chart for
the answer. Instruction, class practice and homework on fifth grade curriculum took twice as
long this way, and with Criterion Reference Testing and California Achievement Tests in the
spring, time was limited.
My former fifth grade classes also struggled with the area of multiplication fact fluency.
However, with those classes, I simply gave each student a three-minute timed test over 100
multiplication facts once a week. Unfortunately, their fluency did not improve much. I feel that
the timed-test became tedious and too repetitive. Needless to say, many of my students struggled
with long multiplication, division, word problem solving and basic algebra.
After three years of witnessing my students struggle with fifth grade level math, I
realized that something needed to be done to improve the fact fluency. With the implementation
of daily multiplication fact review, I wanted to increase my students’ multiplication fact fluency.

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I hoped that with an increase in fluency, my students would be able to solve more complex,
grade level mathematics with better comprehension and at a faster rate.

This area of focus is as issue that I feel passionate about because it not only affects student
achievement, but teacher planning, instruction and curriculum. If some type of reform does not
take place with the mastery of multiplication fact fluency, students will continue to lag behind in
math throughout middle school.

Problem Statement
The fluent recall of the basic multiplication facts was not only an important issue for me
as a fifth grade teacher, but for most teachers in my district and educators all over the nation.
This area of focus falls into the National Council of Teachers of Mathematics (NCTM)
Standards, the Nebraska State Standards, and my district’s math standards. One of the NCTM
Focal points states,
For grade four, the quick recall of multiplication facts and fluency with efficient
procedures, including the standard algorithm, is a focus. Most importantly is that fluency
emerges through understanding of the multiplication process—how multiplication is
represented, how properties are used when multiplying, etc. Students become fluent
through their understanding of efficient procedures that include the standard algorithm
(2000).
This statement aligns with my dissatisfaction because it states that students should already have
it mastered in fourth grade, not necessarily fifth.
According to the Nebraska State Standards, students in grades five through eight should
have a mastery knowledge of numeration and number sense including standard 8.1.4 where
students will identify and display numbers including prime and composite, factors and multiples,

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divisibility, powers, and properties. The state standards also require students to perform at
mastery level with computation and estimation, including algebra. If students are not fluent with
their facts, success in these standards will be a struggle. In my district, students must master the
multiplication facts in order to be successful within the standards of 50-1: Reads, write whole
numbers, decimals, and fractions (in word, expanded, and standard form), 50-2: Rounds and
orders whole numbers, decimals, and fractions, 50-3: Uses estimation and the four operations to
solve problems, 50-4: Conversion of units of measurements, 50-6: Develops and solves two-step
equations with one variable, and lastly standard 50-7: Identifies, develops, communicates,
applies strategies to solve word problems.

This area of concern did not just stop at students being unable to recall basic multiplication
math facts, but it also stretched into the attitude students had toward math in general. Educators
want all students to be engaged and successful in math, and if students struggled with the basics,
how would they be able to succeed in complex math and continue to feel positive toward the
subject?

Literature Review
National Council of Teachers of Mathematics (NCTM) (2000) states that students in
grades three through five are expected to a) develop fluency with basic number combinations for
multiplication and division and use these combinations to mentally compute related problems
and b) develop fluency in adding, subtracting, multiplying and diving whole numbers. Many
students entered fifth grade lacking the basic fluency skills needed to solve multi-step, higher-
level math concepts, and the struggle to solve these problems hindered students from enjoying
mathematics. Recent theories indicate that students might perform at higher levels and enjoy
solving challenging math problems if they are fluent in their basic multiplication math facts.

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Many journal articles and research studies include similar themes that relate to implementing
daily multiplication fact review and fact fluency into math class in order to increase student
performance and confidence in this subject area. The themes I found in reading research about
student math achievement and basic facts include the impact of fact fluency on student attitude,
impact on more challenging math problems, and student self-assessment and confidence in
mathematics.
Student Attitude

Student attitude plays an important role in education. This is especially true in the field of
mathematics and student achievement. According to McCallum, Skinner, Turner, and Saecker
(2006), if students find math tasks unacceptable, they may be less likely to choose to engage in
assigned math work. For this particular study, the researchers from the University of Tennessee,
Knoxville evaluated the effects of a taped-problems intervention on the multiplication fact
fluency of 18 students from a general education third grade classroom. This study also indicated,

students who can perform basic math operations both rapidly and accurately may (a) be
more likely to choose to do additional math tasks, (b) learn advanced math concepts and
tasks more rapidly and with less effort, and (c) be less likely to have math anxiety than
students who can perform basic operations accurately but slowly. (2006, p. 427)
In others words, if students feel self-assured in their learning, they may feel more confident to try
newer and more challenging tasks. The same theory goes for most adults as well. John
Woodward, a professor from the School of Education, University of Puget Sound, Tacoma,
Wash., made a similar statement in his 2006 study of the effects of timed multiplication practice
drills on fact fluency and student attitude. Woodward chose 58 fourth-grade students with a
range of academic abilities to determine the best strategy to help students develop multiplication

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fact automaticity. As part of the results, he concluded that “students who struggle in math, after
implementation, showed greatest improvement in attitude” (Woodward, 2006, p. 285).

Thomas Caron, an assistant professor in the Department of Curriculum and instruction in
the College of Education at East Carolina University in Greenville, North Carolina, presented an
innovated approach to teaching multiplication facts for children in middle school or younger. In
his study, Caron (2006) discussed how his eighth graders felt when confessing that they did not
know their multiplication facts. Caron stated,

I cannot shake from my memory a familiar look on some eighth-grade faces. It is at once
confident, smiling, challenging, and self-satisfied, however, not confident of success but
of failure. The students attached to these faces are failing. They do not adjust well to any
possibilities of success. (2007, p. 278)
When students continually fail due to lack of knowledge, they may begin to gain a pessimistic
view on that particular area. The students were always used to failing; therefore, their attitude
was focused on the negative side of math in terms of being successful. McCallum (2006),
Woodward (2006) and Caron’s (2007) studies expressed how struggling with a basic math
concepts can easily change a student’s attitude toward mathematics in a negative way. If the lack
of the basics is left unresolved, continued reluctance to attempt mathematical questions could
lead to math anxiety with serious negative consequences, including lack of effort and positive
attitude in mathematics.
Fact Fluency and Challenging Mathematics
Many of the students in America may also lack the fluency needed to be successful in
more complex mathematical concepts introduced within the fifth grade math curriculum. If
students struggle with the basics, then how can they begin to focus on the complexity of long

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division or fractions? Mauro, LeFevre and Morris (2003) conducted a study on the relationship
between multiplication and long division. The result of this study supported their hypothesis that
“large division problems are solved in terms of multiplicative representations” (2003, p.166). In
this study, participants were mentally transforming large standard division facts into an
equivalent multiplication-based form prior to retrieving the solution. This piece of evidence
supports the idea that students must be able to recall and understand the basic multiplication facts
before moving on to more challenging math.

Mauro, LeFevre and Morris’s study (2003) closely relates to one completed by Singer
and Greer (2005). Mauro, LeFevre and Morris compared two training procedures to determine
which of the two procedures allowed students to retain learned information longer to use for
more higher-leveled math. The participants included four adolescents with developmental
disabilities who attended a private but publicly funded school in a suburb of a large metropolitan
area. Just as in the previous study, results showed that once students understood the basics,
higher-level math followed.

McCallum, Skinner, Turner and Saecker’s (2006) study also corresponded to this idea of
the importance of multiplication fact fluency to higher-level math. The authors stated,

The ability to accurately respond to basic math facts is often required for success when
attempting to complete more complex math tasks. Higher-level math requires the ability
to solve problems accurately and students should also be able to arrive at the correct
answers rapidly. Fluency, automaticity, and proficiency are terms often used to describe
rapid and accurate responding (2006, p. 420).
This research correlates to what I experience as an educator. Students who struggle with their
basic multiplication math facts struggle even more with more challenging math that requires

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more steps or procedures. Those struggling students tend to spend the majority of their work
time just trying to work out the basic portion of a given problem. Most of the time students
never reach the end of the problem. This has caused many of my students to give up and lose
focus.

Woodward’s research (2006) compared two ways to teach students multiplication facts
that enable students to improve their performance on higher-level math concepts on the Iowa
Test of Basic Skills (ITBS). The integrated group was taught strategies to solve basic
multiplication facts whereas the timed drill group was given more explicit instruction on how to
multiply two numbers and memorizing the product. As the result, Woodward stated, “An
integrated approach and timed drills are comparable in their effectiveness at helping students
move toward automaticity” (2006, p. 287). About 70 percent of teachers found rote memory to
be successful with their students (Caron, 2007). Caron mentions how rote memory is one of the
“least effective ways of memorizing and takes a great deal of time and effort on the part of the
learner” (2007, p. 279). Woodward’s study correlates to Caron’s in that they both agreed that
simply attempting to memorize the multiplication table was not always effective.

De Brauwer and Fias (2009) are from Ghent University. The researchers investigated the
simple multiplication and division problems of 8-year-old children longitudinally to determine
the developmental trajectories of both operations. The authors of the study concluded that, “If
students understand that multiplication and division are conceptually related, a similar and
synchronized development time course can be expected for both operations” (2009, p. 1481).
Results showed that there is a strong connection with multiplication and division performance.
Again, this supports the idea that students must master multiplication fact fluency in order to
successfully understand more complex math such as division.

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According to Axtell, McCallum, Mee Bell and Poncy (2009) of the University of
Tennessee, Knoxville and Oklahoma State University, “The need for higher levels of math
competence has increased in this technology-based world, and a lack of knowledge,
understanding, and skill development can close doors for students” (2009, p. 526). The
researchers also stated in their study, “…the ability of a student to automatically respond to a
stimulus may free limited cognitive resources that can be applied to the more complex
computations and concepts…. This also applies to time-limited tests and assessments” (2009, p.
527). This relates to Caron’s (2007) study in that when students are unable to feel or be
successful in math due to the lack of the basic fact knowledge, the strength or ability to move on
to higher-level mathematics seems nearly impossible. Based on their studies, all of the above
researchers agree that fact fluency is crucial in moving forward in mathematics. Students need to
be able to perform the basic computations prior to moving on to problems requiring more steps
and procedures.
Self-Assessment and Confidence in Mathematics

If students lack the basic multiplication fact knowledge, not only will they struggle with
more complex mathematics, but also they will lack the self-confidence needed to be successful in
math (Caron, 2007). If students continue to struggle and fail in an area, their self-confidence
decreases (2007, p. 278). Students need to feel successful in math. One way for students to feel
this way is for them to self-assess their progress and achievement in math (Brookhart, Andolina,
Zuza, & Furman, 2004). When students can visually see their progress, confidence is more likely
to increase. According to Brookhart, Andolina, Zuza and Furman (2004), motivation theorists
suggest that student self-assessment will contribute to feelings of control over one’s own
learning, of choice and of agency and of self-worth. The themes of self-confidence and self-

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worth were also mentioned by McCallum, Skinner, Turner and Saecker (2006), where the
mastery of basic facts increases student confidence in the math field.

Caron (2007) presented an innovative approach to teaching multiplication facts for
children in middle school or younger. The method was to give the students a worksheet
consisting of 110 multiplication problems of a given factor (e.g., 3). On the top of the paper,
however, is a row of multiplication problems along with their answers. The answers to all the
problems were there in front of the students. The participants practiced the sheet several times a
day. This activity became more of a race and sense of achievement for the students. Results
from this teacher’s independent study showed that following the intervention, students’ self-
concept and motivation for math increased because they were able to finally move “beyond the
hurdle that stopped them form math learning for years” (2007, p. 281).

In addition to Caron (2007), Brookhart, Andolina, Zuza and Furman’s (2004) research
about correspondence of fact fluency and higher student confidence in math, Axtell, McCallum,
Mee Bell and Poncy (2009), concluded that, “Students who are fluent in math skills show lower
levels of math anxiety and choose to engage in math activities more often than less fluent
students” (2009, p. 527). This idea is true for any subject, not just mathematics. When people
feel confident with something, they feel more comfortable discussing it and sharing their
thoughts and feelings about it.

The studies mentioned above all relate to the theme of confidence in mathematics.
However, each study mentioned approached the topic in a different way. While Brookhart,
Andolina, Zuza and Furman’s (2004) uses self-assessment as a method for increasing student
confidence, Caron (2007) and Axtell, McCallum, Mee Bell and Poncy (2009) use more of a
strategic and competitive method to improve student confidence in mathematics. All of the above

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methods found to have improved student confidence in math. It simply illustrates that there is
more than one way to accomplish the same goal.
Conclusion

When I began studying my research topic, my main concern was how to engage all of my
students to aid in their fluent recalling of the basic multiplication facts. After reading various
researchers’ studies, I received many ideas on ways to involve my students to improve their
attitude, fact fluency within challenging math, and confidence within the area of mathematics.
The research shows that many students enjoy competition. This was one approach I noted as I
began my research. Another approach, that surprisingly was not included in any of the research I
collected, was the use of technology. In today’s society, everything is on the Web. Students learn
so much and enjoy learning via the Internet, that I felt I could implement it in my classroom.
There are so many engaging and interacting Web sites that could grab any students’ attention
that, to me, it would be difficult not to engage all students. However, many of the technological
games result in the self-assessment of progress in achievement and even competition, which
relates to the research of Caron (2007), Woodward (2006), Brookhart, Andolina, Zuza and
Furman (2004).

Purpose Statement
The purpose of my research was so see the impact of daily multiplication fact review
through fact fluency, student achievement in math, student confidence in long division and
attitude toward mathematics. I wanted to see if the constant practice and use of the basic
multiplication facts help students recall the basic multiplication facts better and faster and aid in
solving more challenging and multi-step math concepts.
Through the project, I wanted to understand just what needed to be done for students to

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retain the facts longer. Again, basic multiplication was a concept introduced in third grade, yet
the students still do not remember them. I also wanted to observe and understand any
connections between the fluent recall of the facts with the achievement and confidence of long
division. During this study, I focused on investigating three questions: What happens to students’
multiplication fact fluency when I implement daily multiplication fact review? What happens to
student confidence with long division when I implement daily multiplication fact practice? How
does my instruction change while I focus on daily multiplication fact review?

Methods
The daily fact review was presented through various methods: timed tests (MAD
minutes), games and flash-card practice. Throughout the study, both qualitative and quantitative
methods of data collection were beneficial for this plan. The participants in this study were five
target students: A, B, C, D and E. These students were randomly selected from our class
fishbowl where each name was drawn. I began by giving my target students a baseline
assessment of the multiplication facts. It was a three-minute timed test consisting of 60 facts. A
mid-quarter timed assessment was given to record progress and aid in showing the impact of the
implementation of daily review. The post-assessment was supposed to be a final timed-test
assessment that mocked the baseline and mid-quarter assessments, but due to time constraints, I
used the mid-quarter as my final assessment.
I conducted two interviews (Appendices A through C) with the five target students on
their comfort level of the facts as well as surveys (Appendices D and E) that gathered
information on their feelings and beliefs of the importance of multiplication fact fluency. The
first interview and survey were both given in early February while the second interview and
survey were given in late April.

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The target students also recorded weekly journal entries about their experiences and
feelings of daily fact review. Prior to the study, I thought this would be a great piece of
evidence, and that I would get a great idea about my students’ true feelings. However my
students struggled to write in their journals weekly and when they did write, I feel that my
students did not put much thought and effort into the entries. One of my intentions was to get
some feedback on long division through my target students’ journal entries, but due to lack of
motivation or carelessness, none of my target students focused on or even mentioned long
division in their journals. Thinking more about this disappointing issue made me reevaluate my
teaching and expectations. Prior to this research, I never required my students to write about
math. I never expected them to even reflect about what they learned or how one concept would
affect other concepts in math. As a teacher, I did not model how I wanted the journals to look. I
simply gave my target students five journal prompts to respond to. I thought that my students did
enough journaling in writing and reading, that there was no need to model how to write an
acceptable reflection for mathematics. Based off this experience, however, I was wrong. Writing
about math is different from writing about your favorite food or how a weekend was spent.

In addition to the baseline and mid-quarter assessments, data were collected from weekly
three-minute timed test called MAD minutes. This activity consisted of 99 basic multiplication
facts that assessed the students’ progress throughout the study. My intentions were to give a
MAD minute assessment every Friday, but with standardized and state testing occurring at this
time of the school year, the MAD minutes were given biweekly. As the educator and researcher,
I completed weekly journal entries that described each week in terms of the impact of daily fact
fluency.

Once I collected all the data, I created a chart to organize my baseline and mid-quarter

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assessments (Appendix A). The chart gave a percentage for each assessment so it was easy to
compare each one. The last column of the chart gave the difference from the baseline result to
the mid-quarter result.

Two charts were created for the surveys (Appendices C and D). The columns represented
each question while the rows represented the five target students. Each student’s answers were
recorded in the chart. The second chart looked similar to the first with the exception of any
changed responses. Any changed responses were highlighted in yellow to represent a different
reply. A copy of the survey can be found in Appendix B.

The interviews were typed up and scripted with each of the five target students labeled
Student A, Student B, Student C, Student D, or Student E (Appendices E and F). I developed the
questions based off my topics of inquiry: importance of fact fluency, confidence in long division,
and attitude toward mathematics.

Findings
An “average” day of teaching during this action research project was fairly simple. I
began most of the days with my anticipatory set, which was my daily multiplication fact review.
When I created my lesson plans a week prior, I decided on a daily fact review activity. If I felt
that the day’s math concept would take longer for my students to understand, my daily fact
activity would only last about three to five minutes. If the material to be covered that day would
be an easier concept to grasp, my daily fact review activity would be about 10 minutes long. I
started the year off having my students practice the facts with flash cards and board races, but
began to notice my students getting bored with these methods. I collaborated with my school’s
technology specialist and other classroom teachers in my building in search for new and
engaging ideas. I received various master copies of interacting multiplication activities and

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games the students were able to reuse many times as well as Web site ideas such as
Funbrain.com and mathplayground.com, in which I used for my whole class on the
SMARTBOARD. There were many days when daily fact review did not occur due to state
testing or simply lack of time.

An obstacle I faced during the study was having time to complete the daily multiplication
fact review. We have had so many days off of school due to various reasons; it was difficult to
have a full week. Not only had my class missed out on daily fact reviews due to days off of
school, but by also by me simply forgetting to do it during math class or not having time for the
review. Sometimes I would have my daily fact review planned as my anticipatory set, but once I
started introducing the new concept to my class, I forgot to do the daily fact review. Due to the
California Achievement Testing and State Reading tests, my class missed out on math altogether
some days. It did get frustrating at times, but some of it was uncontrollable.

I had many tensions playing the role of both teacher and researcher. One example would
be time management. Not only did I try to keep up with the basic duties of a teacher (i.e. grading,
lesson planning, etc.), but I was also trying to keep up with my research and five target students.
Journaling usually did not take long to do each week, but it was difficult to remember to
complete it. Usually on Fridays, I wanted to get home as soon as possible. I also struggled with
reminding my target students to write in their journals each Friday.

One thing that went well, however, was the fact that I found fact practice methods that
engaged all students. I found that using computers or SMARTBOARD activities allowed
students to work at their own pace, and it made learning their facts fun. I also found through
discussing with students that they enjoyed competing with one another during math games. I
would not normally like this type of practice, but I took an anonymous vote and my students all

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wanted to do it.
What happens to students’ multiplication fact fluency when I implement daily
multiplication fact review: Fact Automaticity

After analyzing my data, an increase in fact fluency was apparent in all five-target students.
Student A began the study with a baseline score of 45 facts correct out of 60 within three
minutes. This student’s mid-quarter/final score increased by three facts by getting 48 out of 60
facts correct. Student B began the study with 47 out of 60 facts correct and ended the study with
52 facts out of 60 correct, an increase of five facts. Student C began the study with 46 facts out
of 60 correct and ended the study with an increase of four facts or 50 facts out of 60 correct.
Student D started out with knowing 44 facts out of 60 correctly. The student also increased by
four facts with 48 facts out of 60 correct. Lastly, Student E performed the highest in both the
baseline and mid-quarter assessments. Student E began the study with 51 out of 60 facts correct
and ended the study with 55 out of 60 facts correct. This gave the student an increase of four
facts.

Based on student journal entries, with the exception of one student, all the target students
felt as if their fluency was getting better. Student D replied,

My fact fluency is getting better whenever I practice and play math games! I’m so happy
that it’s getting better and better every day. When my class didn’t really play math games
and practice, I always counted on my fingers and it took me a long time but I still had the
right answer! Now I can get them faster and not count by my fingers.
Student D’s response was accurate, since she did improve her fluency. This was a student who,
at the beginning of the year, always used her fingers to calculate her multiplication facts or
looked at the multiplication chart from my front wall. At the end of the research, she no longer

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relied on her fingers or the chart. Her class work and homework took less time to complete.
Although Student A increased by three facts from the baseline to the final assessment, she

did not feel as if her fact fluency increased. She stated in a journal entry, “I haven’t really seen
any difference in math…I still need more practice.” As an educator, it appears that Student A did
not make enough of an improvement in her mind that made a significant impact on her
confidence of fact fluency.

When analyzing the portion of the survey that focused on fact fluency and its importance
to mathematics, four out of five students stated that they did not know their basic multiplication
facts fluently. Three out of five students stated that daily fact fluency would help improve fact
fluency. The remaining two students either did not think it would help or were not sure. All of
the students felt they would improve fact fluency by using flash cards, and playing computer
games was the other popular way the five target students felt would improve fact fluency. The
majority of those tested believed that multiplication fact fluency is important for all math. When
asked if they feel if being able to recall multiplication facts quickly would help them perform
better in math, they all felt that it would. I was also informed that just about the entire group of
target students did not practice their facts at home. This was an important piece of information to
me. If teachers do not work with the basic multiplication facts at school, and the students do not
practice at home, where did they learn them? This made me realize that it is imperative that
educators work with the facts to bridge any gaps students may have in their fluency. Lastly, I
received a variety of responses for the question, “What would help you do better in solving
division problems?” Two students felt that getting help from a teacher would help them, while
two other students felt that extra practice would benefit them.

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Looking over the second survey, I noticed that all the target students changed their
responses a bit in terms of the way they learned their facts. I think this is due the various
strategies we practiced in class. Only one student changed her responses in both importance of
fact fluency and fluency compared to peers. Three out of five students changed their response in
terms of how often they work on facts. They all responded that they work more with the facts at
school. The two responses I received for how to improve their fact fluency were practice and
play more math games. I tried to base my daily fact review off this response, but also incorporate
technology into the games and practice.

What happens to student confidence with long division when I implement daily
multiplication fact practice: Math confidence and attitude

Given the data collected through interviews and surveys, student confidence did not
increase due to the daily multiplication fact review. According to the first interview, all of the
target students, with the exception of Student D, already had a negative attitude toward long
division and had low confidence levels with the concept. Based on this study, Student A suffered
from math anxiety. I questioned her about it. Her response was, “I’m not good at math. I don’t
know my math facts very well, and I just don’t get division.” This particular student rarely
volunteers in class and chooses not to participate in extra-curricular activities that consist of
math.

When asked, “Has your attitude about long division changed during your 5th grade year?”
Student A responded, “It didn’t. I still don’t really like long division. It is still hard for me.”
Student B replied, “I think I like it better. I know my facts better. I just get stuck on how to
divide.” Student C had similar feelings as Student A by stating, “I still don’t know how to
divide.” Student E continued to believe that long division was a little hard. When I thought

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about my students’ responses, I found myself a little confused by their replies. The whole idea
about long division was to see the how fact fluency impacted long division. The responses stated
that the students either liked long division or did not know how to do long division. Knowing
how to do long division is different from calculating a long division problem better due to fact
fluency. I think my students were unclear with this idea. As the educator, however, I should
have explained the question more clearly.

According to the surveys, every target student, except Student B, felt that the basic
multiplication facts are important to long division. However, after working with daily fact review
and class work that consisted of division problems, Student B’s response changed on the second
survey to “Yes, multiplication facts are important to long division.”

Each target student received a sheet of paper they stapled in their journal that included a
list of possible journal prompts to write about (Appendix G). My intention was to have my target
students write their feelings and attitudes toward long division in their weekly journals based on
those prompts, but they did not include such information. Instead, I collected class work that
consisted of both short and long division. One assignment was a worksheet consisting of 10 long
division problems. Student A got 5 out of 10 problems correct , Student B got 2 out of 10
problems correct, Student C got 0 out of 10 correct, Student D received 5 out of 10 problems
correct, and Student E received 2 out of 10 problems correct. Results showed that all of the
students performed poorly on each assignment. After looking over each student’s work, mistakes
were made from incorrect answers due to subtraction and misunderstandings on the division
process. Most of the multiplication was correct.

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How my instruction changes while I focus on daily multiplication fact review:
Incorporating technology in my lessons

When looking back through my own journal entries, I noticed that my instruction did
change a bit throughout the implementation of daily multiplication fact review. I found new
innovative ways to engage my students in math by using math computer games as well as other
technological methods such as the SMARTBOARD. As stated in a journal entry from the week
of February 24th,

Based off my last week, I noticed that I needed to change my way of presented daily fact
practice. I decided to use my SMARTBOARD for a whole group activity. We found a
Web site on Funbrain.com that worked with being timed to find the product of two
factors. THEY LOVED IT!
I also researched new activities and collaborating with other teachers in my school about
engaging math fact activities and games. In terms of normal math instruction, however, I did not
notice much of a change in instruction. Since I did the daily fact review as my anticipatory set,
my actual lessons did not change. I would have liked to say that my students showed much more
independence during work time, but I cannot. According to my journal entry written in the week
of February 24th,
Only about half of my students grasped this concept. I really had to work with small
groups with those struggling students. I have yet to see a large increase in independence
within my students during work time. This could mean that their confidence is not yet
where I would like it to be or have even anticipated. I have noticed, however, that they
have not been asking me what the product of two factors is. This shows me that their fact
fluency may be increasing. This is a start!

20

As mentioned above, the only impact I noticed since the implementation of the review was that
my students did not ask questions about the basic multiplication facts (i.e. “Mrs. Bystrom, what
is 4 x 5? Or what is 6 x 8?”) as they consistently did at the beginning of the year. The students
did show a little more independence in terms of the recalling of facts but not much. I stated in my
February 12th entry, “We played ‘Multiplication Quizmo’ this week. This game was well liked
by everyone. And just by observation, I was able to notice progress with some of my students
and their fact fluency.”

My students did comment about my new way of incorporating technology into my
instruction of the daily fact review in their weekly journals. Student E included a response about
using laptops to practice multiplication facts, “I like it when we are using laptops because it is
fun and I learn in a really cool way.” Student A stated, “For daily fact review I really want to
play on computers.” My target students also commented on instruction through the surveys.
When asked the question, “I can learn basic math facts better when I…” four out of five of the
students answered by playing computer games. I was not surprised with these comments since
society is based on technology. Students enjoy technology such as computers and
SMARTBOARD. It engages all of the students. Technology grabs students’ attention and keeps
their minds active.

Conclusions
Given all the collected data through surveys, interviews, class work, student journals,
personal journals and three-minute timed tests, I believe that the daily multiplication fact review
did increase my students’ fact fluency. Having the students engaged and motivated enabled them
to want to learn. The students enjoyed the technology along with the friendly competition of the
flash cards and MAD minute drills. When the students worked with partners and timed each

21

other on flashcard drills, it gave the students a sense of independence and accomplishment.
Brookhart, Andolina, Zuza and Furman (2004) support this idea by stating, “Motivation theorists
suggest that student self-assessment will contribute to feelings of control over one’s own
learning, of choice and of agency and of self-worth” (2004, p. 214). Students need that sense of
ownership and pride in their learning.

According to Woodward (2006), in the students who developed automaticity, an
improvement in their attitude toward mathematics occurred. I do not feel as if my students had
enough time with the daily fact reviews to make a noticeable impact on their attitudes and
confidence in math as a whole. I believe that the daily fact review will need to be implemented in
the beginning of the school year in order to work correctly so that it will begin as a math routine
and continue with the students and myself until the end of the year.

Implications
As a result of this study, I plan to continue the daily multiplication fact review with my
current class as well as my future classes. Even though my study did not show a significant
increase in confidence and achievement in long division or student attitude toward mathematics,
I feel that their multiplication fact fluency did increase enough to make a positive impact on the
success of future math concepts. I strongly believe that because of the standardized assessments
and testing this spring, my students did not receive the daily fact review as often as I had hoped
and planned. If I had been more consistent with the review, the students may have increased their
fluency even more as well as their confidence and feelings toward math. Starting at the
beginning of the year may also have a more positive impact on the implementation of the daily
multiplication fact review. This implementation will be an ongoing study that will continue until

I feel it is no longer benefiting my students.

22

References

Axtell, P. K, McCallum, S., Mee Bell, S. & Poncy, B. (2009). Developing math automaticity
using a classwide fluency building Schools, 46(6), 526-536.

Brookhart, S. M., Andolina, M., Zuza, M. & Furman, R. (2004). Minute math: An action
research study of student self-assessment. Educational Studies in Mathematics, 57, 213-
227.

Caron, T. A. (2007). Learning multiplication: The easy way. Clearing House: A Journal of
Educational Strategies, Issues and Ideas, 80(6), 278-282.

De Brauwer, J. & Fias, W. (2009). A longitudinal study of children’s performance on simple
multiplication and division problems. Developemental Psychology, 45(5), 1480-1496.

Jiban, C. L., & Deno, S. L. (2007). Using math and reading curriculum-based measurements to
predict state mathematics test performance: Are simple one-minute measures technically
adequate? Assessment for Effective Intervention, 32(2), 78-89.

Lee, D. L., Stansbery, S., Kubina Jr., R., & Wannarka, R. (2005). Explicit instruction with or
without high-"p" sequences: Which is more effective to teach multiplication facts?
Journal of Behavioral Education, 14(4), 267-281.

Mauro, D., LeFevre, J. & Morris, J. (2003). Effects of problem format on division and
multiplication performance: Division facts are mediated via multiplication-based
representations. Journal of Experimental Psychology: Learning, Memory, and Cognition,
29(2), 163-170.

McCallum, E., Skinner, C., Turner, H. & Saecker, L. (2006). The taped-problems intervention:
Increasing multiplication fact fluency using a low-tech, classwide, time-delay
intervention. School Psychology Review, 35(3), 419-434.

Singer-Dudek, J., & Greer, R. D. (2005). A long-term analysis of the relationship between
fluency and the training and maintenance of complex math skills. Psychological Record,
55(3), 361.

Woodward, J. (2006). Developing automaticity in multiplication facts: Integrating strategy
instruction with timed practice drills. Learning Disability Quarterly, 29(4), 269-289.

23

Appendix A

Impact of Daily Multiplication Fact Review interview: February 19, 2010

• Question 1: What makes math easy or difficult for you?
Student A: The teachers not explaining things to us clearly.
Student B: I don’t like to do long division because I get confused on what number to

bring down. It’s hard.
Student C: I don’t really know my math facts. I still have to use my fingers. It takes

so long to solve a problem and then I get confused.

• Question 2: Have you ever had a really bad experience with division? If so, what
happened?
Student A: YES!! Last year I did not know how to divide. I hate division. My teacher
wouldn’t help me.
Student D: No, I like division. I think I did good on it.
Student E: Kind of. I always get confused with it. It is too long and I sometimes get

mixed up with multiplying and subtracting.

• Question 3: What could teachers do to help students with division?
Student A: They could help us when we need help or explain it in other ways if the

students don’t get it. I also think that if kids don’t know their facts they will not do as good
on division.

Student C: Teachers could spend more time helping kids so we will understand it.

• Question 4: What do you feel is the purpose of the daily fact review?
All Students: To help us know our multiplication facts better. So we can be faster
with them.
Student C: It might help us on other math…like division.

• Question 5: What do you hope to get from these review sessions?
All Students: To be faster at my multiplication facts.
Student C: To memorize the facts so we don’t have to use our fingers or look at
the chart from our assignment notebook or wall.

• Question 6: Do you think knowing your multiplication facts is necessary to division?
Student A: Maybe. If you think about it, a division problem is pretty much like little

multiplication problems.
Student B: I think so.
Student C: I don’t know. Maybe.
Student D: Yes. Just like (Student A) said, division is like multiplication. If you don’t

know your multiplication facts, you will not be good in division.
Student E: I think so.

• Question 7: Is there anything else I should know about you to better understand
your problem solving in math or your general math experience?

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Student A: I don’t like long division!
Students B-E: No...not really

• Question 8: How much time on average do you spend on homework assignments?
Student A: A couple of hours (with division)
Student B: About one hour
Student C: I don’t know. Sometimes one hour.
Student D: I don’t spend that much time on homework. I get a lot of it done in class.
Student E: I don’t do a lot at home. Maybe an hour.

• Question 9: What do you think is the purpose of math homework?
All Students: To get better at math. To help us practice.

• Question 10: What do you like best about math? What do you like least about
math?
Student A: I don’t really like math at all.
Student B: I like all of math except long division.
Student C: I don’t know.
Student D: I don’t like division very much. But I like other types of math.
Student E: I like all math. It is easy to me.

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Appendix B

Impact of Daily Multiplication Fact Review second interview: April 8, 2010

• Question 1: Did you enjoy working math before this school year? Why do you think
this was the case?
Student A: No, not really. Sometimes it is hard and I don’t understand.
Student B: Sometimes.
Student E: I never really liked math until this year. You made me like math, Mrs.
Bystrom. (WHY?) You explain stuff to us better. I like math now.

• Question 2: Has your attitude about long division changed during your 5th grade
year?
Student A: It didn’t. I still don’t really like long division. It is still hard for me.
Student B: I think I like it better. I know my facts better. I just get stuck on how to

divide.
Student C: I still don’t know how to divide.
Student E: It is still a little hard.

• Question 3: What else could teachers do to help students with division?
Student A: Keep making us practice…even though I don’t really like it.
Student B: Let us do more computer games. I really learn better that way.
Student C: Teachers could spend more time helping kids so we will understand it.
Student D: We just need to practice more.

• Question 4: What do you feel is the purpose of the daily fact review?
All Students: To know all the multiplication facts.

• Question 5: What do you hope to get from these review sessions?
All Students: To know our facts better so we don’t fall behind the other kids in the
class.
Student D: Since you took down the fact chart…I need to memorize the facts by
myself. It will help me.

• Question 6: Do you think knowing your multiplication facts is necessary to division?
Student A: Yes, kind of.
Student B: Yes.
Student C: Yes.
Student D: Yep.
Student E: Sure. Multiplication and division are like opposites.

• Question 7: This semester I have changed some of my teaching practices. What
advice would you give me about continuing these changes next year?
All Students: I love the math games. They are so fun.
Student B: I like the SMARTBOARD games. Oh, and the computer games.

• Question 8: What do you like best about Math? What do you like least about Math?

26

Student A: I don’t like almost everything! Math is sometimes hard. I kind of like the
games.

Student B: I like the math games. I think I learned my facts better with them.
Student C: I like to play games. I don’t like division. I’m not really good at it.
Student D: I like everything in math. I really like Algebra. But I don’t like
division.
Student E: I like everything.

• Question 9: What do you think is the purpose of math homework?
All Students: To get better at math. To help us practice.

• Question 10: Do you think you learned your multiplication facts better since the
review?
Student A: Kind of. It seemed to go by fast, like I didn’t learn much about facts, but I

think I did.
Student B: Yes.
Student C: Kind of.
Student D: I really learned my facts by the reviews. It was fun.
Student E: I think a little. I already knew my facts, though.

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Appendix C

Student Survey:
This survey will be given at the beginning of the study and at the end. It is designed to give the students
feelings about division, fact fluency, and math in general. It will also give me an idea on how they feel about
their own fact fluency rate.

1. Math is easy for me.
a.) Always
b.) Sometimes
c.) Never

2. I enjoy solving math problems.
a.) Always
b.) Sometimes
c.) Never

3. I know all of my basic multiplication facts.
a.) Yes
b.) No

4. It is important to know the basic multiplication facts when dividing.
a.) Yes
b.) No

5. Long division is easy for me.
a.) Always
b.) Sometimes
c.) Never

6. Daily fact practice will help improve my fact fluency.
a.) Yes
b.) Maybe
c.) No

7. I can learn my basic math facts better when I (Circle all that apply):
a.) practice with flashcards
b.) take multiplication timed-tests
c.) play math computer games
d.) look off of the multiplication chart from my assignment notebook

8. I think multiplication fact fluency is important for:
a.) just long multiplication
b.) just division
c.) just word problems
d.) all math

9. Compared to my fifth grade peers, my fact fluency is
a.) faster
b.) on the same pace
c.) slower

10. Do you think being able to recall multiplication facts quickly will help you do better at math?
11. How often do you practice your basic multiplication facts at school? Home?
12. What would help you do better in solving division problems?

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Appendix D

According to the first math survey:

Math is I enjoy I X facts Long Daily I learn Fact Compared Would How often I What
easy for solving know import Division is fact multi.facts fluency is to peers, being practice would
me. math all for easy for practice better by important my fact able to math. help you
problem basic long me. will for… flue is.. recall do better
x division help me Flash facts Not a lot in LD?
facts improve cards, All math slower help
fact flue computer in Sometimes More
A Sometimes Never No Yes Sometimes No games, All math Same pace math? at teacher
chart Yes school/never help.
B Sometimes Sometimes No No Always Yes Flashcards, Just long x Same pace at home
Computer All math Same pace Yes Never at Don’t
C Sometimes Sometimes No Yes Sometimes Yes games All math Faster home know
Sometimes Maybe
D Sometimes Sometimes No Yes Sometimes Maybe Flashcards, A lot at Practicing
computers Yes school/ little division
E Sometimes Sometimes Yes Yes Yes at home facts
Flashcards, Yes Everyday Practice a
Look off lot
of chart
Computer Get help
games at my seat

29

Appendix E

According to the second math survey:

Math is I enjoy I X facts Long Daily I learn Fact Compared Would How often I What
easy for solving know import Division is fact multi.facts fluency is to peers, being practice would
me. math all for easy for practice better by important my fact able to math. help you
problem basic long me. will for… flue is.. recall do better
x division help me facts Only at in LD?
facts improve All math slower help school
fact flue in Math
math? games
A Sometimes Never No Yes Sometimes Maybe computer Don’t
games, know

B Sometimes Sometimes No yes Sometimes Yes Computer Just faster Yes Every More
games division couple of math
days at games
C Sometimes Sometimes yes Yes Sometimes Yes Flashcards, Just long x Same pace yes school/never
Same pace Yes at home Keep
Faster Yes yes practicing
at school
computers,

mutli. Timed

tests.

D Sometimes Sometimes yes Yes Sometimes yes Flashcards, All math A lot at Practice a
school/ little lot
Look off of at home

chart

games

E Sometimes Sometimes Yes Yes Sometimes Yes Multiplication All math Everyday Practice
everyday
timed test

*The highlighted items represents when a response for the second survey differed from the first.