RUNNING HEAD: USING ROCKET MATH PROGRAM
Using Rocket Math Program to Increase Rate of Multiplication Fact Accuracy
Jessica R. Dennings
Michigan State University
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USING ROCKET MATH PROGRAM TO INCREASE RATE OF MULTIPLICATION
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Abstract
Students in an elementary school were identified as having a deficit in multiplication fact
recollection. Previous methods taught hindered the success of students memorizing basic
multiplication facts. A program was requested upon the teachers to pilot, which leads into the
topic of this paper. The purpose of this project is to analyze a piloted program called Rocket
Math and answer the question if implementation of the program will increase the rate of
multiplication fact accuracy. The participants involved were a group of 27 fourth grade students
from a local charter school. Methods used involved daily tracking of student progression
through various levels. Each level contained two multiple groups and the data produced from
this experiment was compared to data from a previous method not involving Rocket Math. The
findings indicated students progressed at a more rapid rate due to the use of Rocket Math. In
discussing the findings one may consider the fact that students were only given forty problems
versus 100 problems and daily practice was a component as well. These two factors were
considered when looking at the results and tt was concluded that students did progress more
rapidly and demonstrated accuracy.
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Using Rocket Math Program to Increase Rate of Multiplication Fact Accuracy
As I taught a math lesson on multiple digit multiplication, I grew alarmed at the site
before me. When multiplying individual digits, students were using their fingers to count up by
the numbers verses remembering the fact. Multiplication facts that should take seconds were
taking longer and I begin to realize what dilemma I was dealing with. My students lacked the
skills of quick recall when it came to their multiplication facts from numbers 0 – 12. This basic
skill is a must when it comes to mathematics as it works as a building block for other concepts.
For example, when performing three by two digit multiplication problems, it is important to
know the single digit facts in order to solve the bigger problem. Another example is in long
division where the students must know their facts in order to determine the quotient.
The problem my students had was recalling their basic multiplication facts at a fast rate.
To test my theory that this problem existed for my students, I decided to give them a
multiplication-timed test. There were 100 problems of variable facts. Instead of writing down
their answers quickly, I had students counting up with their fingers to solve the problems. What
should have taken 5 minutes to complete ended up being a situation where 75% of my students
did not finish. I had to solve this issue in order for them to be successful in more complex
problems.
A math specialist at my school told me about Rocket Math, which is a program that helps
students recall basic multiplication facts at a quick rate. This program is the basis of my paper
USING ROCKET MATH PROGRAM TO INCREASE RATE OF MULTIPLICATION
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and my research. My question for research is: Will using Rocket Math increase my students’
speed and accuracy for recalling multiplication facts?
Definitions: automaticity- the ability to do things without occupying the mind with the low-level
details required
Theoretical Framework
The theoretical viewpoint of behaviorism is, “An approach that focuses entirely upon
learners understanding the “what” through methods like rote memorization, identification, and
association. This theory is concerned with illuminating only what learners need to know”
(Mcleod, 2003). The way my students were taught multiplication in third grade was through
songs that taught them to memorize the multiples of each number from two through nine. They
sung songs that had a different tune for each number family. My theory is that the students are
using these songs in their heads when counting up on their fingers. This is important for my
research. I can see that my students do not have their facts memorized and are using a different
method that has not benefited them in this subject. This is a problem because I can see the
evidence of them counting up when using their fingers and I have seen them do this while taking
a test they knew was timed. I have also seen them not finish a test they should be able to finish
in the time allotted. Furthermore this problem has affected their other math concepts because it
takes them that much longer to finish complex problems that involve these basic facts and in
return creates fatigue and disinterest in solving the problems. Since I have seen all of this occur,
I know it is a problem that exists and needs to be resolved.
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Literature Review
Teaching multiplication facts is one of the mandatory components of a successful math
class in 4th grade. Students first learn this skill, and later use it in more complex problems. An
example of using basic multiplication in more complex problems is when performing a long
division problem, because one must be able to recall what the product is of two single digit
numbers. Students who do not master this skill take longer and often fatigue while working on
problems such as these because they lack the intrinsic ability to perform the most basic
multiplication. Meaning that students are having difficulty with basic facts, therefore taking
along time on more complex problems using those facts, and then getting tired or giving up do to
the length of time it takes for the solution of the problem to be calculated. My students do not
have such skills and are behind in their ability to recall basic multiplication facts.
When given a timed test, I saw students using their fingers to count up to the product
verses quickly recalling it in their minds. Most were unable to finish the timed test. I used a
method of instruction that involved giving basic facts for one number such as one times various
numbers up to twelve, two times various numbers up to twelve, and so on. What I noticed was
that once the more difficult facts were present such as three times various numbers, or four time
various numbers, many students stayed behind while only two continued forward consistently. I
did not like what this method was doing to the self-esteem of my students as well as the lack of
progress I was seeing from many. A program called Rocket Math was brought up at a staff
meeting and I offered to pilot the program in my classroom so my question of research is: Will
the implementation of Rocket Math increase the rate of automaticity of multiplication facts with
my fourth grade students.
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In order to fully investigate this process, one must research the background of such
concepts. I decided to divide my sources into three categories. The first category is Origins and
Definitions: What is Rocket Math all about, and what case studies have been done. I will then
discuss articles dealing with Key Theories and Concepts: Developing Automaticity and end the
review with discussing Key Issues and Debates. I have searched twelve sources, mostly at which
are from math or educational journals. My hope is that this research will allow me to develop
the needed background information to fully adapt and commit to this implementation.
Origins and Definitions: What is Rocket Math and what does it entail?
When implementing a program it is imperative to explore its origins and what defines the
program. This foundation gives the necessary background information to support implementing
the program. In researching what Rocket Math entails, I found a case study involving
implementation of Rocket Math with a student labeled at risk. Looking deeper into Rocket Math,
I also discovered that its foundations are based on peer tutoring so I found two articles that
described effects of peer tutoring and their positive influence on students. Another article
disclosed information regarding the importance of math fact fluency on more advanced math
problems involving 4th graders. All of the articles found were important pertaining to the basic
foundations of what Rocket Math derives from.
The case study performed discusses a student named John who was stated to be “at risk of
school failure” (Martella, 2011, p. 250). His test scores were low and he also suffered from ADHD
(Attention Deficit Hyperactivity Disorder). The study was done to see if John’s test scores
improved with using Rocket Math. After the case study was complete, it was found that not only
did John’s ability to recall multiplication facts increase but his self-concept increased as well.
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There was sufficient evidence proving that memorizing the facts by focusing on two facts a day
on timed daily one-minute tests and one-minute peer tutoring was effective.
In addition to the quick focus on two facts a day, peer tutoring was a factor. Peer tutoring
is a major component of Rocket Math. An article I found regarding peer tutoring was a dissertation
from North Central University. This dissertation focused on the effectiveness of peer tutoring.
The data showed that students who received peer tutoring to recall multiplication facts
outperformed those students who did not receive peer tutoring (Smith, 2010, p. 106). This
evidence supports the theory that Rocket Math students benefit from such interventions as peer
tutoring.
The case study involving Rocket Math was specific to the program and therefore concluded
the positive effects it had on a student whereas the second article focused on the concepts of peer
tutoring and other interventions. What both articles advocated was the importance of recalling
multiplication facts and the deficit seen in 4th and 5th grade students. I also noticed a common
theory that recalling these facts will support higher functioning math problems.
Key Theories: Developing Automaticity
The key theories of Rocket Math are not only regarding peer tutoring but also the
importance of the development of automaticity. Automaticity involves the ability to recall
multiplication facts at a quick speed. Several articles were found discussing the importance of
automaticity and its fundamentals.
Two articles were discovered that described the development of automaticity. One article
was from an instructional solutions company. This article pertained to the fact that there are three
stages of learning math facts and the third stage is in fact automaticity. It stated the definition of
USING ROCKET MATH PROGRAM TO INCREASE RATE OF MULTIPLICATION
automaticity and described its importance in the final completion of completing a problem.
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The
other article was a comparison of students whom were taught math facts conceptually and those
taught using rote learning, “The students involved in rote learning scored significantly better on
tests not only involving math facts but also higher involved math scenarios involving multiple
steps” (Woodward, 2006, p. 14). The first article was a description of what automaticity is and its
importance in learning math facts and the other was an actual study involving such concepts. One
article supports the other in that one defines and the other give evidence of such theories.
A strong component of automaticity is speed. I found two articles that incorporated speed
in their findings regarding the recollection of math facts. The first article was a study done by
Walden University in which students were given timed practice drills daily for several weeks and
another group was not. “The group who received daily, timed drills scored higher on post tests
than the control group” (Knoules, 2010, p. 3). The second article was a dissertation from the
University of Tennessee, which assessed the need of speed computing basic multiplication facts.
It described the benefits of being able to quickly solve math facts. One major benefit it continued
to reflect on was a child’s ability to do well on more complex problems.
These articles differed in their use of speed with math facts. One was a study that showed
progress for students who were timed on daily math tests and the other reflected on the importance
of speed when it comes to solving problems. It still seemed that the articles complemented each
other because one was a study and the other was an explanation or description.
Issues and Debates: Conceptual vs. Rote Learning
This debate is a constant battle amongst educators. The idea that a child must fully
understand a problem and why the answer is what it is. Whereas others believe rote learning helps
USING ROCKET MATH PROGRAM TO INCREASE RATE OF MULTIPLICATION
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the child achieve at higher levels. The articles found for this theme were pertaining to the idea of
conceptual learning so one could see what the argument is against automaticity and speed
involving mathematics.
Three articles were included involving the conceptual learning of math. One involves the
use of music to learn math facts. This article is a study reflecting the benefits of using songs to
remember math facts. The study does show that the students learn the facts, but the problem with
this is one in which I have seen in my classroom. Counting with your fingers and humming a tune
will delay a student when it comes to higher-level math problems. If a student needs to do long
division but cannot quickly recall 5 x 6, he/she will be delayed and potentially give up on the
problem. This is known as a problem at my school because that is how the students were
previously taught and they are suffering in the higher-grade levels.
The second article written by Hope Martin reflects on the importance of Math Literacy.
She makes a valid point of stating that, “students learn math in functional, realistic ways before
entering school and then discover a new method of memorizing of facts. This then causes the
realistic applications to fade” (Martin, 2007, p. 2). Her point is valid in that real world application
of math is important, but that needs to come after the students are fully successful in the basic
facts. Another article comparable to this is one written by Debra Saunders. Her article is in regards
to what is called “New New Math” which is basically real world application. This math is one
where you could find a problem involving figuring out how many trees will be planted over a
period of time and then writing a proposal to the principal. The article also expresses the
‘hindrance” of memorizing facts on students (Saunders, 1995, p. 2). Both articles propose the use
of real world math problems verses rote memorization.
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In opposition, the previous article is one comparing the use of automaticity with the use of
a calculator. This article is a proponent of recalling facts verses simply using a calculator. One
could say that in real world applications, a calculator can be of use for such simple facts, but the
study done in this article demonstrates evidence of importance of recalling facts when it comes to
solving more complex problems. Students who were studied expressed it was more helpful in
completing such complex problems when using recollection verses a calculator.
Summary
The question is, will teaching basic facts using rote memorization be more beneficial than
conceptualization of the facts? The articles found valid points comparing different methods of
instruction for teaching multiplication facts. This review focuses on various ideas involving music,
conceptual learning, and rote memorization. It argues over which method is more beneficial to
students. The articles advocated their points of which method was proven to be successful in
various case studies. Other articles were based on teaching practices in schools.
In beginning the review, the question of which method should be used for students in order to fully
master their multiplication facts arose. The articles addressed this question by giving various
answers. The conclusion can be taken that in Martin’s article, using music is a better option
because it focuses on the conceptual learning of multiplication. Similarly, Saunders’ article refers
to “New New Math” which is also the conceptual learning process. However, in the studies that
were done, one could see the positive effects of rote memorization of multiplication facts out
weighed the conceptual learning theories.
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It is still unknown which in fact is the better option. This is an opinion component. If you
ask Martin or Saunders you would get a different answer than if you looked at the results of the
dissertation from Tennessee, you would see valid results boding for the benefit of quick recall.
The gap in the literature was the fact that each article was either on one side or another.
There were no articles found that discussed how both could be used, or if it would even be
beneficial to use both. Knoules’ case study demonstrated results from students based on rote
learning and Martin talked about music and conceptual ideas, but neither mentioned the benefits
of the other side. Another perceived gap could be that this debate may be dependent on the student.
All of which further research would need to be done and documented.
Research Design and Data Collection Methods
The research was conducted in a classroom setting where 27 fourth graders participated
in the research. The ages were 9-10 years old with 70% white, 20% black, and 10% other in
ethnicity. In order to protect the identities of the students, numbers were used when referring to
the students verses using their names. The study was a quantitative study using the descriptive
design method of observational research and the reason for using this method was because the
data involved quantitative results in which scheduled observations were made and involved the
tallying of scores. The data collection methods included daily assessments and a tally sheet that
tracked the rate of student progress. The daily assessments were 1 minute timed tests that
focused on two math facts such as 1 multiplied by numbers 1-12 and 2 multiplied by numbers 112.
Each of the students had a partner that they practiced with for 2.5 minutes. Student A
was the given the title of “practicer” and student B was called “the checker”. The practicing
student would practice by stating the math problem and answer then moving on to the next.
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He/she was to practice 40 problems at his/her level, if finished early he/she would do a victory
lap, which required the student to run through the practice routine again. The teacher stopped the
timer at 2.5 minutes and then student A and B would switch. Student A was now the checker
and student B was the practicing student. They would follow the same pattern as previously
stated. During the practice and check session, students would monitor their progress. If the
practicing student got the problem wrong or delayed by 3 seconds in their response then the
checker would have them restate the problem and answer three times, move back three problems,
and begin again.
Once the practice session was over the students would go to their seats for the 1 minute
timed test. They were each given a number that disclosed how many problems they were
expected to finish based on how fast they could write. A timed writing test was distributed
before the program started and each student was given a goal, which indicated how many
problems to finish in the 1 minute timed tests. Most students were expected to finish 40
problems in 1 minute. In the 1 minute timed tests, the students had to complete the problems left
to right and row-by-row. They had to get all 40 correct or the total number of their goal. If they
did this then they passed to the next level, if they did not do this then they would remain at that
level. Their partners did the correction of the tests. Each student had a practice book and test
book with answers on the backs of the pages. The partners would check the problems using the
answer sheets then they would give the test booklets back. If students passed, they were to bring
the teacher their test and receive a sticker on their chart. The teacher also made a check on her
chart to indicate the date and the level passed by the student.
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In order to assess where the students’ levels were prior to the implementation of the
program, a timed test was given using sample problems from various levels. Students were
given 20 problems and expected to complete the first 10 problems correctly in 15 seconds. If
students were successful they were given the next level that increased difficulty of math facts.
After this assessment was complete, it was concluded that two out of 27 students would
begin at the second level and the remainder of the students would begin at the first level. The
second method used to help assist in the tracking of students was to give a timed test at the
beginning and at the end of the research period to see level of improvements of the students.
Along with pre and post research assessments, were daily assessments to continue tracking the
progress of students and record data. This method was a chart created that had each student and
the levels. Each day it was recorded if the student was able to pass the level they were given that
day. Students whom passed were given a check on the chart; students whom stayed were left
blank. The students were also given a chart to track their own progress where they received a
star for passing and a black square for not. To ensure trustworthiness, 27 students were observed
and the data only related to the research question posed.
Data Analysis
When analyzing the data, a descriptive statistics method was used. This is a result of
there being a large number of data and scores recorded to analyze. The teacher observed the rate
at which students passed the levels by looking at the days of when the levels were passed as well
as comparing this data with the data of the previously used method prior to using Rocket Math.
The limitations were how long it took the program to start. The implementation of
Rocket Math was expected to begin the first week of March, but parent volunteers were putting
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together the needed materials for daily practice, which is a major component of the program, and
took longer than expected.
Findings
After analyzing the data, several components were revealed. These components were in
comparison to what was observed using the previous method of simply using timed tests with
100 problems. The components or themes that were observed were student engagement,
accountability, and improved recall of multiplication facts.
Student engagement was more prevalent in using Rocket Math. This was observed
through listening to students’ comments and seeing their reactions. When using the timed tests
from the previous methods, students would moan or complain when it was time to start. When
students saw their progress compared to other students, they would seem disappointed and in one
situation even emotional because of their self-concept. With Rocket Math, students were excited
when it was time to start. The fact that they were working with partners has been observed to be
a positive attribution to this fact. On one occasion Rocket Math had to be taken off the schedule
due to a half-day and more than half of the students were quite disappointed. Student
engagement was also evident in that classroom behavior was satisfactory. Each student was
engaged and therefore on task with what they were doing. The teacher walked around the room
and monitored. All that was observed was the recitation of multiplication facts, the monitoring
of the checker, or congratulatory praise for passing a level.
Accountability was also a result of this implementation. Students could not count using
their fingers to determine a math problem. This would cause delay and they would be forced to
restate the problem and answer three times. Having a partner who monitored such behaviors was
USING ROCKET MATH PROGRAM TO INCREASE RATE OF MULTIPLICATION
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also beneficial in accountability. Each student knew if they delayed or got the problem wrong
they would have to restate the problem. Even if students knew the answer and misspoke
themselves, it was still mandatory to follow the procedure. Accountability was also evident in
checking their classmates’ work. They needed to check each problem using the answer sheet and
reassure what was correct and not. If this process was not met it affected their partner. The
restating of the problems and answers also promoted accountability because as they did this it
helped aid in their memorization of that particular problem which is what the program promotes.
That last point leads into the final theme of the findings. The recollection of
multiplication facts was one of the desired purposes of this program. Students were using their
fingers to count up or singing a song in their head to find the answer of basic multiplication
problems when given the timed tests before Rocket Math was used. After a week of Rocket
Math, the students realized this was not possible to do and still be successful with this new
program. Students saw that memorizing the facts is what made them proceed to the next level.
The repetition of the multiplication facts that were stated incorrectly was evident in helping this
component. Another aspect was the fact that students had to state the problem and answer when
practicing. This method of stating the problem and answer allowed them to recall it when
performing the 1-minute timed test.
Discussion
The students involved in this research project were taught using creative methods to learn
their multiplication tables. As previously stated, songs and counting up were the ways in which
they learned their facts. This process may have been entertaining for them but had hindered their
ability to recall basic facts. Before Rocket Math, often times when solving a long division
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problem, students would take a long time to figure out what to multiply to figure out what goes
into the dividend. For some students they would give up and ask for help, use their
multiplication charts, or they would take 7 minutes on a 3-minute problem, which would delay
them for the remainder of the assignment. This was a major concern and therefore the push for
Rocket Math.
In reflecting on the findings and results, it was observed how Rocket Math did not allow
for the methods they were using prior. Students who still tried to use the older methods soon
realized this would hinder their progress. They were required to switch their mindsets from the
older methods to using basic recall or rote memorization. In implementing this switch in
mindset, their results were evident that this new way would produce more success.
When looking at the data on the progress chart, it was evident that students were
progressing at a faster rate compared to before. Prior to Rocket Math, students took a timed test
with 100 facts. They would have 5 minutes to finish. If they finished in 5 minutes and had no
errors, would move on to the next fact. All students started at 0 and moved on from there. Two
months into this system, it was evident what was happening. Two out of 27 students were on
their 7’s, and other small groups of students were staggered. The other evident fact was that at
least 9 students were still trying to accomplish their 3 times tables. If this program had
continued, some of those students never would have succeeded. The reason being that they were
given the daunting task of 100 problems. There was no practice time and therefore no new
teaching to take away from their old way of practice.
Then Rocket Math came into view and the teacher was able to teach math fact
recollection as well as students performing basic recollection because that is what the new
USING ROCKET MATH PROGRAM TO INCREASE RATE OF MULTIPLICATION
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program entailed. Students recited math problems repeatedly so it was engraved in their minds.
This carried over once they took a timed test that had 40 problems and which was based on their
ability to write down numbers. Rocket math provided the differentiation that the other did not.
In looking at the new set of data. Students were progressing at the same rate. The first
day all but 1 student passed to the next level and that was only because of student error in what
test she took. As time progressed students did pass at different rates but what was observed was
that it only took 1 or 2 days for a student to pass a level whereas the other program took weeks in
some cases.
Using this program will undoubtedly help the students involved. They are developing
necessary skills to help them with more complex problems. Knowing multiplication facts is a
building block for many higher order math concepts. Students need to be able to successfully
recall such facts at a quick rate in order to solve the multistep problems they learn later in fourth
grade as well as in later grades. The progress observed indicates their success in basic recall thus
far, which will carry over in their future math endeavors.
Not only has this helped the students but also helped the teacher as well. The practices of
the teacher will be to follow the methods Rocket Math entails. She will begin the first weeks of
school with using Rocket Math and will continue to implement it throughout the year. The
previous methods of counting up to determine facts will not be encouraged. Basic recall and rote
memorization will be the desired and supported method.
Conclusion
In moving forward with this research it is imperative that the behaviorist theory of rote
memorization be used with this topic. The question was whether Rocket Math would increase
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the rate and accuracy of recalling multiplication facts and thus far the results portray that answer
as positive. In order to produce more results, this study should be implemented in the grades
prior to fourth grade to provide an earlier foundation for such methods of practice.
Furthermore, Rocket Math should be implemented in first and second grade with addition
and subtraction so students at those grades are accustomed to basic recall and memorization.
Then as ideas expand and multiplication is taught, the multiplication facts should be added in
third grade and fourth grade. Fourth grade should also expand and use division facts.
When it comes to the teaching of these concepts, the meaning of addition, subtraction,
multiplication, and division should be taught first. After students have mastered what it means to
multiply two numbers or add two numbers, the basic recall should then be implemented. By
incorporating these methods at every grade from first through fourth will build successful
students who can master the complex problems in which involve higher order thinking skills and
multistep processes.
In reflecting on my practices I see that implementing a program such as this over halfway
through the year is a shift for the students, which is why, implementing it at the beginning of the
year would be the more beneficial option for my students. I also plan to use the division unit of
Rocket Math in my further implementation of this program. I also observed the benefits to using
it everyday. The more practice students have, the better they are with memorization. I now see
the errors in using the previous method of two days a week. Furthermore, what Rocket Math
does is, it focuses daily on two times tables so students are focusing on two areas verses one.
This helps with passing each level at a quicker rate. I am confident in the positive results Rocket
Math produced and will continue to use it in my future teaching practices.
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Ezbicki, K. E. (2008, May). The effects of a math-fact fluency intervention on
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Knowles, N. P. (2010, October). Automaticity drills practice. 1-82.
Martin, H. (2007, January). Mathematical literacy. Principal Leadership, (7), 1-5.
Oliver, K. K. (2010, March). A content analysis of educational music for teaching
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Saunders, D. J. (1995, September). New new math. National Review, 47(18), 1-2.
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Smith, C. R., Merchand-Martella, N. E., & Martella, R. C. (2011). Assessing the
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USING ROCKET MATH PROGRAM TO INCREASE RATE OF MULTIPLICATION
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USING ROCKET MATH PROGRAM TO INCREASE RATE OF MULTIPLICATION
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