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Running Head: Comparison between Math Fluency and Achievement
1
COMPARISON BETWEEN STUDENT MATH FLUENCY AS ASSESSED
BY AIMSWEB MCOMP TEST AND GRADES 3, 4 & 5 STUDENT ACHIEVEMENT AS MEASURED BY STATE ASSESSMENTS IN THE
STATE OF MISSOURI
By
KRISTINA RINARD
Submitted to
The Faculty of the Educational Specialist Program
Northwest Missouri State University Missouri
Department of Educational Leadership
College of Education and Human Services
Field Study Committee Members
Submitted in Fulfillment for the Requirements for
61-724 Field Study
November 28, 2012
Running Head: Comparison between Math Fluency and Achievement
2
ABSTRACT
Just as in most other states in the United States, educators in the state of
Missouri are eager to predict student outcomes on the state mandated
test, in this case the Missouri Assessment Program (MAP). Schools and
districts are anxious for students to perform at a proficient or advanced
level in both mathematics and reading. The more information they can
collate to tell them where their students are performing at the beginning of
the year, the more specialized and specific educators can be in their
instruction. Many schools have turned to private assessment and data
collection systems, like AimsWeb, to help them ascertain which students
are at risk for performing below the proficient level on the MAP. For this
study, individual student MAP scores were collected from the district as
well as individual scores on the AimsWeb Math Computational
Assessment. Research indicated that there is a moderate correlation
between students’ scores on the AimsWeb M-COMP assessments and
the MAP test.
Running Head: Comparison between Math Fluency and Achievement
3
TABLE OF CONTENTS
ACKNOWLEDGEMENTS ………………………………………………… 1
ABSTRACT …………………………………………………………………. 2
LIST OF TABLES
Table 1 Summary Statistics of Correlation Study …………..21
CHAPTER ONE: INTRODUCTION TO THE STUDY
Background …………………………………………………………..…6
Conceptual Underpinnings for the Study ………………………...…..7
Statement of the Problem ………………………………………..……8
Purpose of Study …………………………………………………….....9
Research Questions ……………………………………………………9
Null Hypotheses ……………………………………………………......9
Anticipated Benefits of Study ………………………………………….9
Limitations of the Study………………………………………………10
Definitions of Terms……………………………………………..........10
Summary ……………………………………………………………….11
CHAPTER TWO: REVIEW OF RELATED LITERATURE
Running Head: Comparison between Math Fluency and Achievement
4
Introduction ……………………………………………………………12
Importance of Effective Math Instruction……………………………12
Fluency as an Important Math Component………………………...13
Best Practices in Math Fluency Instruction…………………………14
Summary ………………………………………………………………16
CHAPTER THREE: RESEARCH DESIGN AND METHODOLOGY
Problem and Purposes Overview …………………………………...18
Research Questions ……………………………………………….…18
Study Group …………………………………………………………...19
Data Collection and Instrumentation ………………………………..19
Statistical Analysis Methods to Be Used …………………………...20
Findings ………………………………………………………………..20
Presentation of Data Analysis ……………………………………….20
Summary ……………………………………………………………….20
CHAPTER FOUR: OVERVIEW, FINDINGS, CONCLUSIONS AND
RECOMMENDATIONS
Running Head: Comparison between Math Fluency and Achievement
5
Overview ………………………………………………………………23
Discussion of Findings ……………………………………………….23
Conclusions and Implications for School Policy …………………..24
Recommendations for Further Study …………………..…………..24
REFERENCES ………………………………………………………………..25
Running Head: Comparison between Math Fluency and Achievement
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CHAPTER ONE
INTRODUCTION TO THE STUDY
Background
The Missouri Assessment Program, well-known as the MAP,
“was created in response to Missouri’s Outstanding Schools Act of 1993”
(Practical Parenting Partnership, 2006). Since the No Child Left Behind
Act passed in 2001, its importance has increased a great deal. All public
school children in Missouri are required to take the assessment.
MAP scores provide information about what individual
students know and can do relative to the Show-Me
Standards. For individual students, DESE and CTB report a
MAP scale score, a MAP achievement level, and a Terra
Nova national percentile (Missouri Afterschool Programs,
2009).
This study will address the individual scale score of the students
involved. It is certainly important for teachers to have the tools needed to
understand poor math performance better (Rutherford-Becker &
Vanderwood, 2009). It has been found that math assessments measuring
Running Head: Comparison between Math Fluency and Achievement
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the math computation skills of students is “strongly correlated to how well
students do on applied math assessments” (2009). This study will also
look at individual student scores on AimsWeb Math Computational (M-
COMP) scores. M-COMP is defined by AimsWeb as a test that “assesses
basic computational skills” (Using AimsWeb, 2011). This study will look at
each of these individual scores—the MAP scale score and the M-COMP—
to determine if between these scores there is a significant correlation.
Conceptual Underpinnings for the Study
It would be very valuable for educators to have the tools to predict
student achievement on the MAP early on and throughout the school year.
Schools have access to students’ scores from the previous year (and from
the years preceding). However, since students progress as the year
continues, they could fall behind during the new school year. It is even
possible that they could experience negative gains during the summer
break. Simply looking at a once-a-year exam cannot be enough to guide
the kind of specific instruction that students need. By finding an
assessment that can continually and accurately assess where students are
in their math fluency, teachers and administrators can adjust their teaching
to be specific and individualized. They can group students according to
their needs, and change these groups on a weekly, monthly, or quarterly
Running Head: Comparison between Math Fluency and Achievement
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basis. In addition to this, knowing if there is a correlation between math fact
fluency and students achievement on the MAP will help teachers focus
instruction in the most effective way.
Statement of the Problem
Since No Child Left Behind passed, schools are required to show
they are in constant improvement. They cannot afford to sit idle hoping for
the best from the Missouri state assessment. There needs to be a way to
monitor student, teacher, and school achievement during the year. One
way some schools are already doing this is through Response to
Intervention (RTI). “RTI is a systematic way of connecting instructional
components that are already in place. It integrates assessment data and
resources efficiently to provide more support options for every type of
learner” (Searle, 2010). In the first step of RTI teachers use constant data
collection to group and monitor students according to level. In order for this
to be effective, teachers and schools need to be sure the data collection
they are using truly works. If students’ success is measured in terms of
their scores on the MAP (which is currently the case in Missouri public
schools), then teachers and districts need a tool that will measure student
success-rate throughout the school year.
Running Head: Comparison between Math Fluency and Achievement
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Purpose of Study
The purpose of the study is to determine if there is a relationship
between AimsWeb M-COMP scores and the MAP Assessment.
Research Questions
RQ1: What are the summary statistics for the third, fourth and fifth grade
scores on the M-COMP and Missouri Assessment Program?
RQ2: What is the correlation between student scores on AimsWeb M-
COMP and MAP?
Null Hypotheses
Ho 2. There is no correlation between AimsWeb M-COMP scores and the
Missouri Assessment Program.
Anticipated Benefits of Study
The benefit of the study will be to verify the use of AimsWeb testing
as a year-long monitoring device of student achievement and as a
predictor of students’ scores on the MAP. Teachers can focus instruction
on fluency if there is a correlation or focus instruction in other areas if there
is no correlation.
Running Head: Comparison between Math Fluency and Achievement
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Limitations of the Study
The findings of the study are limited to elementary schools in the
state of Missouri as well to teachers of mathematics in grades 3, 4, and 5.
It could also be limited somewhat to users of AimsWeb; however this study
may encourage administrators of other districts and schools not currently
using AimsWeb to begin, if the null hypothesis is rejected.
Definition of Terms
MAP: Missouri Assessment Program “assesses students’ progress toward
mastery of the Show-Me Standards which are the educational standards in
Missouri” (About the Assessment, 2011).
AYP: Annual Yearly Progress is the percentage of students in a school and
school district that must make either Proficient or Advanced on the state
standardized test.
AimsWeb: “AimsWeb is a web-based assessment, data management, and
reporting system that provides the framework for Response to Intervention
(RTI) and multi-tiered instruction” (Using AimsWeb, 2011).
Running Head: Comparison between Math Fluency and Achievement
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M-COMP: Math Computation is an assessment within AimsWeb that
measures students’ proficiency at basic computational skills.
Public School Choice- Part of a school improvement plan that allows
students who are enrolled at a school which has not met AYP for at least
two years enroll at another school of the parents’ choice within that district
at the cost of the district.
Advanced: The highest of four score levels on the MAP.
Proficient: The second highest of four score levels on the MAP. Schools are
required to improve the amount of students receiving either proficient or
advanced each year.
Basic and Below Basic: The two lowest levels of the four score levels on
the MAP.
Summary
This study will establish the connection between math fluency and
performance on the MAP in elementary schools in the state of Missouri.
Running Head: Comparison between Math Fluency and Achievement
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CHAPTER TWO
REVIEW OF LITERATURE
Introduction
There has been much research done in the area of student
achievement in mathematics. Some evaluate the meaning of a student’s
basic math fact fluency. Some studies evaluate what is the best way to
teach math fluency. Some studies focus on certain programs and others on
students with special needs. In addition to the research done on math fact
fluency, there has also been a lot written on state standardized testing and
meeting AYP. The research done on math fact fluency has an effect for
classroom teachers. With the stakes of meeting AYP driving them, all
educators need to focus instruction on best practices.
Importance of Effective Math Instruction
By nature, teachers have the desire to provide the best instruction
for their students. So the question remains as to why we are still performing
lower than our international friends:
U.S. fourth graders perform poorly, middle school students
worse and high school students are unable to compete. In
the 2006 Program for International Students Assessment,
Running Head: Comparison between Math Fluency and Achievement
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US students ranked… 24th out of 30 in math. (Arroyo, Royer,
& Woolf 2011)
Smith, Marchand-Martella & Martella (2011) report that “(NAEP) reported
fewer than 30% of students in grades 8 and 12 achieved proficiency in
mathematics.” This is alarming for citizens of the United States and
especially frustrating for educators. There is a great need for this country
to find instruction that works for its students. School districts also have a
vested interested in competing here at home. Schools’ AYP reports are
published in the media. If a school fails to make AYP two years in a row,
they begin an ominous school improvement plan. In this plan, they must
contact all parents to inform them of their failure to meet AYP, offer Public
School Choice, and go through a list of five other requirements that
involve accountability to the state and parents (Missouri Department of
Education, 2011). To say the least, that is not a position a district wants to
find itself in. So the question remains as to why, when there is so much
motivation to do well, students still are not making the grade.
Fluency as an Important Math Component
Teachers and students know that they need to succeed in
mathematics at a higher level. Fluency is an issue that most educators
Running Head: Comparison between Math Fluency and Achievement
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agree is important. Math fluency is defined as “the ability to quickly and
accurately perform arithmetic problems” (Korn, 2011). It is hardly argued
that fluency in mathematics is not needed to achieve at high levels. Arroyo
et al. (2011) states “computational fluency is a construct that has been
shown to be related to mathematics achievement.” Smith et al. (2011) tell
us how important fluency is. They say it is “essential for the success of
students in primary education because it serves as a foundation for
mathematical applications.” It makes a great deal of sense that a student
would do better when he or she is fluent in basic math facts. It is then that
the student will be able to focus his or her attention on solving the more
difficult parts of problems. Having a solid foundation for math will carry a
student far. Being fluent at those foundational skills will allow the student to
maintain a higher level of success.
Best Practices in Math Fluency Instruction
There are many studies done on the best ways to teach math fact
fluency. Teachers are barraged with programs and texts and computer
software that offer some great options for students. It is important for
teachers and administrators to pay attention to the research that is
available to make the best choices when presenting them to their students.
Running Head: Comparison between Math Fluency and Achievement
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Scholastic Research and Results (2005) states that there are two
classifications of math fact knowledge. The first is declarative knowledge,
which is how strong the student’s relationship is to each math fact. If one
has a stronger relationship with a fact it will take less time for him or her to
retrieve the answer. The second classification of math fact knowledge is
procedural knowledge. This is what students who lack the strong
relationship with the math facts use. It is the process that students can go
through to figure out that answer. To be effective, teachers should teach to
both of these classifications, according to this study. The study found that
Scholastic FASST Math was a sound way to help students achieve both
types of math fact connection.
Frawley (2012) reports a meta-analysis done on the issue of math
fact fluency. Frawley’s article shares three strategies that are effective ways
to teach math fact fluency. The first is “Taped Problem Intervention” in
which students use audio recordings of basic math facts. Students use the
recording and try to answer more quickly that the voice they are listening to.
The second strategy that Frawley suggests is “Copy, Cover, Compare.” In
this model, students study a list of problems. They then cover the answers
up and try to answer them. Finally, the student uncovers the answers and
compares the two numbers. He or she fixes any errors and repeats. The
last strategy suggested is “Incremental Rehearsal.” While completing this
Running Head: Comparison between Math Fluency and Achievement
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activity, students are given flashcards with facts that they know and one
flashcard with a fact they don’t know. They work until these until the one
they don’t know becomes familiar. Then they repeat the activity. According
to their research, these strategies are helpful in student gaining math fact
fluency.
In the study done by Smith et al. (2011), Rocket Math Program was
tested for effectiveness with high risk students in an elementary school
setting. It was found by this study that these students improved at a faster
rate than their peers. Rocket Math, according to this study, is another
program to use in teaching students to become fluent in basic math facts.
Summary
There are several ways that are effective in teaching math fact
fluency. The fact remains that it is an important issue for educators to
acknowledge. Without a fluent background, kids struggle with the higher
level math concepts. When students become fluent in the basic math facts,
they are more easily able to focus on the complex structures of what comes
next in mathematics. Teachers and administrators more than enough
reasons to find ways to assess their students understanding of math fact
fluency. The stakes are higher than ever. What should be the most
important stake, the learning of young people, is now taking a back seat as
Running Head: Comparison between Math Fluency and Achievement
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our country focuses on the legislation that is now driving our schools. In
order to remain in funding, schools need to meet AYP. One way they can
do this is by assessing kids’ knowledge throughout the year so they can
pinpoint instruction in a prescribed way.
Running Head: Comparison between Math Fluency and Achievement
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CHAPTER THREE
RESEARCH DESIGN AND METHODOLOGY
Problem and Purposes Overview
School districts are expected to show growth in all areas of the
MAP, including mathematics. Time is of the essence in the classroom. If
teachers are wasting time with the wrong focus or the wrong instruction,
students will not improve as rapidly as a district would like. Even worse, if
teachers are using a less effective strategy, students might regress. It’s
important to use data to determine what the best practices are in the
classroom. The purpose of this study is to determine if a student’s fluency
on basic math facts and concepts has a causal relationship with their score
on the MAP.
Research Questions:
RQ1: What are the summary statistics for the third, fourth and fifth grade
scores on the M-CAP, M-Comp and Missouri Assessment Program?
RQ2: What is the correlation between student scores on AimsWeb M-CAP
and MAP and M-Comp and MAP?
Running Head: Comparison between Math Fluency and Achievement
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Ho2: There is no correlation between students’ AimsWeb scores and the
MAP.
Study Group
Students in this study were taken from a Missouri public elementary
school. This group consists of boys and girls in grades 3-8. The students’
MAP scores were recorded in addition to their AimsWeb, M-CAP, and M-
COMP scores. Students who were not present the previous year or who
had left the year the data was collected were not counted. The study group
consisted of 106 students.
Data Collection and Instrumentation
The data were collected from an elementary school in Missouri.
The individual MAP scores were collected from a list of individual scores
given to the school. The M-Comp scores were collected from the AimsWeb
reporting data spreadsheets that AimsWeb has available on the website as
part of its program. The scores were pulled from 3rd, 4th, and 5th grade
students during the 2010-2011 school year. Any student that left before the
data was collected during the 2011-2012 school year had their data
removed. Any students that were enrolled in the 2011-2012 school year
but had not been enrolled previously were not included. In all, there were
106 students whose data was included in this study.
Running Head: Comparison between Math Fluency and Achievement
20
Statistical Analysis Methods to be Used
Research design began with reporting summary statistics for
students’ scores on AimsWeb M-CAP and students’ scores on the MAP.
The mean and standard deviation were figured for these numbers. A
Pearson product-moment correlation coefficient was calculated to
measure the relationship between students’ scores on AimsWeb M-COMP
and the MAP. There was a slight positive correlation between the two
variables, r = 0.557, n = 106, p = 0.000. A scatterplot summarizes the
results (Figure 1). There was a positive correlation how well students do
on the AimsWeb assessment measuring students’ math fact fluency and
how successful students are on the MAP. Increases math fact fluency is
coordinated with high scores on the MAP. The Alpha level chosen to
reject the null hypothesis was 0.25.
Findings
The summary statistics for research question one are recounted in
the results for question two.
Research Questions 1 & 2. A presented in Table 1, a Pearson
correlation was figured exploring the connection between the students’
Running Head: Comparison between Math Fluency and Achievement
21
scores on AimsWeb M-COMP tests and the MAP. A moderate positive
significant correlation found (r=0.557, p= .000) between the two sets of
students’ scores. The scores that students receive in testing their basic
math fact knowledge on the AimsWeb M-COMP assessment are related
to the scores students receive on the math portion of the MAP
assessment, therefore the null hypothesis is rejected.
Table 1
Summary Statistics of Correlation Study
Source N Mean SD R
MAP Scores 106 623.76 36.37 .557
M-CAP Scores 106 15.11 5.68 .557
*Note: significant =<0.1
Figure 1. Relationship between the MAP scores and the M-COMP scores
taken from 106 students. Pearson’s r=.557.
0
5
10
15
20
25
30
35
0 200 400 600 800
M-C
OM
P S
core
s
MAP Scores
Running Head: Comparison between Math Fluency and Achievement
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Presentation of the Data Analysis
The data show that there is moderate positive correlations
(r=0.557) between the students’ scores on the math MAP test and their
scores on the M-CAP assessment. There is a significant correlation
(p=0.00) and reasonable (r2=31%).
Summary of findings
In this study, it was found that there was a moderate positive
correlation between how students score on the math MAP test and how
they score on the AimsWeb M-CAP assessment. The null hypothesis was
rejected in this study.
Running Head: Comparison between Math Fluency and Achievement
23
CHAPTER FOUR
OVERVIEW, FINDINGS, CONCLUSIONS, AND RECOMMENDATIONS
Overview
Because of the No Child Left Behind legislation and the higher
stakes for to make the grade on standardized tests, schools need a way to
monitor their students as the year progresses. Student achievement is
being monitored by entities much greater than the classroom teacher. It is
a different playing field. Companies are popping up all over claiming that
they can predict student achievement on standardized tests such as the
MAP. This study’s findings will aid districts and school in pinpointing a
program that will effectively monitor their students.
Discussion of Findings
It is statistically significant that the AimsWeb test can moderately
predict students’ scores on the Math MAP. I think it is more important,
however, that success on the MAP is affected by basic math fact fluency.
This can guide schools in their decision making when deciding what to
assess during the year and what to have teachers focus their instruction
on.
Running Head: Comparison between Math Fluency and Achievement
24
Conclusions and Implications for School Policy
Schools all over are looking for ways to measure student progress
in order to implement RTI. It’s important to base the assessment
measures used on research and proven methods. AimsWeb M-CAP tests
effectively measure how well students do on the MAP. This study also
shows that student mastery on basic math facts affects performance on
the MAP. This information will aid schools in the tough decisions they
need to make on if they should spend time on math fact fluency instruction
and how they should assess math fact fluency.
Recommendations for Further Study
By looking at the data, it is clear that there need to be some further
study on the matter of data collection and math fact fluency. The first
recommendation is for other AimsWeb to be analyzed to consider their
effectiveness. It is also recommended that the assessments within
AimsWeb are compared with each other as well as compared with other
ongoing assessments of a similar type. In following these
recommendations, schools would be sure to have the data and
information available to choose the best assessment of math fact fluency
for their students.
Running Head: Comparison between Math Fluency and Achievement
25
References
Arroyo, I., Royer, J., Woolf, B. (2011). Using an intelligent tutor and math fluency training to improve math performance. International Journal of Artificial Intelligence in America, 21, 135-152
Frawley, C. (2012). Developing math fact fluency. Innovations and
Perspectives. Retrieved June 10, 2012 from http://www.ttacnews.vcu.edu/2012/02/developing-math-fact-fluency.html
Korn, A. (2011). Building calculation fluency. Retrieved on July 2, 2012
from http://eps.schoolspecialty.com/downloads/other/acad-math/research_math_fluency.pdf
Missouri After School Programs. (2009). Missouri baseline evaluation
data. Retrieved on June 10 from http://portal.kidscarecenter.com/sites/DESEPortal/Missouri%20Afterschool%20Program%20Statistics/1/Evaluation%20Monitoring%20Report%202009-2010.doc
Missouri Department of Education. (2011). About the assessment.
Retrieved on June 14, 2012 from http://dese.mo.gov/divimprove/assess/grade_level.html
Missouri Department of Education. (2011). Understanding your adequate
yearly progress [brochure]. Retrieved on May 11, 2012 from http://dese.mo.gov/divimprove/sia/dar/documents/qs-si-understanding-your-ayp.pdf
Practical Parenting Partnerships. (2006). A parent’s guide to the MAP
[Brochure]. Retrieved June 10, 2012 from http://rolla.k12.mo.us/fileadmin/rpsweb/home/Mark_Twain/teacher_files/TMadras/Parents_GuidetoMAP.pdf
Rutherford-Becker, K., & Vanderwood, M. (2009). Evaluation of the
relationship between literacy and mathematics skills as assessed by curriculum-based measures. California School Psychologist, 14, 23-34.
Running Head: Comparison between Math Fluency and Achievement
26
Scholastic Research and Results. (2005). Research foundation and
evidence of effectiveness for FASST math. Retrieved June 12, 2012 from http://www.scholastic.com/administrator/math/pdf/FM_White_Paper.pdf
Searle, M. (2010). What every school leader needs to know about RTI.
Retrieved on May 12, 2012 from http://www.ascd.org/publications/books/109097/chapters/What-Is-RTI-and-Why-Should-We-Care%C2%A2.aspx
Smith, C., Marchand-Martella, N., & Martella R. (2011). Assessing the
effects of the rocket math program with a primary elementary school student at risk for school failure: A case study. Education and Treatment of Children. 247-258.