COMPARISON BETWEEN STUDENT MATH FLUENCY AS … Kristina… · COMPARISON BETWEEN STUDENT MATH FLUENCY AS ASSESSED BY AIMSWEB MCOMP TEST AND GRADES 3, 4 & 5 STUDENT ACHIEVEMENT AS

Running Head: Comparison between Math Fluency and Achievement

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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


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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.


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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


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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


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Overview ………………………………………………………………23

Discussion of Findings ……………………………………………….23

Conclusions and Implications for School Policy …………………..24

Recommendations for Further Study …………………..…………..24

REFERENCES ………………………………………………………………..25


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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


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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


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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.


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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.


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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).


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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.


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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,


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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


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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.


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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


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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


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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.


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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?


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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.


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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’


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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


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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.


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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.


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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.


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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.

http://eps.schoolspecialty.com/downloads/other/acad-math/research_math_fluency.pdf

http://eps.schoolspecialty.com/downloads/other/acad-math/research_math_fluency.pdf

http://portal.kidscarecenter.com/sites/DESEPortal/Missouri%20Afterschool%20Program%20Statistics/1/Evaluation%20Monitoring%20Report%202009-2010.doc



http://dese.mo.gov/divimprove/assess/grade_level.html

http://rolla.k12.mo.us/fileadmin/rpsweb/home/Mark_Twain/teacher_files/TMadras/Parents_GuidetoMAP.pdf

http://rolla.k12.mo.us/fileadmin/rpsweb/home/Mark_Twain/teacher_files/TMadras/Parents_GuidetoMAP.pdf


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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.

http://www.scholastic.com/administrator/math/pdf/FM_White_Paper.pdf

http://www.scholastic.com/administrator/math/pdf/FM_White_Paper.pdf

http://www.ascd.org/publications/books/109097/chapters/What-Is-RTI-and-Why-Should-We-Care%C2%A2.aspx

http://www.ascd.org/publications/books/109097/chapters/What-Is-RTI-and-Why-Should-We-Care%C2%A2.aspx

Documents

COMPARISON BETWEEN STUDENT MATH FLUENCY AS … Kristina… · COMPARISON BETWEEN STUDENT MATH FLUENCY AS ASSESSED BY AIMSWEB MCOMP TEST AND GRADES 3, 4 & 5 STUDENT ACHIEVEMENT AS