Running Head: Comparison between Math Fluency and Achievement

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 1

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. 2

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 3

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 4

Overview 23 Discussion of Findings.23 Conclusions and Implications for School Policy..24 Recommendations for Further Study....24 REFERENCES..25 5

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 6

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 7

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. 8

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. 9

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). 10

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. 11

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, 12

US students ranked 24 th 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 13

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. 14

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 15

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 16

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. 17

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? 18

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 3 rd, 4 th, and 5 th 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. 19

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 20

M-COMP Scores Running Head: Comparison between Math Fluency and Achievement 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 35 30 25 20 15 10 5 0 0 200 400 600 800 MAP Scores Figure 1. Relationship between the MAP scores and the M-COMP scores taken from 106 students. Pearson s r=.557. 21

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 (r 2 =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. 22

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. 23

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. 24

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-factfluency.html Korn, A. (2011). Building calculation fluency. Retrieved on July 2, 2012 from http://eps.schoolspecialty.com/downloads/other/acadmath/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%20afte rschool%20program%20statistics/1/evaluation%20monitoring%20 Report%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-siunderstanding-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. 25

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. 26