Brain_Gym_08

Team Research Design Project Annie, Gerri, Lydia, Heather** __CLASS SIZE__
 * __EDC 529__

1. __Introduction:__ ** The issue of class size is one that continues to be in the spotlight after many decades of exploration and debate. Parents are concerned about the quality of instruction their child receives while districts must be mindful of the expense of such a reform when budgets are tight. Many teachers affirm that smaller classes are easier to manage and provide more opportunity to build close relationships with students that enhance learning. Phrases drawn from abstracts for a number of studies help capture the controversy that continues to circle around the topic of class size: “inconclusive findings”, “vociferous debate”, “inconsistent findings” and “ambiguous”, to list a few. Our group chose to investigate this reform and its potential effects on math achievement in a Rhode Island since none of the research we reviewed had taken place in a New England state.

Is there a statistically significant difference in math performance, as measured by the NECAP math assessment test, between third grade students who have spent grades K-2 in classes with 15 students or less and third grade students who have spent grades K-2 in classes with 20 students or more? //__Independent Variable__//: Third graders who have remained in a class size of 15 students or less from K-2nd grade. ** Easier just to say 'class size' ** //__Dependent Variable__//: Math achievement as measured by NECAP math assessment.
 * __Research Question__**:

2. **__Hypotheses__**: //Null hypothesis:// There will be no difference in the NECAP math scores of third grade students in classes with 15 students or less and the NECAP math scores of third grade students in classes of 20 students or more.

N//on-directional hypothesis:// There will be a difference in the math state assesssment scores of third graders who have spent grades K-2 in classes with 15 students or less and the math state assessment scores of third graders who have spent grades K-2 in classes with more than 20 students.

D//irectional hypothesis:// Third grade students who have spent grades K-2 in a class with15 students or less will score significantly higher on the NECAP math assessment than the third grade students who spent grades K-2 in a class with more than 20 students.

A number of large-scale studies have explored class size and its impact on student’s academic performance in elementary settings. In Indiana, a state-supported program called PRIME TIME investigated student learning in its rural schools by reducing class size in kindergarten through third grade. As part of the PRIME TIME program, classes were reduced to 15 to 22 students during the 1984-1985 school year. Subjects were first graders enrolled in rural schools in western Indiana . Student scores from the Iowa Test of Basic Skills, Stanford Achievement Test, Metropolitan Achievement Tests, Gates MacGinitie Reading Test, Art is Fundamental, and locally prepared basic skills tests were analyzed to see if differences existed between classes before and after the introduction of Project PRIME TIME. It was found that state sponsored programs to reduce class size can increase student achievement and teacher efficiency in primary grades (Gilman & Antes, 1985). In Project PRIME TIME, (1) students in smaller classes scored higher on standardized tests than did those in larger classes, (2) the smaller classes had fewer behavioral problems, and (3) teachers of smaller classes reported themselves as more productive and efficient than they were when they taught larger classes as reported by Bains and Achilles in 1986 (as cited in Mosteller, 1995). While results from this project are overwhelmingly in favor of smaller class sizes, they need to be considered with caution due to a number of flaws in the pilot study. Teachers were carefully chosen, and publicity surrounding the study caused teacher expectation to be high, thereby producing a reactive effect that contributed to high post test scores. Although several variables were measured, only those producing significant results in favor of PRIME TIME were reported. The study also had not been done on a uniform basis. For example, some teachers were given strategies on small class instruction while others were not. In some communities the program did not reduce class size. Furthermore, some schools had hired teachers with experience and other schools hired beginning teachers for PRIME TIME. Teachers were informed that student achievement was expected for this program. Some teachers were told of evaluative studies to be done at the end of the year, while others were not (Gilman & Antes, 1985).
 * __3. Literature Review__**

Tennessee was mindful of the study of small class size done in nearby Indiana and the promising benefits, but also knew of the costs associated with more classrooms and more teachers. They also knew of the quantitative method called meta-analysis done in the Glass study that suggested class size of 15 or fewer would be needed to make a noticeable improvement in classroom performance (Glass et al, 1982, as cited in Nye, Achilles, Boyd-Zaharias, Fulton, and Wallenhorst, 1992). Consequently, Tennessee performed its own study called Student-Teacher Achievement Ratio (Project STAR). It was a four year study (1985-1989) that examined student achievement in Kindergarten through third- grade in smaller classrooms with 13 to 17 students compared to regular classrooms with 22 to 25 students with only one teacher in the room and to regular classrooms with a paid aide to assist the teacher in the room. The Tennessee study found math and reading scores up about one-fourth of a standard deviation, which meant that a student could move from the 50th percentile to the 60th percentile, surpassing an additional 10th of the student population. The average of the four tests showed an effect size for minorities that was about double that for other students (Mosteller, 1995).

A three-year follow-up observation (1989-1992) called the Lasting Benefits Study (LBS) was conducted to find out whether the benefits of small class size in primary grades could last when the students are placed in regular-sized classrooms in fourth, fifth, sixth, and later grades (Nye, 1992). In fourth and fifth grades, the children who had originally been in small classes scored higher than those who had been in regular-sized classes or in regular-sized classes with a teacher’s aide. In the fourth grade the effect size was about one-eighth of a standard deviation, and in the fifth grade, it was nearly two-tenths of a standard deviation averaged across six subjects. Observed gain, however, was somewhat larger for fifth grade. Smaller class size seems to have had a continued effect beyond the moment when the children returned to regular-sized classes (Nye, 1992). A large study in 2005 examined data for over 5000 students, followed over a period of thirteen years, who had been a part of the original STAR project with a particular focus on high school graduation rates (Finn, Gerber, & Boyd-Zaharias). The researchers found that small classes in the early grades had a positive long-term impact on graduation rates. In particular, those students who spent 4 years in a small class had 80% higher odds of graduating, especially low SES students.

A number of other follow-up studies have been conducted in recent years using data from project STAR to further explore the effects of small class size from a variety of perspectives. In his research, Konstantopoulos (2008) used data from the Tennessee project to explore the effects of small class size on narrowing the achievement gap between low- and high- achievers in grades K-3. Although he concurred that // all // students benefit academically from smaller classes, especially in kindergarten and first grade, he found that small class size does not reduce the achievement gap—and high achieving students may benefit even more than their counterparts. It is important to note that Konstantopoulos is not suggesting that lower-achieving children will do better in larger classes—since like all students in the study, their overall academic performance did improve.

LBS was followed by the implementation of Project Challenge in 17 Tennessee school districts as a result of the small class size benefits. The districts were chosen with the lowest per capita income and the highest percentage of free or reduced-price lunch participation among students. Before the project was introduced, these districts had been performing well below the average in the state for math, and had moved to above average after the project. In school districts where small classes were implemented in kindergarten, first, second, and third grades, both the reading scores and the math scores improved, compared with previous performance by children in these districts and with other schools in the state (Nye et al, 1992). The experiment showed that minority groups gained more than other groups in the first two years and that the gain tapered off in later years.

Other studies on reduced class size look beyond achievement alone to other factors that impact successful implementation of this reform. n Wisconsin, the extensive SAGE reform targeted high-poverty schools and focused on class size reduction. A qualitative study using SAGE data focused on nine high-poverty (rural, urban, and suburban) schools (Graue, Hatch, Rao & Oen, 2007). The researchers examined two paradigms of class size reduction: a student / teacher ratio of 15:1 and 30:2. While teachers reported a strong preference for smaller class size, most had little to no professional development to prepare them: “The error is in assuming that teachers can navigate that space without any guidance” (p. 40). When two teachers were assigned to a larger class (30:2), the most prevalent technique was “tag team teaching” (p. 28) where one teacher was delivering instruction while the other was doing clerical work, disciplining, or supporting rather than a true co-teaching model. One strong argument of these findings is that teachers need professional development to fully take advantage of potential instructional opportunities inherent in either paradigm. In their 2008 review of both cost-benefit analysis and experimental analysis of class size, Januska and Dixon-Krauss found that “the importance of teacher quality “ (p. 4) was the one factor that both perspectives agreed upon. Like Graue and colleagues, they stressed the need for focused teacher training to maximize the potential of small class size settings. A study in the UK combining both qualitative and quantitative data using a large sample of slightly older children (aged 7-11) focused on teaching approaches in small and large classes. The researchers concluded that in smaller classes teaching is more individualized, students tend to actively interact with their teachers rather than being more passive, and teachers are more able to effectively handle discipline issues. Interestingly, they also found that whole class teaching is still prevalent, even in small classes, and that teachers need to further explore collaborative group work and other strategies (Blatchford, Russell, Bassett, Brown & Clare, 2005). Compelling evidence that smaller classes help, at least in early grades, and that the benefits derived from these smaller classes persist, leaves open the possibility that additional or different educational strategies could lead to still further gains (Mosteller, 1995).

4. **__Sample__**: This study will evaluate the NECAP mathematical scores of entering 3rd grade students from two suburban schools located in Get Out, RI. A population of 186 students entering third grade included 65 students from Marcus Garvey Elementary school (MGE) and 121 students from Peter Pan Elementary school (PPE). From the total population, we selected 75 third grade students via stratified random sample based, upon gender, demographics, and K-2 school consistency. Therefore, all participants in this study are new 3rd graders, have progressed in the same schools and district since kindergarten, and have just recently taken the NECAP mathematical assessment. Of the 75 participants, our study will compare the mathematical tests scores of a total of 41 male and 34 female students who were in classes of fifteen (15) or less to those students who were in classes of at least sixteen, but no more than twenty-five students.

The 3rd grade students attending Marcus Garvey Elementary (MGE) school are our control group. The 3rd grade students at Peter Pan Elementary (PPE) school are our experimental group.

For the purpose of this study, all variables except class size are equivalent. Demographics; race, gender, age, grade level, SES, group instruction, along with resources and assessments are all equivalent. Over two full academic school years, 75 subjects from our two schools, who progressed from K-2 were randomly assigned to mathematical classes. The participants, have been with permission of their parents, randomly assigned to one of the two classes at each of the schools. At MGE our 27 subjects were placed in one of two mathematical instruction classes comprised of either twelve or fifteen students per class. At PPE our 48 subjects were placed in one of two mathematical instruction classes comprised of twenty-three or twenty-five students per class. The students will be observed on how they appear to demonstrate ability and performance as a result of incremental embedded assessment. The study participants in these classes work at appointed stations, which rotate within the class according to: 1) mathematical problem solving, 2) mathematical reasoning, 3) data analysis, patterns, trends, distributions and predictions. Each station also employs the use of manipulatives.

The NECAP mathematical assessment is given to elementary school students who have been promoted from the 2nd grade and are now entering the 3rd grade level.

//Experimental Design:// Quantitative, Stratified Random Sample.

R X O R C O R= Random Sampling (stratified) ** Remember, this means random assignment to groups ** X= K-2 Math classes with more than 16 students C= K-2 Math classes with 15 students or less O= NECAP Math Assessment Test


 * This is an interesting situation, in that I'm not sure you could call one or the other a control group. My inclination is to assume that 20 or more students is the standard class size, which would make it more suited to the label 'control' **

5. **__Data Collection__**: This is a quantitative study that used the NECAP standardized mathematical assessment as the instrument. The NECAP mathematical assessment is an instrument that has been used throughtout the state and has undergone years of rigorous testing that measure instrumentation reliability. Based on the data obtained through this assessment we will be able to determine whether there is a statistically significant difference in students improved mathematical proficiency as it correlates with class size.

The study will examine two programs and a control group-classes of 15 or fewer geared towards improved math scores; classes of 16 or more students geared toward improved math scores; and control groups where preparation for the math exam is not a priority.

This study seeks to investigate the relationship between small class size and improved mathematical proficiency. Therefore, our data analysis will use a correlational coefficient to describe whether the relationship is positive or negative. The correlational coefficient will further determine for this study the strength of the trend. Also, by prforming a simple t-test, the mean scores of the two samples can be compared and the value of t will state whether the null hypothesis is accepted or rejected. A t-test will look at the scores of the same group of children over a period of time.
 * 6. __Data Analysis__:**

Correlation, however, does not imply causation, as we have allowed for other factors that might impact higher scores for the students in smaller classes; lower scores for the students in smaller classes; higher scores for the students in larger class and lower scores for the students in larger classes. These other factors include, but are not limited to the student's access to study time outside of school; the support structure of each student; the environment that each student goes to afterschool; history (negative or positive) that each student has in his or her educational history; attention deficit issues; access to health care and learning ability assessment and relationship with teachers and other faculty. ** This is a tricky element in your study. Ideally, the impact of these other variables should be minimized if the groups are equivalent. **


 * 7. __Validity and Reliability__:**

__Threats to Internal Validity__: One threat to internal validity is __history__ because some students might have attended a Pre-school program with a larger or smaller class size that doesn't correlate with the group they were placed with for grades K-2 as part of the study. Another effect history could have on the study is that students who transfer to the school district after the start of the study will be randomly placed in either the control group or the treatment group with no knowledge of the class size at thier previous school. However, by doing stratified random sampling this threat to validity is reduced because it controls for including those students who have not from grades K-2 been consistently attending the two schools used in our study.

__Mortality__ is another threat to the internal validity of this study because students might move out of the district at any point during the study. This threat could be reduced because the rates of mortality in the control group and the treatment group should be relatively equal.

Another threat to the internal validity is __maturation__ that is unrelated to the treatment. Students in either group could be receiving extra math assistance either at home or through an extra-curricular program. Additionally, as children grow they often exhibit differences in their developmental processes. This threat could be reduced because both the control group and the treatment group were selected from the same school district so the families and extra-curricular involvement should be similar in both groups. Furthermore, by doing random assignment to groups, both the control group and the experimental groups should mature at the same pace.

__Threats to External Validity__: __Selection Bias__ could have possibly been a threat to the external validity of this study had this research team not utilized random sampling in participant selection. By using stratified random sampling this threat to external validity was removed.

A second threat to the external validity of this study is __researcher expectancy,__ because the educators in the treatment classrooms are aware of the potential effects that smaller class size could have on the NECAP test scores. This could cause educators of the treatment group to spend more time on mathematics during the school day as compared to the control group educators, because their students are expected to perform better on the NECAP assessment tests. One way to reduce this threat would be to keep the researchers blind to which group of students is the treatment group.

__Obtrusiveness and reactivity__ could also threaten the external validity of the study through the desire for treatment and the rivalry between experimental and control groups. This threat is reduced by obtaining parental permission for students to participate in the study in either the control group or the treatment group based upon which elementary school the child attends. The threat of rivalry can be reduced by assuming that all the educators involved in this study are aware of the biases that exist surrounding smaller class size. Therefore, all educators involved in the study are assumed to be teaching the mathematic curriculum using the same text, lessons, and manipulatives with the same amount of time per school day devoted to mathematic instruction.

8. __**Strength of design**__: A major strength to our research design was the use of a control group and the use of random stratified sampling. The control group enabled us to reduce many threats to both the external and internal validity of the study. The control group specifically helped to reduce the threats of history, mortality, and maturation as mentioned earlier in the validity section of the research design.

The use of random sampling provided us an unbiased sample for both the control group and the experimental group that were equivalent based on gender, race, age, grade level, SES, group instruction, and assessment. The use of random sampling also helped to reduce the threat of selection bias to the external validity of this study.

Another strength of our research design is that both the control group and the experimental group were taken from the same school district in Get Out, RI which enabled us to ensure that the educators in both groups were using the same mathematics curriculum, manipulatives, and assessments. Also all the educators in this study were devoting the same amount of time per day to mathematics instruction, leaving the class size as the only variable that differed between the control group and the experimental group.

The main weakness of our research design was the size and location of our sample group. Our study only sampled from one school district within the state of Rhode Island. Although a small state, Rhode Island has a diverse population of cultures and socio-economic status that vary across different school districts. All school districts in the state and country are made up of vastly different populations so it is therefore difficult to generalize our findings to all schools throughout the United States.

A qualitative study concerning class size that perhaps followed groups of students throughout an academic year or several years prior to taking the NECAP assessment test would be an interesting comparison to the quantitative research that has already been done. A qualitative researcher would have a much more in depth view of the effect that mathematics instruction in a smaller class setting as opposed to the instruction in an average class setting has on student achievement in mathematics.

A furthur quantitative study could possibly investigate the relationship between teachers that receive additional professional development training in the teaching of mathematics to use in classrooms with smaller class size as opposed to teachers that are teaching the same mathematics curriculum to a classroom with an average class size. This could possibly be investigated by studying a charter school that has smaller class sizes across all grade levels and the professional development experiences the teachers have available to them there as opposed to a public elementary school with average class sizes.

Blatchford, P., Russell, A., Bassett, P., Brown, P., & Martin, C. (2007). The effect of class size on the teaching of pupils aged 7-11 years. //School Effectiveness and School Improvement//. //18//, 147-172. Finn, J. D., Gerber, S. B., & Boyd-Zaharias, J. (2005). Small classes in the early grades, Academic achievement, and graduating from high school. //Journal of Educational Psychology//. //97//, 214-223. Gilman, D. A. & Antes, R. L. (1985). //The educational effects of the introduction of a state supported program of smaller classes. A study of the first year of// // indiana //// ’s project prime time and its effects on test results. // Indiana State  University, School of Education. Graue, E., Hatch, K., Rao, K., & Oen, D. (2007). The wisdom of class-size reduction. //American Educational Research Journal//, //44//, 670-700. Januszka, C., & Dixon-Krauss, L. (2008). Class size: A battle between accountability and quality instruction. //Childhood Instruction//. //84//, 167-171. Konstantopoulos, S. (2008). Do small classes reduce the achievement gap between low and high achievers? Evidence from project STAR. //Elementary School Journal//. //108//, 275-291. Milesi, C., & Gamoran, A. (2006). Effects of class size and instruction on kindergarten achievement. //Educational Evaluation and Policy Analysis//. //28//, 287-313. Mosteller, F. (1995).The tennessee study of class size in the early school grades. //Critical Issues For Children And Youths//. //5//, 113-126. Nye, B. A. (1992). //The lasting benefits study. A continuing analysis of the effect of small class size in kindergarten through third grade on student achievement test scores in subsequent grade levels: Fifth grade.// Tennessee  State  University, Center of Excellence for Research in Basic Skills. Nye, B. A., Achilles, C.M., Boyd-Zaharias, J., Fulton, B.D., & Wallenhorst, M.P. (1992). //Small is far better. A report on three class-size initiatives:// // Tennessee //// ’s student teacher achievement ratio (STAR) project, lasting benefits study (LBS), and project CHALLENGE as a policy application // (Paper No. 5). Tennessee State  University, Center of Excellence for Research in Basic Skills.
 * __References__:**

This team has collaborated on every aspect of this research proposal. There has been a continuous exchange of ideas, group meetings and emails regarding proposal subject and content. The team participated in the literature search and review in ERIC and via Google to find the appropriate scholarly and peer reviewed journals that correlated with class size as it relates to improved mathematical abilities. Furthermore, everyone on this team took turns editing all sections until the final product was mutually acceptable. We truly enjoyed working together.
 * __Distribution of Duties__:**


 * Annie:** Wrote introduction, literature review (with Gerri) w/ /APA citings, and edited.


 * Heather**: Wrote directional hypothesis, validity and reliability, and strength of design. Typed the references in APA style format, and edited.


 * Gerri**: Wrote research question, null and non-directional hypothesis, and literature review (with Annie), and edited.


 * Lydia**: Wrote sample, data collection, data analysis, and edited.


 * Nicely done, team. This is a thorough and thoughtfully created proposal. My few comments are embedded above. 25/25 **

<<EDC 529 - Summer 2008