Table of Contents

Acknowledgments

In addition to his active role on the committee, Mr. Ewert also assisted in the early stages of the project by agreeing to modify the third grade assessment instruments so that class size information could be collected in May 1997 throughout the state. He regularly answered questions about the assessment process and resulting data. It was through his assistance that the Center obtained the data files from Advanced Systems in Measurement and Evaluation, Inc., the state's contractor for the assessment program. Ms. Cherie Dudley of Advanced Systems was helpful in providing information regarding the structure of the computer data files, codes used, scoring methods, and other factors.

Finally, we would like to thank the sixteen thousand third graders in New Hampshire's public schools who answered an additional question so that this study would be possible.
 

I. Introduction

At the beginning of the project it became clear that the necessary class size information had not been collected during the 1996 testing. The Center and the NH Department of Education staff discussed how such an analysis could be performed. It was agreed to collect the necessary class size information during the tests that were to be administered in May 1997. While the intent at that time was to collect necessary class size data from both third and sixth grades, the actual data collection occurred only at the third grade level.

There were 16,419 third grade public school students at the time the tests were administered. Of these 15,799 took the Language Arts test and 15,944 took the mathematics test.

The tests were scored and analyzed by Advanced Systems in Measurement and Evaluation, Inc., a Dover, NH, firm under contract with the New Hampshire Department of Education. The Department released its annual report on the 1997 tests in October 1997. Shortly thereafter a database of results was provided to the Center by Advanced Systems.

The results contained in these files have been analyzed in conjunction with other readily available data and reports to form the basis for the findings and conclusions contained in this report.

As stated in RSA 193-C, the state law that established the NHEIAP, the purpose of the state tests and curriculum frameworks are "to establish what New Hampshire students should know and be able to do and to develop and implement effective methods for assessing that learning and its application so that local decisions about curriculum development and delivery can be made." We hope that this report contributes to that purpose.
 

II. Summary of Findings and Recommendations

Results of the study demonstrated that:

• Third grade students show very little difference in average achievement among class sizes from 15 to 30 students as measured by the NHEIAP.

• Family Income - Average achievement results are related to measures of family income such as: the percentage of students in a school who receive free or reduced price lunch; average income of two-parent families; and percentage of a community's population that are poor. Schools serving communities with higher percentages of lower income families have lower achievement test results.
• Adult Education - Average achievement results are related to measures of adult education in a community. The higher the educational attainment of adults, the higher the achievement levels of the children in the schools.
• Gender - On average, girls have slightly better test results than boys in language arts while boys score somewhat better in mathematics. Thus, differences in gender composition of classes can affect year-to-year and school-to-school comparisons.

• Contrary to common belief, students in the largest class sizes tend to be from the "wealthier" schools while students in smaller class sizes tend to be from the "poorer" schools.
• Special education students constitute approximately 12% of students in all class sizes in the range of 15-30 students. However, they are disproportionately represented in classes of 1-14 students, constituting 19% of that group.

• Decisions about appropriate class size should not be based on an expectation that reducing class sizes will necessarily result in higher levels of student achievement, at least as measured by the third grade NHEIAP tests. School boards and administrators have many important factors to consider when deciding whether to split larger classes to create smaller ones, but the expectation of higher achievement levels should not be one of those factors.
• Policy makers should proceed with extreme caution in using NHEIAP test scores as a measure of the overall accomplishments of a school or district. Parents and voters would like to see changes made at their schools to increase student achievement. However, factors that are strongly related to achievement levels are ones over which schools have no control. This does not argue against the need for increased accountability. To the contrary, accountability remains an important requirement. Instead, it argues for a need for the public to grapple honestly with the difficulties of achieving better results and to be realistic in expectations.
• The NH Department of Education should divide schools and districts into 4-6 groups based upon demographic factors that are known to be related to achievement. NHEIAP test results from any school should first be compared to the average and distribution of all schools in the same demographic group. Possible factors for use in creating the groups include the percentage of adults with higher levels of education and the percentage of households with higher incomes. Communities with students from families where parents themselves have completed more years of education and/or have higher incomes will, on average, always be at an advantage over others. On average, how well kids do in school is much more a reflection of their families, their community, and their society than it is of their schools.
• Any new formula for basic state education aid should take into account demographic differences among school districts and schools into account. The formula should be constructed with a weighting mechanism that modifies the amount provided per pupil to each district based on one or more demographic factors. This is the natural consequence of the understanding that a uniform resource distribution per pupil will not result in comparable levels of student performance in schools that do not have comparable student populations.

• The third grade analysis should be repeated with information collected about potentially relevant classroom factors.
• A similar analysis should also be conducted for sixth and tenth graders.
• In all grades, some brief personal information on each student should be collected to allow for better statistical analysis.
• Testing the validity of the NHEIAP would help assure the accuracy of its measurements.
• The state should annually test the relationship of various school-based factors to student achievement levels, track changes over time, and determine which factors are most effective at improving student performance.

III. Analysis and Findings

A. Students by Class Size

Each student was asked on the student questionnaire that was part of the assessment process to answer the following question:

1. 1-14
2. 15-20
3. 21-24
4. 25-27
5. 28-30
6. 31 or more

The number of students in very small classes (1-14) is also small, only 2.8% of all third graders. The reasons for excluding the results for students in this smallest class size grouping are discussed in the Appendix: The Smallest Class Size Group.

Figure 1 displays the relative percentage of the students that fall into each category.
 

B. Results by Class Size

Proficiency levels in both language arts and mathematics are Advanced, Proficient, Basic, and Novice.

We aggregated the students by class size and examined the results.
 

Proficiency Level in Language Arts

There is only a very slight and inconsistent variation in results among class sizes of 15-30.

 Proficiency Level in Mathematics
Table 3 and Figure 3 show the distribution of proficiency levels in mathematics among each of the class size groupings.

 

The percentage of students at the Advanced and Proficient levels is somewhat greater in larger class sizes. This relationship is consistent, though small, across the groupings studied.
 
 Writing Score
As part of the language arts test, each student is asked to write a short essay of a few sentences. Two independent reviewers use the Annotated Holistic Scoring Method to score a student's writing sample. Each reviewer can assign an integer score from 1 to 6 with higher scores indicating better writing. Each student, therefore, receives a combined score of an integer in the range 2-12.

The average writing score of all third grade students in 1997 was 6.49. We investigated whether the average writing score differed by class size and what difference might exist between boys and girls. The results are shown in Table 4 and Figure 4.
 

Multiple-Choice Language Arts Questions

Table 5 and Figure 5 display the percentage of correct answers by gender and by class size.
 

Multiple-Choice Mathematics Questions

Table 6 and Figure 6 display the percentage of correct answers by gender and by class size.
 

On average, boys had 1.5% more correct answers than girls. This is a smaller difference than the opposite gender difference in language arts identified above.

Open-Ended Language Arts Score

We investigated whether the average score of students in different size classes differed in any consistent or significant manner. Table 7 and Figure 7 display the results.
 

Open-Ended Mathematics Score

Table 8 and Figure 8 display the differences we found in the average score of students in different size classes and gender.
 

Girls had slightly higher scores (0.1 point) than boys on this part of the test. This is in contrast to the multiple choice mathematics questions where boys' achievement surpassed that of the girls.

C. Factors Related to Achievement

We decided to explore other factors that may be related to achievement test results. Because little information is collected on each student by the NHEIAP, there was no way to investigate what individual background factors might be related to achievement. However, previous reports on New Hampshire's public schools have found factors such as family income and parental education to be strongly related to student achievement. We proceeded to collect school- and community-wide data related to these factors and to aggregate student results accordingly. The result is that, in contrast to class size, these demographic factors show strong relationships to achievement.

Measures of Income

Free and Reduced Price School Lunches

Average Two-Parent Family Income in the Community

The schools were ordered according to these figures and then aggregated into five groups (each with approximately the same number of students) and average scores were calculated for all students in each of the five groups of schools.

Table 10 and Figures 10a-c display the results. These results are not as striking or consistent as those above. Nevertheless, they do confirm in a general way that communities with higher family incomes are more likely to exhibit higher average achievement test results.
 

A similar analysis was done for the percentage of each community's population with incomes below 185% of the official poverty level in 1989. The results are very similar, showing that in communities with poorer populations, achievement of third grade students is generally lower.

Education of Adults

Both factors show a strong and consistent relationship with the third grade test results. The higher the percentage of adults in the community with a college education, the higher the average achievement results of third graders (Figures 11 a-c). The higher the percentage of adults in the community with a high school education or less, the lower the test results (Figures 12a-c).

 

The 1990 US Census was used to obtain for each school or school district the percentage of all households that were renters. Test scores were sorted by schools based on this factor and aggregated into five groupings, each with as close to 20% of the students as possible.

As shown in Figures 13a-c, this factor shows only a muted relationship to achievement. There appears to be little or inconsistent difference in average test results in the 60% of schools where the percentage of renters is 23% (homeowners are 77% and above). For schools where the renters are an even lower percentage of all households, average test results are higher in those communities with very low percentages of renters. Because of these results and the weakness of the proxy factor itself, it would be inappropriate to conclude that schools where larger percentages of students are relatively transient have lower average achievement levels. The data in this study is not adequate to draw a conclusion either way in this regard.

D. Comparing Strength of Relationships

A close review of these graphs indicates how small a variation is seen in average achievement across class size groupings in comparison to that seen across groupings based on other factors.

In addition to average achievement, it is possible to also look at the complete distribution of scores. This can most easily be done with the multiple-choice components of the language arts and mathematics tests.

Each student taking the language arts test answered 35 multiple-choice questions and obtained a score in the range from 0 - 35 correct. Figure 15a displays the percentage of students who achieved each score. The curve is an expected normal curve with negative skew and a peak (mode) of 30.
 

Figure 15c displays another set of distribution curves. One is for students in class sizes of 15-20 students while the other is for students in classes of 28-30 students. In this case there is little apparent difference. The two curves are nearly identical.

The figures for the multiple-choice mathematics results are very similar to those for language arts presented above. They are not reproduced here because they do not provide any new insights but simply lead to the same conclusion.

Statistically, there is little relationship between the class size in which third grade students spend most of their classroom time and their average achievement or the distribution of their achievement test scores. In contrast, factors associated with the economic situation of the families sending children to the school (as measured by the percentage of students at the school eligible for free and reduced-price lunches) is related to measured achievement levels. So too is the degree to which adults in the community are themselves educated.

E. A Surprise: Schools with Higher Income Families Have Larger Class Sizes
As described above, students in larger classes obtained higher average scores in the open-ended mathematics test items than did those in smaller classes. Although the strength of this relationship is much smaller than those related to socioeconomic variables such as family income and adult education, it is the largest and most consistent of those related to class size. It is also contrary to intuition.

Because we have shown that achievement is most strongly (and inversely) related to the percentage of students receiving free and reduced school lunches, we asked whether it was possible that the larger class sizes had a disproportionate share of students from schools where few students received any lunch subsidy.

Such a possibility seemed contrary to intuition. A common assumption is that schools in communities of higher socioeconomic status are most likely to have higher spending per pupil and, therefore, likely to have smaller average class sizes, not larger.

We determined the percentage of students in each class size that come from each of the 5 school lunch groupings. The results are shown in Table 11.
 

We then asked whether the open-ended math scores of the class sizes could be predicted based simply on the skewed distribution of students from the different school lunch groupings.

The average score of all students on the open-ended math questions was 5.02 while for those in class sizes of 28-30 students it was 5.44, 0.42 higher than the average. The predicted result based solely on the distribution of school lunch groupings is 5.26. In other words, after accounting for the unexpected preponderance of students from the lower lunch subsidy schools, the difference from the average score is only 0.18. This remaining unexplained difference is not large and our conclusion is that there is little or no relation between class size and the results in this portion of the NHEIAP.

The surprise that schools from "wealthier" communities tend to have larger class sizes, however, deserved further investigation.

Dividing all students into 4 class size groupings and simultaneously into 5 school lunch subsidy groupings, however, results in 20 different subgroups. Some of these have too few students from too few schools to be able to draw useful statistical conclusions. The schools were therefore divided into only two school lunch groupings, each containing approximately half the students. 8,131 students were from schools where 18.75% or fewer students receive school lunch subsidy and 8,140 were from schools with higher school lunch subsidy rates. For ease of reference, the former group is termed the "wealthier" schools and the latter the "poorer" schools. The latter group has more students from low-income families than the former group. (148 students are from schools with 9 or fewer 3^rd graders. These schools are unidentified and thus listed as "unknown" in regard to school lunch subsidy.)

Table 12 and Figure 16 display the percentage of students in each class size grouping that come from the wealthier and poorer schools.
 

This finding raises the following question: "Is it possible that there is a measurable and consistent advantage of smaller class size that is masked by the increasing percentage of students from wealthier schools in large class sizes?"

To determine whether this might be true, we re-analyzed the five components of the NHEIAP this time dividing all students into the two groups based on school lunch subsidy rates: the wealthier and poorer schools. The results are displayed in Figures 17a (open-ended language arts), Figure 17b (open-ended mathematics), Figure 17c (writing score), Figure 17d (multiple choice language arts), and Figure 17e (multiple choice mathematics).
 

 

 

 

 

There is considerable variation but we found no strong and consistent relationship between class size and resulting scores for either group. At the same time, students from the wealthier schools consistently score higher than the students from the poorer schools.

The only exception to this occurs in open-ended mathematics scores in the largest class size grouping. In this case, the students from the "poorer" schools did somewhat better than students in "wealthier" schools. They scored much better than the students from poorer schools in other class size groupings. This exception is so striking that it deserves further investigation.
 

IV. Cautions and Caveats

The presence of a teacher's aide in the classroom could affect student achievement. It is possible that larger classes are more likely to have such an aide than smaller classes. As we lack information about the presence of teacher’s aides in each classroom, we cannot determine to what extent this factor could explain or confound some of our results.

Our research does not conclude that smaller classes are without benefit. There may well be benefits to students and teachers in categories such as fewer discipline problems, better morale, more individual attention, or greater class cohesiveness. However, those benefits do not result in significantly different achievement levels as measured by the NHEIAP.

The NHEIAP 3^rd grade test attempts to measure achievement of a limited set of specific skills and knowledge related to mathematics and language arts. It does not attempt to measure knowledge in subject areas such as science, an understanding of community or nation, achievement in art or music, social skills such as cooperation, respect for others, or traits such as dependability, self-motivation, and imagination. Accordingly we cannot come to any conclusion about the effect that class size might or might not have on these important topics.

Much of this analysis relies on average scores. Each is the average of hundreds or thousands of individual scores. Within each grouping, some students score higher and others lower than the average. There is no attempt to imply that all students in a particular school or classroom environment will have test scores of a certain level. It is certain that some students in poorer schools will fall at the extreme upper end of the achievement spectrum while some students from the wealthier schools will score very poorly and vice versa. These averages do not predict the results for any one student nor do they imply that all students in a particular group will have similar achievement.
 
 

V. Implications for Policy and Recommendations

A. Making Class Size Decisions

There are many rationales for smaller class sizes in the elementary grades and those should be discussed and debated. But the data do not lend support to the notion that reducing class sizes in a school will result in higher average test scores.

Decisions about appropriate elementary school class sizes are continually made by each school board and school administration in the state. The decision about when to split a class that is "too large" or to redistribute students by adding another section are important decisions for each school and district. There are many factors that should be taken into consideration, including physical crowding, level of discipline problems, teacher and student morale, operating costs, available classroom space, etc. Decisions about appropriate class size, however should not be based on an expectation that reducing class sizes will necessarily result in higher levels of student achievement, at least as measured by the third grade NHEIAP tests.

B. The Importance of Community Demographics

However, this study shows that underlying community demographics (whether measured by income, education, or other factors) are strongly related to average NHEIAP scores of students. Factors that are most predictive of higher achievement test scores are ones over which teachers, schools, and school boards have no control.

Policy makers should proceed with extreme caution in using NHEIAP test scores as a measure of the overall accomplishments of a school or district. Using the results without accounting for differences in the underlying community demographics will be misleading and potentially damaging.

C. Appropriate State Reporting for Improved School Accountability

Recently enacted New Hampshire legislation requires the Department to report "comparisons with state averages" and "statewide rankings of each district and school". While the Department must comply with this law, it should go further and provide additional information that would be more informative and useful.

The state's annual NHEIAP results should be tabulated, analyzed, and presented so that districts or schools are shown how they fare in comparison to those with which they share common population characteristics. The Department should divide schools and districts into 4-6 groups based upon demographic factors that are known to be related to achievement. Test results from a school should first be compared to the average and distribution of all schools in the same demographic group.

A school should be considered to be performing well or poorly to the extent that it falls below or above average for its group.

Such a system is not novel. Georgia and other states already provide this kind of analysis when reporting the results of their statewide assessment tests.

D. Devising a Formula for Distributing State Aid

A common working assumption has been that some (as yet undetermined) uniform dollar amount of state aid per pupil distributed to each school district will suffice to accomplish this end. Such an assumption is contrary to the findings that student body and community demographics have great impact on performance as measured by the NHEIAP tests.

If all schools are to be held to the same fixed standard of performance measured by assessment test results, regardless of the differences in the makeup of their student bodies and communities, then it is important to recognize that different resource mixes will be needed.

An example: one measure of an adequate education may be that fewer than 15% of students in a school score at the novice level in 3^rd grade NHEIAP tests. If so, then it must be recognized that different resources will be needed to accomplish this in a district where only 10% of the adults have completed a college education than in one where 80% have done so.

It will be important for any new formula for state aid to take into account such differences. The formula should be constructed with a weighting mechanism that modifies the amount provided per pupil to each district based on one or more demographic factors. Exactly what factors should be used and how much they should be weighted can be worked out and altered over time. However, from the beginning it should be clear that a uniform resource distribution per pupil will not result in comparable levels of student performance in schools that do not have comparable student populations.

This will be especially important if, in the next few years, the state legislature or Board of Education should enact standards of performance and distribute rewards or penalties to schools or districts that are based, in part, on outcome measures such as the NHEIAP results.
 

VI. Future Research

• This 3^rd grade analysis should be repeated. Changes that should be made include collecting class size by a separate instrument completed by test administrators in each school rather than (or in addition to) the students’ questionnaire. Teachers’ experience, presence of general classroom aides, and other classroom factors could be captured by the same instrument.
• A similar analysis should be performed for the 6^th grade NHEIAP results.
• An analysis of class size in 10^th grade should be designed, recognizing that in high school the class size experienced by any student may vary by academic subject.
• In addition to birth month and year, special education status, and kindergarten experience, a small number of other personal factors should be collected on each student. These might minimally include school lunch status, the number of different schools attended in the past three years, and parental education level(s). For upper grades it might include sports participation.
• The validity of the NHEIAP tests must be shown. At the present time there is no assurance, through comparison to other validated norm-referenced tests, that the NHEIAP actually measures achievement in its designated subjects at the end of 3^rd, 6^th, and 10^th grades. We believe the tests do measure what they purport to, but it would be useful to have this belief tested.
• With the data already available and with the new data suggested above, the state should annually investigate and report on factors that appear to be related or not related to achievement. How these relationships may change over time (as school districts adapt their curricula to state frameworks, for example) should be analyzed and reported. Some analysis of this sort is already done in the National Assessment of Educational Progress (NAEP) but it suffers from a limited sample size in New Hampshire and is not geared to the New Hampshire frameworks.

VII. Literature Review and Bibliography

What does this research show? A 1997 review of the research by the Education Commission of the States concluded, "The research about whether small classes improve student achievement has produced mixed results." Some studies - like ours - have shown little or no relationship between class size and achievement. Other studies, most recently from Tennessee’s Project STAR, have shown a positive relationship between smaller classes and achievement. Yet others have found a positive relationship only for certain students (non-English speakers), or only when other conditions are met (changed teaching methods).

Our results speak for themselves. We believe they reflect accurately the situation among New Hampshire 3^rd graders in 1997.

One important distinction between our research and that of other studies is the size of the population being studied. Almost all of the other studies have looked at small samples of students or schools and then tried to draw statistically valid conclusions about the untested student population. Our research, however, looked at all 3^rd graders in all public schools in the entire state. We can describe the entire population, not just a sample. It also has the advantage of being a study of the very population New Hampshire policy makers are concerned about – New Hampshire students. Studies done in locales outside our borders are too often dismissed by policy-makers as irrelevant to their concerns because "of course, our students/schools/teachers/systems are different."

This bibliography has been selected to place an emphasis on the reports and studies of the past decade, but also to include some of the more influential reports and publications of the late 1970s and 1980s.

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Achilles, C. M. (1997, October). "Small Classes, Big Possibilities." The School Administrator, 6-15.

Achilles, C., Harman, P., & Egelson, P. (1995). "Using Research Results on Class Size to Improve Pupil Achievement Outcomes." Research in the Schools, 2(2), 23-30.

Achilles, C., Kiser-Kling, K., Owen, J., & Aust, A. (1994). Success Starts Small: Life in a Small Class. Final Report. University of North Carolina, Greensboro, NC.

Achilles, C., Nye, B., & Bain H. (1994 1995). "Test-score 'Value' of Kindergarten for Pupils in Three Class Conditions at grades 1, 2, 3." National Forum of Educational Administration and Supervision Journal (NFEAS), 12(l), 3-15.

Achilles, C., Nye, B., & Zaharias, J. (1995, April). Policy Use of Research Results: Tennessee’s Project Challenge. Paper presented at the annual convention of the American Educational Research Association, San Francisco, CA.

Achilles, C., Nye, B., & Zaharias, J. (1995, April). Policy Use of Research Results: Tennessee's Project Challenge. Paper presented at the annual convention of the American Educational Research Association, San Francisco, CA.

Achilles, C., Nye, B., Zaharias, J., & Fulton, B. (1993). The Lasting Benefits Study in Grades 4 and 5 (1990-1991): A Legacy from Tennessee’s Four Year (K-3) Class Size Study (1985-1989), Project STAR. Paper presented at North Carolina Association for Research in Education, Greensboro, NC.

Achilles, et. al. (1994). The Multiple Benefits of Class-Size Research: A Review of STAR’s Legacy, Subsidiary and Ancillary Studies. (ERICdocument number ED 390913).

Bain, H., & Achilles, C. (1986). "Interesting Developments on Class Size." Phi Delta Kappan, 67 (9), 662-5.

Bain, H., & Jacobs, R. (1990, September). "The Case for Smaller Classes and Better Teachers." Streamlined Seminar, Volume 9, No. 1. (ERIC document number ED 322632).

Bain, H., Achilles, C., Zaharias, J., & McKenna, B. (1992). "Class Size Does Make a Difference." Phi Delta Kappan, 74, 253-256.

Beattie-Smith, G. (1994). Class Size Regulation: A Dossier of International Comparisons. Research and Information on State Education Trust, England.

Berger, M. (1982, April). Class Size Is Not the Issue. Paper presented at the annual meeting of the National School Boards Association, Atlanta, Georgia.

Blatchford, P., & Mortimore, P. (1994). "The Issue of Class Size for Young Children in Schools: What Can We Learn From Research?" Oxford Review of Education, 20 (4), 411-28.

Boozer, M., & Rouse, C. (1995, June). Intraschool Variation in Class Size: Patterns and Implication. (Working Paper No. 344). National Bureau of Economic Research, Industrial Relations Section, Washington, DC. (ERIC document number ED 385935).

Bourke, S. (1986). "How Smaller is Better: Some Relationships Between Class Size, Teaching Practices and Student Achievement." American Educational Research Journal, 23, 558-571.

Bracey, G. (1995). "Debunking the Myths About Money for Schools." Educational Leadership, 53 (3), 65-9.

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Cacha, F. (1982). "The Class Size and Achievement Controversy." Contemporary Education, 54, 13-17.

Center for School Assessment. (1986, July). PRIME TIME: The Relationship Between Class Size and Achievement for First Grade Students in Indiana 1984-85. Indiana Department of Education, Indianapolis, IN.

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Cockman, D., Bryson, J., & Achilles, C. (1989). High School Size and Student Participation in School Activities: North Carolina, 1988-89. Paper presented to the North Carolina Association of Research in Education Annual Conference, Research Triangle Park, NC.

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Cullen, B. (1979). "Lessons from Class Size Research – An Economist’s Perspective." Trends in Education, Winter 1979, 29-32.

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Ferguson, R., & Ladd, H. (1996). "How and Why Money Matters: An Analysis of Alabama Schools" in H.F. Ladd (Ed.), Holding Schools Accountable. Performance-based Reform in Education (pp 265-298). The Brookings Institution. Washington, DC.

Filby, N., et. at. (1980). What Happens in Smaller Classes? A Summary Report of a Field Study. Far West Laboratory for Educational Research and Development, San Francisco, California.

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Finn, J., & Voelkl, K. (1994). "Class size" in T. Husen & T. Postlethwaite (Eds.), International Encyclopedia of Education (2nd edition). Pergamon Press, Oxford, England.

Finn, J., Achilles, C., Bain, H., Folger, J., Johnston, J., Lintz, M., & Word, E. (1990). "Three Years in a Small Class." Teaching and Teacher Education, 6(2), 127-136.

Finn, J., Fulton, D., Zaharias, J., & Nye, B. (1989). "Carry-over Effects of Small Classes." Peabody Journal of Education, 67(l), 75-84.

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 Appendix: The Smallest Class Size Group

Intuition holds that smaller class sizes in public elementary schools should result in better educational results, whether measured by standardized tests or other means. Yet our analysis showed that the results among students in this grouping were considerably lower on every measure than those of the four groupings covering class sizes from 15-30. This result, so contrary to intuition, required us to investigate the makeup of this group further.

Differences in achievement results cannot be attributed to class size if there is reason to believe that the student populations in different class sizes were not reasonably equivalent.

Special Education Students

We determined the number and percentage of students in each class size grouping who were coded for special education. Table A1 and Figure A1 display the results. Special education students seem to be relatively equally distributed in class size groupings of 15-30 students, constituting between 11.5% and 12.3% of students in each group. However, they constituted 19.1% of the students in classes of 1-14 students. Special education students are disproportionately represented in the smallest classes.
 

Similar results were found for other components of the language arts assessment program as well as the mathematics tests.

If all students were randomly assigned to classes there would be no disproportionate share of special education students in the smallest classes.

Small Schools and Small Communities

We concluded that this group, in addition to being very small in number of students, differed greatly in makeup from the four larger class groupings. This grouping contains an unusually high concentration of students from very small schools and has a disproportionately high representation of special education students.

We have therefore not included the results from this smallest class size grouping in the body of our report.

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