For generations, the nation has struggled with how to improve its public schools.
Since the late 1970s and early 1980s those concerns have risen, prompted largely by threats to our nation’s economic supremacy and prosperity. Trends on standardized tests have been stagnant since they were first begun in 1970, and international comparisons of student performance generally indicate that U.S. children, particularly in the upper grade levels, are not competitive (Ferguson).
Following the 70’s, many different kinds of educational reforms have been attempted – ranging from a student’s testing and assessment, bigger district budgets, changes in the academic curriculum, magnet, charter and voucher schools, etc. School administrators, teachers and parents have long thought that the number of children in a classroom affects the quality of learning; however, it has proven difficult to directly measure the direct effects of class size on student achievement. Various key factors need to be addressed:
- Does the amount of money spent per child have a positive effect on overall performance?
- Does the income distribution of a school district have any impact on a student’s learning? Do schools with a higher per capita reduced meal plan percentage perform any differently than schools with a lower reduced meal plan percentage?
- Are computers positively correlated with student achievement?
- How important is class size relative to other factors including individual student
background and the mix of students, the nature of physical space occupied, and other resources available in the classroom?
- Is student performance biased socio-economically?
- Do students experiencing smaller class sizes learn more, as measured by student
achievement tests, than otherwise similar students?
- What is the nature of the relationship between class size and student achievement – will this relationship be linear, or does class size have to be below a certain level for any kind of impact to occur?
- Do the benefits of smaller class sizes outweigh the costs associated with the resources required (extra teachers, extra facilities)?
- How important is class size relative to other factors including an individual student’s background?
- Does the type of student targeted matter? Some states have put all children in reduced size classes; others have targeted the policy to at-risk students.
- Whether class size reduction is mandatory or expressed as a goal?
In order to come to a solid conclusion on these inquiries, a conclusion not based on feelings but on hard data, standardized tests (the STAR exam) were implemented in all California public schools. The data has conveniently been made available for people (statisticians, perhaps!) to view, and hopefully our analysis of the figures will give further insight into this conundrum. The following chart is the set of descriptive statistics analyzing specific factors of the various variables:
The following table was used to predict what variables were significant:
From the above calculated values it is predicted that percentage of students qualifying for reduced meal plan, the average district income, and the percentage of English learners will have the most impact on test scores. However, because millions of dollars should not be appropriated based on “feelings,” it is necessary to examine, using statistical regression and inference, the actual significance of each variable.
Technology and Resource Allocation:
The regression for the “Expenditures per Student” variable gives surprising results. One would normally consider higher spending on each student to be a strong factor in his performance. For example, higher paying districts can attract the better teachers, afford the better textbooks, and provide the better facilities. While this logic appeals to common sense, it does not appear to hold an equal attraction to the actual figures. The analysis shows that the variation in expenditures per student only explains an astonishingly low 3.7% of the variation in the test scores. The slope further elucidates that when the expenditures per student increases by one unit, the average test score goes up by 0.006. How can something that seems so beneficial be so worthless? In explaining this, it is probably best to ponder how schools would spend the money they receive. Perhaps the schools that receive the most money are the ones failing, and an increased budget is seen as the most efficient way to boost their performance. However, perhaps these schools spend their funds on increased campus security and metal detectors. Whatever the reason, some districts must not be allocating their money as efficiently as they could or have non-score-increasing needs (such as safety) that drain their budgets, but to determine this would require a whole new set of data.
The regression for “Computers per Student” gives promising but perhaps misleading data. The R2 statistic asserts that 7.3% of the variation in the data is explained by variations in the computer to student ratio. Something to note is that even though the slope of the line is 79.4, it is unrealistic to assume that one would ever increase the independent variable here by one unit. Given that it is a computer to student ratio, an increase of one would imply that the school bought a new computer for each student, in addition to what they already have. Perhaps it is more useful to say that if the school provides one more computer for every ten students, the score is likely to jump eight points. Again, these numbers may be misleading. The schools that score well may be the very schools that have less of a need to spend money on campus safety and instead pour their savings into computers. Common sense would assume that because the STAR test measures reading and math, not technological proficiency, students will score equally well on the exam regardless of their school’s computer to student ratio. Therefore, one may probably rightly assume that computers are not the cause of high test scores but that schools that enjoy a greater abundance of these machines also enjoy a greater preponderance of students who can score better on the STAR tests. In any case, one cannot determine causality with the methods that we are using, so one is only allowed to note that some relationship does exist, that the cause is somewhat unknown, and that computers at least do not seem to harm test scores.
Socioeconomic Varibles:
Test scores are affected by a variety of factors. Many theories state that lower income districts have a lower average testing score, so common sense as well as our descriptive statistical predictions necessitate that it be examined.
As seen above, average income and test scores have a positive relationship. In fact, the regression line is. Or in English, as the district average income increases by 1 unit ($1,000) then the test scores are raised by 1.88 points. Also the R2 = 0.51, or, in other words, 51% of the variance in the data can be explained by the single variable of district average income, which seems much more significant, being approximately 20 standard deviations from the mean, than the student teacher ratio on test scores. This can be explained by many hypotheses. One could assume that in a lower income district the focus at home is different. For example, when the students leave school, they may go to a day care or they may go home to be by themselves. Therefore, homework may not be done directly after school to reinforce what was learned that day, so later in the evening they may have more difficulty time remembering the material. Also, when someone is not home to force the student to complete his homework, he is more likely to suffer from low motivation. Another possibility is that both parents may work full time or even double jobs to make ends meet. Hence, the students cannot receive extra attention while they are learning, which is especially harmful when the material is complicated. In addition, the students may have other responsibilities at home, such as working at a job in the neighborhood or watching siblings, which results in a lack of study. Also higher income districts usually have a higher educational level of the parents. Therefore, it is reinforced in the home of the importance of education with a very tangible example of educated parents. So those students may get more direct encouragement or direct support for their studies. Even if the high-income districts are not well educated, they can provide more of the necessary learning aids, such as calculators, rulers, and books.
Average income also corresponds to other variables in the data, such as qualifying for CalWORKS (a welfare program that gives cash aid and services to needy California families), being an English learner, and qualifying for reduced price lunch. Therefore, to get a better understanding of the data one needs to perform a multiple regression of the test scores against those three variables associated with lower income districts combined with the average district income. This regression line is
whereand When the multiple regression is done the R2=0.80 and the multiple R=0. It should be noted that, given a lack of dramatic significance changes with the multiple regression above, we concluded taking the partial derivatives, which requires that all else be held constant, is valid. Hence, combining these variables gives a much better understanding of the variance of the data, as seen in the below graphs:
Multiple Regressions:
When considering the above data, one must account for the fact that more than one variable can explain the variance. This phenomenon, also known as the “Omitted Variable Bias,” can be thought of as excluding a variable of importance, which would result in skewed data analysis. Therefore, it may be helpful to reevaluate, with multiple regressions, the significance of the student teacher ratio, English learning percentage, and average income against test scores. Again, it should be noted that multiple regressions will not be hindered by the “holding all else constant” requirement because the variables are not interlocked in such a way that negates the principle of partial derivatives (e.g. expenditures and teachers must change together). To determine the significance of the combined factors of average district income and student teacher ratio upon test scores the R2 value was calculated and found to be 0.51 with a regression equation of , with student teacher ratio and the average district income. Furthermore, the standard deviation for the observed data for student teacher ratio is –1.83, and for district income is 19.82. Next, a multiple regression was performed upon the following variables: student teacher ratio and percentage English learners against the average test scores. The R2 value of this analysis was found to be 0.43 with a regression equation of , when student teacher ratio and percentage of English learners. In addition, the standard deviation for student teacher ratio was calculated at –2.90, and for percentage English learners is –16.52. Finally we did a regression combining all factors - student teacher ratio, , and average district income, , percentage English learners, . Again, the R2 was calculated at 0.71, the regression equation was , and the standard deviations were –0.25, 19.97, and -16.67, respectively. Notice, when all variables were combined in one regression the standard deviation of the student teacher ratio decreased to less than one standard deviation away from the mean. This indicates that as more significant values are included, such as basic knowledge of the English language and the average district income, student teacher ratios lose statistical significance. This means that even though the student teacher ratio is easier to adjust than the more significant factors, it will not definitely increase the test scores. A better way to approach the problem is to separate the adept English speakers from the students who have minimal mastery of the English language. Moreover, in order to promote an efficient learning environment, it is of the utmost importance for a teacher to address the specific learning needs of the students, especially those who struggle with English.
Student Teacher Ratio
Does a smaller class size have a significant effect on student test scores? To answer this question, a regression was performed on the two variables and can be seen below:
Unsurprisingly, student teacher ratio and test scores have a negative relationship. In fact, the regression line is. This can be interpreted that for every unit increase in student teacher ratio, the test scores decreases by 2.28 points. Moreover, the R2 value was calculated at 0.05, meaning that 0.05% of the variance in data can be explained by the single variable of student teacher ratio. Although a low student-teacher ratio may lead to an improvement in test scores, an R2 value of 0.05 is very weak, suggesting that other variables have a greater impact on student performance.
Several factors are needed to create a successful school. As previously noted, income has a significant effect on test scores. Public schools, remarkably, are a reflection upon the many inequalities in American social and economic life. By every measure of student achievement, students from middle class and wealthy families outperform students who qualify for “free and reduced lunch.” It also is undeniable that whites and Asians outperform African Americans, Latinos and Native Americans. The problem is not that American public schools do not produce excellent students, but that different Americans have dramatically different educational outcomes. In evaluating what a school district can do to ameliorate the financial inequality, while promoting a productive and efficient learning environment, we came up with the following:
An ample financial base (measured counter to student needs) to provide small class size, modern equipment and the like. Surprisingly, middle income schools, on average, spend almost twice as much as what low-income schools spend per student.
Money must be spent wisely on the classroom rather than on bureaucracy. In middle class areas, it is more likely that the pressure is less intense to make education a heated issue, so bureaucracies are less likely to be bloated.
An orderly environment. Middle income schools generally have less behavioral problem and disorder than low income schools.
A stable student and teacher population. In low income schools, the teacher turnover ratio is much higher that that of the middle income schools. Moreover, low income students continually suffer from problems with student absence (Brydolf).
Hire qualified principals and teachers trained in the subject they are teaching. Teachers in middle class schools are usually licensed and less likely to teach out of their field of expertise, less likely to have low teacher test scores, less likely to be inexperienced,
and more likely to have a higher educationEven when paid comparable salaries, teachers consider it a promotion to move from poor to middle class schools, and the best teachers usually transfer into middle income schools at the first opportunity (Brydolf).
A rigorous curriculum with high expectations. Curriculum in middle income schools is generally much more challenging and expectations are higher.
Active parental involvement. In middle class schools, parents are four times as likely to be members of the PTA and much more likely to participate in fundraising.1
Motivated peers who value achievement and encourage it among classmates.
Peers in middle income schools are more academically engaged, more likely to do
homework, less likely to watch TV, less likely to cut class and more likely to graduate – all of which have been found to influence the behavior of classmates.
High achieving peers, whose knowledge is shared informally with classmates throughout the day. In middle class schools, peers come to school with twice the vocabulary of low-income children, so any given child is more likely to expand his vocabulary through informal interaction.
Well connected peers who will help provide access to jobs down the line.
Children attending middle class schools are given access to informal connections
that serve children well in finding jobs after graduation.
Conclusion
Diminishing returns:
With all this incontrovertible evidence regarding the seeming non-importance of the student teacher ratio, one might ask why a bright CMC (or other 5C) student would choose to pay huge sums to attend a school lauded for its small class sizes instead of going to a UC, for example. Obviously there is some feeling that small classes are not just helpful for teachers but aid the student as well. Perhaps some speculation here is in order. A popular concept that most learn in economics is the law of diminishing marginal returns, and this theory may very well apply to this case. Largely, the Californian law requiring small classes in the lower grade levels affects the data examined. This is exemplified by the fact that the maximum student-teacher ratio listed is 25.8, which suggests that there is a lack of large class sizes. Therefore, a reduction in the student teacher ratio in large (above 40, for example) classes may have very significant and economical results on the test score. However, as the class sizes grow smaller, a change in the student teacher ratio may matter less. The diminished returns that one finds at an average class size of just under twenty should not be taken to mean that at all levels a change in the student teacher ratio is economically insignificant.
Since student teacher ratios were calculated to be statistically insignificant -- minimally effecting overall student performance, economically, an allocation of resources devoted to lowering this ratio would be absurd. Therefore, it is imperative to focus on the crux of the issue at hand, which is determining the factors that can be manipulated to promote teaching efficiency. The most noteworthy factors affecting student test scores were the socioeconomic variables: percentage qualifying for CalWORKS, percentage qualifying for reduced meal plan, average district income, and students for whom English is not the primary language spoken at home. As previously stated, these factors effecting scholastic success are difficult to manipulate. Barring a macroeconomic miracle, it is challenging to alter the financial status of low-income families. The most realistic factor to address is improving the English language skills for those students with minimal comprehension of the language.
Rather than lowering the student teacher ratio a more economically efficient and statistically significant approach is to create classes catering specifically to the learning needs of English as a second language students. Correlation does not necessarily indicate causation; meaning although ESL students on average score lower on standardized test does not suggest that they are of below average intelligence. Rather, if these students were given the same standardized tests in their native language, one can be certain that their test scores would increase dramatically. However to excel in the United States one needs a commanding knowledge of the English language. Therefore, programs that integrate English into all aspects of life: cooking skills, theater, television, household chores and sports would ease the burden in comprehending English. Through integration of everyday activities, the student would not have to struggle comprehending foreign concepts - the student would have a hands-on approach to associate concepts and ideas in their own native tongue with their English cognates. Also, by incorporating non-academic activities to build an English vocabulary, the students may learn faster and find more personal enjoyment and motivation.
However, there are drawbacks to progressive programs such as this. One must account for student transportation to and from school and since this would be in addition to the regular class day, paying teachers more. Furthermore, capital would be diverted to training programs familiarizing teachers with the curriculum and necessary skills. Resultantly, the economics of funding a program such as this must thoroughly be investigated to test the financial feasibility and the effect it would have on a district’s budget. However, it would create specific programs for ESL learners and address a more statistically significant variable that could have a lasting effect on student performance in the future, if implemented.
The Class Size Controversy:
The Validity of Lowering the Student Teacher Ratios to Raise Standardized Test Scores
NE Colraine
Ryan Greene
Elizabeth Jones
Econ 120
February 20, 2003
References
Ashton, P. & Crocker, L. (1997). Systemic study of planned variation: The essential focus of teacher education reform. Journal of Teacher Education, 38, 2-8.
Brydolf, C. (1997). Class size: Is less more? Peabody Journal of Education, 67, 123-154 .
Evertson, Hawley. (1995) Making a difference in educational quality through teacher education. Journal of Teacher Education, 36, 2-12.
Ferguson, R. (1991). Paying for public education: New evidence on how and why money matters. Harvard Journal of Legislation, 28, 465-498.