Abstract

CCNY‘s Mathematics Program is infamous for being difficult with some classes boasting a 67% drop/fail rate. Student: teacher ratios and class sizes are often cited in the academic community as a significant determinant of student performance. The goal of this study was to analyze the relationship between class size ratios and student performance. It was predicted that a strong correlation exists between student performance and class size. Surveys were conducted to measure class size and students’ performances in math classes. Recent testing data was procured directly from the math department to assist in this analysis. There was a slight correlation found between class size and student performance from student surveys. A slight correlation was also found from the raw test average data procured from the math department. More research and analysis of the current data is required to produce conclusive results.

Introduction

STEM degree courses have a reputation for being difficult to succeed in. City College of New York’s (CCNY) Mathematics program in particular has an internal reputation of being rigorous and especially unforgiving. This reputation is earned through any number of reasons; be it fast-paced curriculums or impatient teaching styles. One speculated reason that makes math courses difficult is the overwhelming number of students in some classes in comparison to their respective instructors. One study conducted by researchers at CCNY showed that larger classes had an adverse effect on student performance whereas smaller classes had a beneficial effect on student performance (Kara E, et al. 2021). This is possibly because a larger class size will typically result in a reduction of the professor’s ability to cater their curriculum to each student’s natural learning pace. The goal of this study was to determine if there is a correlation between class sizes and student performance and if it is suggestive of a causal link between the two. We predicted that larger class sizes would result in significantly lower student performances. 

Methods

It was decided that student performance would be measured across two vectors: The students’ comfortability with the subject and their actual recorded test scores. 

The first vector was measured via a questionnaire. 41 math students were randomly surveyed using Google Forms in the Cohen Library. They were each asked to identify their math course, and their professors and to estimate their class size. Students were asked to rate their performance in class. They were asked to rate the difficulty of their class, their understanding of the class material, and their performance on the most recent math exam each on a scale from 1 to 5. Finally, the students were given the option to disclose their most recent exam grades, using options ranging from 50-60, 60-70, 70-80, 80-90, and 90-100. Students who were not currently enrolled in a math course were excluded from the survey.

The second vector was measured using test average data collected from the math department.

Average algebra test scores across every class section in Math 190 were collected with permission from the math department along with their corresponding class sizes. Test averages for math 195 and math 201 were not accessible as they were not yet compiled until the end of the semester.

Results

Class sizes were divided into three types: Type-A for classes between 20-39 students, Type-B for classes between 40 and 60 students, and Type-C for classes between 80-200 students.

Type-A

Of all the students surveyed, most test scores collected were of class Type-A. Type-A also contained the most variance in test scores. 36% chose not to give their test scores. The average score range in this group for students who disclosed their test scores was 72.5-82.5%. The average rating for class difficulty was 3.54. The average rating for understanding of material was 3.59. The average rating for test difficulty was 3.32.

Type-B

Of the surveyed students in class type B, 11% chose not to disclose their test scores. The average score range for surveyed students enrolled in medium-sized classes who disclosed their test scores was 62.85-72.85%. The average rating for class difficulty was 3.55. The average rating for material understanding was 3.22. The average rating for test difficulty was 3.11.

Type-C

Of the surveyed students in class type C, 50% chose not to disclose their test scores. The average score range for surveyed students enrolled in large classes who disclosed their test scores was 74-84%. The average rating for class difficulty was 3.6. The average rating for subject comprehension was 3. The average rating for test difficulty was 3.4.

Math Department Data

5 data points depicting the test averages and class sizes of each section in the Math 190 course were provided by the math department.

Figure 1. Scatter plot of all algebra class sizes plotted against their respective test averages. The coordinates of each point from left to right: (33, 97%), (37, 92%), (39, 94%), (42, 86%), (45, 87%)

Discussion

After an analysis of these results, we found that there is no strong correlation shown between class sizes and student performance. Data depicting the relation between class size and surveyed average student performance only showed a slight negative correlation in regards to class difficulty and material comprehension. As for the data provided by the department, recorded test averages plotted against class sizes across algebra showed a slight negative correlation between the two. More research should be conducted to produce more conclusive results. For example, a method should be developed to interview every student of each class to produce a more comprehensive overview of that class’s perceived performance.

Our first approach was to directly survey math professors who teach courses 190, 195, and 201 and to have them compel their students to our general survey questions. After several attempts to make contact with these professors, we decided that this approach was impractical due to the hectic schedules of professors and our research being a potential disruptor for ongoing class sessions, especially of large class sizes. Rating scores on the survey should be upscaled from 1-5 to 1-20 to account for the nuances between each student’s perceived performance. Questions should be added to account for each class’s grading rubric, inquiring about each student’s tendency to participate in class, come to class on time, and complete homework assignments. Data regarding actual test score averages across all sections in precalculus and calculus could not be recorded as they were not yet compiled. The initial surveys used to collect data in the writing class were poorly designed, missing key questions, and as a result, did not collect any useful data pertaining to the goal of this study. Some data points were incomplete, missing crucial information like class size.

There was not much variance in the class sizes for the students surveyed using the general research survey. However, while the research did not show strong correlation between class sizes and performance, there are other factors that may affect the performance, such as engagement with professor, outside factors, etc. Although the initial hypothesis could not be backed up by the data, this is an issue that had been researched before and it is a latent challenge in the academic world, which is worth looking in to in order to improve teaching efficiency. 

References

Kara E, Tonin M,  Vlassopoulos M. Class Size Effects in Higher Education: Differences across STEM and Non-STEM Fields. Economics of Education Review, vol. 82, 2021, pp. 102104-, https://doi.org/10.1016/j.econedurev.2021.102104.