Maitri Shah, Richa Srivastava, & William Zhou

Calgary, AB

Edited by Danlin Zeng

In the past decades, technological and living standards have risen across the world, amplified by increasingly educated workforces (Berger & Fisher, 2013). As the importance of education increases, it is vital that schools ensure a high standard of tutelage for all students. However, economic disparities across student populations are also increasing, especially in developing nations. Today, international equity metrics still show serious gaps between learners belonging to different ethnicities, genders, and wealth brackets. To combat this trend, this paper examines how different in-school factors impact equity.

Equity refers to test score variance between students of different wealth quintiles; essentially, a more equitable country is one where students perform similarly in standardized exams regardless of their wealth. In-school factors include teacher participation, class size, and availability of special needs programs. The methodology analyzes two sets of correlations. The first is the one between wealth-based inequality and various factors from the Programme for International Student Assessment (PISA); the second is the connection between teacher participation and agency, as measured by the Teacher Participation in Decision-Making Index, and inequality. This factor was chosen because most schools around the world can influence teacher participation without a large change to their budget.

Data was collected from PISA surveys and from the World Inequality Database on Education. Overall, the results of the study show a correlation between the agency given to individual teachers and a reduction in mean inequality. Based on the results, it is recommended that teachers be given an opportunity to increase participation in large-scale decision-making processes as this would help reduce educational inequality (disparities in test scores) due to wealth. Through these developments, teachers would also be able to promote smaller class sizes and the implementation of special needs programs in schools, both factors that have been shown to decrease inequality in education. The results of this study are significant because the ability to promote student equity would be advantageous to the overall well-being of a population and decrease disparity between economic classes.

Key Words: Education, Pedagogy, Equity, Data analysis, Data Visualizations

INTRODUCTION

Objectives
Inequality is prevalent in education, as the availability of resources for students of different genders, ethnicities, and socioeconomic statuses vary worldwide. According to the United Nations, 617 million youth around the world do not have basic skills in mathematics and reading, and most of these youth are either women, come from developing nations, or are part of the minority population in their country (United Nations, n.d.). More specifically, it has been seen that students of lower economic status are affected by these inequalities to a greater extent, with minorities often receiving fewer resources and a decreased quality in education (Darling-Hammond, 2001). For example, Irish children coming from high-earning families have a 90% chance of progressing to further education, whereas those from families with lower income have only a 13% chance (“Huge”, 2004).

Due to the prevalence of inequality, this study aims to determine the ability of different in-school factors to combat it. The primary focus is placed on the role of teachers in decision-making, with analysis of class sizes and proportion of students in special needs programs supplementing the data. Determining the impact of these factors on educational inequality can aid in determining potential solutions to increase equity.

Factors of Inequality in Education
The Gross Inequality Index (GI Index) was constructed to quantify the relevance of factors to educational inequality. The GI Index is calculated by taking the coefficient of variation between the academic performances of students in each wealth quintile. A high GI score indicates that a nation has large differences in academic performances between its wealth brackets. Overall, the Index is used as an estimate of a nation’s general academic inequality.

Teacher participation in large-scale decision-making was compared with the GI Index to determine whether the involvement of teachers has an impact on educational inequality based on wealth. Previous studies have proven that teachers can teach more effectively when they participate in activities such as curriculum development and administrative responsibility (Darling-Hammond, 2001; Young, 2021).

In addition to teacher agency, two other factors are also compared with the GI Index to further explore correlations that can promote the reduction of inequality: mean class sizes and students in special needs programs. Class size has been shown to have a significant impact on academic achievement, with smaller class sizes allowing students to attain greater success (Woods, n.d.; Achilles et al., 2008). The proportion of students in special needs programs has also been linked to positive outcomes for students, as overall educational achievement is contingent on how well the needs of students are being met (Robson, 2019).

Thesis
Teacher involvement in decision-making has been shown to have beneficial effects in the classroom. An analysis of PISA’s educational factors and the GI Index yields significant correlations between in-school factors and educational inequality from wealth. This analysis determines a negative correlation between teacher agency and GI score. The data suggests that increasing teacher participation in large-scale decisions is correlated with lower nation-wide educational inequality. Additionally, class size is shown to have a positive correlation with GI score while the proportion of students in special needs programs shows a negative correlation with GI score. To maximize general equity, a reduction in class sizes and an increase in the availability of personalized programs is advised.

METHODS & MATERIALS

The data used for the statistical analysis comes from two sources: OECD’s PISA (Programme for International Student Assessment) data and the WIDE (World Inequality Database on Education) dataset.

The PISA dataset provides data about different educational metrics (ie. teacher participation, class size, and proportion of special needs learners), while WIDE provides data about learner performance stratified by wealth, gender, and ethnicity. Since the WIDE data groups students by strata, its data can be easily used to see how learners of different ethnic or income groups stack up academically. To focus the search, only data regarding differences by income were considered. Using Python, the data was then further segregated by year, and only the statistics for the year 2015 were used to make a consistent comparison among the PISA and WIDE datasets. Additionally, only data from locations that were shared across all datasets were considered. After this data processing, the remaining data from WIDE consisted of the performance levels of 800 different groups across 33 countries, and the PISA data consisted of a flat average indicator score for each of these 33 nations.

To get a sense of how much academic inequality existed for each nation, coefficients of variation were taken for each academic indicator and then collectively averaged to produce a “gross inequality indicator”. For example, the portion of students that passed level 4 of the PISA Science exam in Macao, China, as shown below, was segregated by income quintile.

**Figure 1**: Proportion of Macao Students reaching Science Level 4, by income quintile.

After the coefficient of variance was taken for each metric (PISA Science, Math, and Reading test levels achieved), the mean of all the coefficients was taken to produce each nation’s overall gross inequality score. These numbers were then used to construct a table of gross inequality scores per country. In the Gross Inequality by Nation graph, as shown in Figure 2, nations around the world demonstrated serious differences in the amount of inequality they experienced.

**Figure 2**: Gross Inequality (in relation to wealth) by Nation.

Afterwards, the national metrics from PISA were compared to the national GI scores derived from the above process. Using a linear regression model, the r-values for the correlations between pedagogical PISA indicators and GI scores were determined. The relations were then sorted from highest to lowest absolute r-value and investigated.

To examine the correlation (and indirectly, the impact) of teacher participation on other academic factors, the Teacher Participation in Decision-Making Index was isolated and directly compared to other PISA factors using the same linear regression algorithm as above. Statistically significant correlations were again sorted for and collated. For all correlations, a Python script was used to iteratively calculate the line of best fit, sort correlations by r-value, and graph the results in a scatter plot.

The code for this analysis was hosted on Kaggle, a machine-learning platform that provides free computing resources. Various python libraries were used to facilitate data exploration and visualization: Numpy, Pandas, Matplotlib, Seaborn, and Scipy.

All data analysis code is openly available and can be found here: Teacher Involvementand Equity — An Analysis.

RESULTS

A total of 33 nations were investigated, with trends being explored across countries. The correlations of PISA educational factors with Gross Inequality scores were quantified using r-values. An r-value measures the linear correlation strength between the two variables; an absolute r-value that is greater signifies a stronger correlation. The absolute r-values in question ranged from 0.326 to 0.652. These results show a consistent trend: nations with more equitable educational systems tend to have smaller schools, smaller classrooms, provide more special provisions for students, and give more freedom to educators. In each of the scatterplots below, a purple line of best fit is shown. Additionally, a darker purple region representing the 95% confidence interval was overlaid on each graph. To verify the validity of the linear regressions, a regression plot was constructed for each variable pair and checked for patterns. In a few cases, such as in Figure 3, some clustering was observed. This is primarily due to outlier values — like the unusually large mean class size of 47 in Figure 3.1 — distorting the graph. In this dataset, outlier removal is infeasible due to the relatively low number of countries surveyed (33), since any removal of data from a sample-low dataset is likely to skew results. Since the outlier data values come from datasets verified by OECD, they are most likely not the result of a sampling error and instead signify points of natural variance. Thus, the outliers were retained.

CORRELATION & GRAPHS

**Figure 3:** Factors relating to GI (Gross Inequality) Score

**Figure 4**: Teacher Participation in decision-making vs Language class size index.

**Figure 5**: Teacher Participation in decision-making vs Proportion of students in Special Needs programs.

DISCUSSION

In many schools, students from affluent families tend to outperform ones from poorer backgrounds by a large margin. Disparities in income, along with ones of gender and ethnicity, tend to be strong predictors of student performance — despite being not related to academics at all. According to a study by Georgetown University, American students from a socioeconomically advantaged background are more than twice as likely to have successfully completed college degrees than their less advantaged counterparts (46% vs 16% for students with below median math scores, and 70% vs 30% for students with above median math scores) (Carnevale et al., 2019). As explained by the Georgetown study, the reason for this gap is that higher-earning families can afford to send their children to better schools, and spend more on enriching extracurricular activities.

Correlation Analysis - Teacher Participation vs. Inequality
Teachers are the most pivotal part of the education system and can have lasting impacts on a student’s academic success and mindset. Though many factors contribute to a student’s learning experience, teachers are estimated to have two to three times the effect of any other school factor (including services, facilities, and leadership) when it comes to student performance on reading and math tests (Opper, n.d.).

Teachers have the ability to shape their student’s lives and often act as a support system for students who may lack strong figures in other areas of their lives. This is especially true for children in low-income households, as they often have fewer present parental figures in the household. In Canada, for example, children living in a one family are more than three times as likely to live in a low‑income household as children in a two‑parent family (Statistics Canada, 2017). In situations like these, children often rely on external figures for guidance and acceptance, most commonly their school teachers.

By allowing teachers to have more of a say in the practices of the education system, it will provide them with more resources to effectively handle the challenges that come with their career. Figure 3.3 compares teacher participation in decision-making with gross inequality scores. The linear regression reveals a moderate negative correlation (r-value = -0.597) between the two, showing that nations with greater teacher agency tend to have less wealth-based inequality. This is likely because instructors are the ones directly responsible for educating their students. This gives them first-hand experience, which allows them to contribute valuable insights if they are consulted during decision-making. Teachers being able to better advocate for the needs of their students can effectively help ameliorate the inequality in academic performance caused by wealth disparities.

To substantiate this claim, case studies were performed on the nations with the highest and the lowest equity. In Figure 2, it can be seen that the Dominican Republic has a gross inequality score of 1.02, which is the highest on the chart. Also, in the Dominican Republic, teachers are held to rigorous standards and allowed less freedom in what they do in their classrooms. In 2014, the Dominican Republic explicitly defined what they expect from each teacher when the Ministry of Education published the “Professional and Performance Standards for the Accreditation and Development of the Teaching Career”. This document defined the nation’s expectations of classroom performance, as well as the attitudes and values that define pedagogical excellence (Saavedra & Baron, 2018). Based on the trends and correlations identified in this paper, it is very likely that this invariable standard for educators, combined with a lack of meaningful input from teachers and other socioeconomic factors, contributed to the nation’s high gross inequality score. Furthermore, increasing teacher agency would allow educators to play a greater role in the implementation of smaller class sizes and special needs programs, both factors that are discussed to a greater degree below.

Correlation Analysis - Class Sizes vs Inequality and Teacher Participation
Figure 3.1 compares the average size of language classes in a nation with its gross inequality score. Language classes refers to the native language class of a school (ie. in Canada, it would be the English language); generally, large language class sizes indicate overcrowded classrooms.

The r-value of 0.652 shows a moderately strong positive correlation between increasing class sizes and GI scores. This is likely because hosting smaller classes is costly. This indicates that institutions with less funding (and accordingly more students with lower income) have greater student to teacher ratios. Since these trends are seen across nations and wealth quintiles, the data shows that smaller class sizes improves academic performance in isolation from other factors. The explanation behind the correlation’s strength is probably the fact that smaller class sizes allow for more personalized interaction with students, which can help properly identify their needs and foster a productive and fruitful learning environment; this subsequently helps improve the quality of education and reduce inequality.

The aforementioned claim is substantiated not only by the data compiled in this report, but in numerous other studies as well. Typically, smaller classes — which teachers consistently advocate for — outperform their larger counterparts. The Student/Teacher Achievement Ratio (STAR) clearly shows this; it was a class-size study in which over 7,000 students in 79 schools were randomly assigned into one of three interventions: small class (13-17 students per teacher), regular class (22-25 students per teacher), and regular-with-aide class (22-25 students per teacher with a full-time teacher's aide). These classes took place for the entirety of the students' education from the beginning of kindergarten to the end of grade three. During the grade eight final assessments for reading and mathematics, a significantly larger percent of small-class students passed the exam compared to their larger class counterparts. These discrepancies continued to grow as the years went on, showing a clear and lasting benefit of smaller class sizes (Woods, n.d.). Another example is Estonia’s education system, which is characterized by its low student to teacher ratios (some of the lowest in the OECD) (National Center on Education and the Economy, 2018). As shown in Figure 2, they also have one of the smallest gross inequality scores.

As mentioned before, if teachers were provided more agency in the decision-making process, class sizes would be expected to decrease. Figure 4 compares teacher participation in decision-making and average language class sizes. The r-value is -0.736 (a strong negative correlation) clearly showing that nations with more autonomous teachers also tend to have lower class sizes. This is partly due to the worldwide movement of teachers clamouring for smaller classes. During a teachers’ union meeting in Los Angeles, America, the call for smaller classes was second only to higher salaries, and a national survey of 50,000 Americans found that reducing class sizes was perceived to be the best way to reform schools (Woods, n.d.). Not only do less crowded classrooms allow students to benefit from having closer relationships with their instructors, but it gives teachers more time and flexibility to structure their classroom and lessons.

Proportion of Students in Special Needs Programs vs Inequality and Teacher Participation
Figure 5 shows the relation between the percentage of students in special needs programs and GI scores. The r-value of -0.453 shows a moderate negative correlation between these factors, indicating that a greater population of special needs students in a school corresponds to decreased inequality in education due to wealth.

This relationship is partly due to the importance of special needs programs in schools because of the personalized learning they provide. Numerous case studies have shown that personalized learning is highly beneficial to students because areas in which they require growth can be pinpointed and focused on. For example, the education system in Finland focuses on personalized learning strategies for students based on individual needs (Wilkins & Corrigan, 2019). As shown in Figure 2, Finland has one of the lowest GI scores. Predominantly, it is often seen that positive academic outcomes in students are dependent on how well their needs are met by the education system [Robson, 2019]. Therefore, an increased number of students in special needs programs would indicate that there is a greater population of students being given the personalized assistance that they require to succeed, increasing educational equity. The results lead to the conclusion that implementing various special needs programs in schools is very important. These programs, such as language proficiency aid and behavioural assistance via learning aides, not only benefit students in regards to their academic achievements but also promote a sense of belonging and equality in the school environment (New Brunswick Association for Community Living, n.d.). For instance, English as a Second Language (ESL) programs, in which immigrant students are provided with extra assistance in understanding English fundamentals, have been shown to provide immense benefit. Since such a program allows the student to better communicate with their peers, ESL results in an increase in self-confidence, comfort in the school environment, and academic achievement (Gonzales-Herrera, 2018).

As elaborated on previously, if teachers were allowed greater participation in decision-making, they would have the ability to use their experience to implement programs customized to benefit local students the most; in essence, teachers would be able to choose to advocate for a greater number of special needs programs for their students. Figure 5 compares teacher agency with the proportion of students in special needs programs, showing a somewhat strong positive correlation with an r-score of 0.490. Circling back to the example of increased personalization and reduced inequality in Finnish schools, it is important to note that teachers in Finland are given autonomy in classroom and managerial decisions. For instance, it is required for teachers to be included in school boards, where they would play a direct role in creating special needs programs (Wilkins & Corrigan, 2019; Varlas, 2011). Therefore, as increased proportions of students attaining personalized aid is shown to reduce inequality due to wealth (Figure 3), more teacher agency would indirectly support a reduction of inequality in this way as well.

Case studies
The trend of increased teacher agency being correlated with decreased educational inequality by wealth is mirrored in this paper’s findings. From the initial data analysis, several interesting results can be found when nations with the most and the least inequality are examined. In these case studies, first-world nations, like Macao, tended to achieve generally low GI scores. For Macao in particular, further analysis shows that nearly all learners achieved the minimum achievement levels, and both low-and-high earning families had a greater likelihood of achieving the highest ones. This uniformity likely indicates that high-quality academic resources are widely affordable, increasing educational equity among all learners.

Conversely, in areas like the Dominican Republic, many students (both high and low-earning) struggled to achieve basic achievement standards. Only 15.4% of students with families in the bottom-most income bracket achieved level 1 standards in mathematics; richer students scored much higher (56.5%), although it is worth noting that even the richest academic group in the Dominican Republic scored much lower than the poorest group in Macao. Higher performance levels were nearly completely dominated by learners from high-income families.

Confounding variables
Confounding variables are unmeasured third variables that can possibly influence the results of the analysis. There were a few confounding variables that were present in this research, one of them being age. To mitigate as many differences between age groups as possible, only data (PISA scores) from 15-year-olds was considered when compiling gross inequality values for each nation.

Another confounding variable was the socioeconomic climates of the examined nations. When discussing inequality in education, the factor considered was how academic performance varies for students from different wealth quintiles. The discrepancies between different wealth quintiles is different for each nation, which may explain the severity of the difference in scores between nations. Teacher agency is also impacted by the economic welfare of their country.

Since teachers would likely ask for a reallocation of funds towards education, a nation’s ability to provide funds depends on its financial state. This could explain the reason behind less developed nations having greater gross inequality scores (Figure 2). Therefore, it is not entirely accurate to assume that the correlation between teacher participation and gross inequality scores is a sole result of the nation’s education system.

Sources of error
The conclusions drawn by the data analysis are limited by several factors. For one, this methodology does not consider the distinction between the math, science, and reading indicators. By averaging them into one monolithic indicator, the analysis may overlook subtle differences in equity between disciplines. Additionally, the academic performance data in the WIDE dataset is an aggregate from several distinct surveys. Slight differences in survey methodology across nations could have contributed biases to the data. To minimize error, all studies chosen were conducted in 2015.

Additionally, the relatively small sample size coupled with the lack of outlier removal could have contributed to additional variance. While the number of samples per nation were relatively high, the fact that only 33 out of the world’s 193 nations are accounted for could have led to the statistics being analyzed being unrepresentative of the world’s true inequality distributions.

The two groups of relations studied were also not corrected of variables such as technological advancement and national academic environment, could be influencing the explanatory and response variables studied above.

CONCLUSIONS

The data suggests that as teacher participation increases in decision-making, inequality in education by wealth quintiles decreases. Furthermore, smaller class sizes are positively correlated to lower GI scores. The analysis of the relationship between class sizes and teacher agency indicates a clear desire from teachers for smaller class sizes. Figures 5 and 3 show that the percentage of students in special needs programs typically increases as teacher participation increases and decreases as gross inequality scores increase. This data supports the claim that allowing teachers more input in curriculum development and classroom practices helps reduce wealth-based educational inequality. Therefore, it is advised that teachers be provided with agency when it comes to large-scale decisions.

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ABOUT THE AUTHORS

William Zhou

William is a rising senior student attending Westmount Charter School in Calgary, Alberta. He enjoys tinkering with software and machine learning technology, and has aspirations of working as a medical professional in the future. Outside of academia, he enjoys playing guitar, sketching, and hiking.