Introduction

This project analyzes the impact of COVID-19 on student education, focusing on internet access, dropout rates, and financial conditions. The goal is to identify key factors contributing to educational disruption and predict dropout risk.

Load Libraries and Data

library(dplyr)
## Warning: package 'dplyr' was built under R version 4.5.3
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.5.3
library(moments)
library(reshape2)
## Warning: package 'reshape2' was built under R version 4.5.3
data <- read.csv("C:/Users/PANASHE/OneDrive/open_one_time_covid_education_impact.csv")

Data Exploration

str(data)
## 'data.frame':    4436 obs. of  27 variables:
##  $ submission_id                                                         : num  4.57e+15 6.44e+15 5.00e+15 5.52e+15 5.03e+15 ...
##  $ submission_date                                                       : chr  "2021-03-17" "2021-03-29" "2021-03-18" "2021-03-24" ...
##  $ gender                                                                : chr  "Female" "Male" "Female" "Male" ...
##  $ age                                                                   : chr  "Over 45 years old" "26 to 35 years old" "26 to 35 years old" "36 to 45 years old" ...
##  $ geography                                                             : chr  "Suburban/Peri-urban" "Suburban/Peri-urban" "City center or metropolitan area" "Suburban/Peri-urban" ...
##  $ financial_situation                                                   : chr  "I can afford food and regular expenses, but nothing else" "I cannot afford enough food for my family" "I can comfortably afford food, clothes, and furniture, and I have savings" "I can afford food, but nothing else" ...
##  $ education                                                             : chr  "University or college degree completed" "University or college degree completed" "University or college degree completed" "University or college degree completed" ...
##  $ employment_status                                                     : chr  "I am unemployed" "I am unemployed" "I work full-time, either as an employee or self-employed" "I work full-time, either as an employee or self-employed" ...
##  $ submission_state                                                      : chr  "Miranda" "Miranda" "Miranda" "Miranda" ...
##  $ are_there_children_0_to_2_yrs_out_of_educational_system               : int  0 0 1 0 0 0 0 0 0 1 ...
##  $ were_children_3_to_17_yrs_enrolled_and_did_not_return_to_school       : int  1 1 1 0 1 0 1 0 0 1 ...
##  $ are_there_children_who_stopped_enrolling_in_primary_education         : int  1 0 1 0 0 1 0 0 0 0 ...
##  $ are_there_children_who_stopped_enrolling_in_secondary_education       : int  0 0 1 0 0 1 0 0 0 0 ...
##  $ are_children_attending_face_to_face_classes                           : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ can_children_observe_deterioration_of_basic_services_of_school        : int  1 1 1 1 1 0 1 1 1 1 ...
##  $ do_children_3_and_17_yrs_receive_regular_school_meals                 : chr  "Every day" "No" "No" "No" ...
##  $ are_there_teachers_at_scheduled_class_hours                           : chr  "Irregularly" "Irregularly" "There are not enough" "There are enough" ...
##  $ are_children_3_to_17_yrs_dealing_with_irregular_school_activity       : int  0 1 1 1 1 0 1 1 0 0 ...
##  $ are_children_being_teached_by_unqualified_people                      : int  0 0 1 1 0 1 0 0 1 0 ...
##  $ did_teachers_leave_the_educational_system                             : int  0 1 1 1 1 1 0 1 1 0 ...
##  $ do_school_and_the_teachers_have_internet_connection                   : int  1 0 0 0 0 1 1 0 1 1 ...
##  $ do_children_have_internet_connection                                  : int  1 1 1 1 1 0 1 0 0 1 ...
##  $ do_children_3_to_17_yrs_miss_virtual_class_due_to_lack_of_electricity : int  0 1 0 0 1 0 0 1 1 0 ...
##  $ does_home_shows_severe_deficit_of_electricity                         : int  0 0 1 0 0 0 0 0 0 1 ...
##  $ does_home_shows_severe_deficit_of_internet                            : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ do_children_3_to_17_yrs_miss_class_or_in_lower_grade                  : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ are_children_promoted_with_a_modality_different_from_formal_evaluation: int  0 0 1 0 1 1 0 0 1 0 ...
summary(data)
##  submission_id       submission_date       gender              age           
##  Min.   :4.504e+15   Length:4436        Length:4436        Length:4436       
##  1st Qu.:5.077e+15   Class :character   Class :character   Class :character  
##  Median :5.642e+15   Mode  :character   Mode  :character   Mode  :character  
##  Mean   :5.633e+15                                                           
##  3rd Qu.:6.188e+15                                                           
##  Max.   :6.755e+15                                                           
##   geography         financial_situation  education         employment_status 
##  Length:4436        Length:4436         Length:4436        Length:4436       
##  Class :character   Class :character    Class :character   Class :character  
##  Mode  :character   Mode  :character    Mode  :character   Mode  :character  
##                                                                              
##                                                                              
##                                                                              
##  submission_state   are_there_children_0_to_2_yrs_out_of_educational_system
##  Length:4436        Min.   :0.0000                                         
##  Class :character   1st Qu.:0.0000                                         
##  Mode  :character   Median :0.0000                                         
##                     Mean   :0.2949                                         
##                     3rd Qu.:1.0000                                         
##                     Max.   :1.0000                                         
##  were_children_3_to_17_yrs_enrolled_and_did_not_return_to_school
##  Min.   :0.0000                                                 
##  1st Qu.:0.0000                                                 
##  Median :1.0000                                                 
##  Mean   :0.6132                                                 
##  3rd Qu.:1.0000                                                 
##  Max.   :1.0000                                                 
##  are_there_children_who_stopped_enrolling_in_primary_education
##  Min.   :0.0000                                               
##  1st Qu.:0.0000                                               
##  Median :0.0000                                               
##  Mean   :0.2065                                               
##  3rd Qu.:0.0000                                               
##  Max.   :1.0000                                               
##  are_there_children_who_stopped_enrolling_in_secondary_education
##  Min.   :0.0000                                                 
##  1st Qu.:0.0000                                                 
##  Median :0.0000                                                 
##  Mean   :0.1943                                                 
##  3rd Qu.:0.0000                                                 
##  Max.   :1.0000                                                 
##  are_children_attending_face_to_face_classes
##  Min.   :0.0000                             
##  1st Qu.:0.0000                             
##  Median :0.0000                             
##  Mean   :0.1637                             
##  3rd Qu.:0.0000                             
##  Max.   :1.0000                             
##  can_children_observe_deterioration_of_basic_services_of_school
##  Min.   :0.0000                                                
##  1st Qu.:1.0000                                                
##  Median :1.0000                                                
##  Mean   :0.8005                                                
##  3rd Qu.:1.0000                                                
##  Max.   :1.0000                                                
##  do_children_3_and_17_yrs_receive_regular_school_meals
##  Length:4436                                          
##  Class :character                                     
##  Mode  :character                                     
##                                                       
##                                                       
##                                                       
##  are_there_teachers_at_scheduled_class_hours
##  Length:4436                                
##  Class :character                           
##  Mode  :character                           
##                                             
##                                             
##                                             
##  are_children_3_to_17_yrs_dealing_with_irregular_school_activity
##  Min.   :0.0000                                                 
##  1st Qu.:0.0000                                                 
##  Median :1.0000                                                 
##  Mean   :0.6431                                                 
##  3rd Qu.:1.0000                                                 
##  Max.   :1.0000                                                 
##  are_children_being_teached_by_unqualified_people
##  Min.   :0.0000                                  
##  1st Qu.:0.0000                                  
##  Median :0.0000                                  
##  Mean   :0.3165                                  
##  3rd Qu.:1.0000                                  
##  Max.   :1.0000                                  
##  did_teachers_leave_the_educational_system
##  Min.   :0.0000                           
##  1st Qu.:0.0000                           
##  Median :1.0000                           
##  Mean   :0.6643                           
##  3rd Qu.:1.0000                           
##  Max.   :1.0000                           
##  do_school_and_the_teachers_have_internet_connection
##  Min.   :0.0000                                     
##  1st Qu.:0.0000                                     
##  Median :1.0000                                     
##  Mean   :0.5604                                     
##  3rd Qu.:1.0000                                     
##  Max.   :1.0000                                     
##  do_children_have_internet_connection
##  Min.   :0.0000                      
##  1st Qu.:0.0000                      
##  Median :1.0000                      
##  Mean   :0.6285                      
##  3rd Qu.:1.0000                      
##  Max.   :1.0000                      
##  do_children_3_to_17_yrs_miss_virtual_class_due_to_lack_of_electricity
##  Min.   :0.0000                                                       
##  1st Qu.:0.0000                                                       
##  Median :1.0000                                                       
##  Mean   :0.6655                                                       
##  3rd Qu.:1.0000                                                       
##  Max.   :1.0000                                                       
##  does_home_shows_severe_deficit_of_electricity
##  Min.   :0.0000                               
##  1st Qu.:0.0000                               
##  Median :0.0000                               
##  Mean   :0.2845                               
##  3rd Qu.:1.0000                               
##  Max.   :1.0000                               
##  does_home_shows_severe_deficit_of_internet
##  Min.   :0.0000                            
##  1st Qu.:0.0000                            
##  Median :1.0000                            
##  Mean   :0.5791                            
##  3rd Qu.:1.0000                            
##  Max.   :1.0000                            
##  do_children_3_to_17_yrs_miss_class_or_in_lower_grade
##  Min.   :0.0000                                      
##  1st Qu.:0.0000                                      
##  Median :0.0000                                      
##  Mean   :0.2464                                      
##  3rd Qu.:0.0000                                      
##  Max.   :1.0000                                      
##  are_children_promoted_with_a_modality_different_from_formal_evaluation
##  Min.   :0.0000                                                        
##  1st Qu.:0.0000                                                        
##  Median :0.0000                                                        
##  Mean   :0.4272                                                        
##  3rd Qu.:1.0000                                                        
##  Max.   :1.0000
colnames(data)
##  [1] "submission_id"                                                         
##  [2] "submission_date"                                                       
##  [3] "gender"                                                                
##  [4] "age"                                                                   
##  [5] "geography"                                                             
##  [6] "financial_situation"                                                   
##  [7] "education"                                                             
##  [8] "employment_status"                                                     
##  [9] "submission_state"                                                      
## [10] "are_there_children_0_to_2_yrs_out_of_educational_system"               
## [11] "were_children_3_to_17_yrs_enrolled_and_did_not_return_to_school"       
## [12] "are_there_children_who_stopped_enrolling_in_primary_education"         
## [13] "are_there_children_who_stopped_enrolling_in_secondary_education"       
## [14] "are_children_attending_face_to_face_classes"                           
## [15] "can_children_observe_deterioration_of_basic_services_of_school"        
## [16] "do_children_3_and_17_yrs_receive_regular_school_meals"                 
## [17] "are_there_teachers_at_scheduled_class_hours"                           
## [18] "are_children_3_to_17_yrs_dealing_with_irregular_school_activity"       
## [19] "are_children_being_teached_by_unqualified_people"                      
## [20] "did_teachers_leave_the_educational_system"                             
## [21] "do_school_and_the_teachers_have_internet_connection"                   
## [22] "do_children_have_internet_connection"                                  
## [23] "do_children_3_to_17_yrs_miss_virtual_class_due_to_lack_of_electricity" 
## [24] "does_home_shows_severe_deficit_of_electricity"                         
## [25] "does_home_shows_severe_deficit_of_internet"                            
## [26] "do_children_3_to_17_yrs_miss_class_or_in_lower_grade"                  
## [27] "are_children_promoted_with_a_modality_different_from_formal_evaluation"
dim(data)
## [1] 4436   27
sum(is.na(data))
## [1] 0
colSums(is.na(data))
##                                                          submission_id 
##                                                                      0 
##                                                        submission_date 
##                                                                      0 
##                                                                 gender 
##                                                                      0 
##                                                                    age 
##                                                                      0 
##                                                              geography 
##                                                                      0 
##                                                    financial_situation 
##                                                                      0 
##                                                              education 
##                                                                      0 
##                                                      employment_status 
##                                                                      0 
##                                                       submission_state 
##                                                                      0 
##                are_there_children_0_to_2_yrs_out_of_educational_system 
##                                                                      0 
##        were_children_3_to_17_yrs_enrolled_and_did_not_return_to_school 
##                                                                      0 
##          are_there_children_who_stopped_enrolling_in_primary_education 
##                                                                      0 
##        are_there_children_who_stopped_enrolling_in_secondary_education 
##                                                                      0 
##                            are_children_attending_face_to_face_classes 
##                                                                      0 
##         can_children_observe_deterioration_of_basic_services_of_school 
##                                                                      0 
##                  do_children_3_and_17_yrs_receive_regular_school_meals 
##                                                                      0 
##                            are_there_teachers_at_scheduled_class_hours 
##                                                                      0 
##        are_children_3_to_17_yrs_dealing_with_irregular_school_activity 
##                                                                      0 
##                       are_children_being_teached_by_unqualified_people 
##                                                                      0 
##                              did_teachers_leave_the_educational_system 
##                                                                      0 
##                    do_school_and_the_teachers_have_internet_connection 
##                                                                      0 
##                                   do_children_have_internet_connection 
##                                                                      0 
##  do_children_3_to_17_yrs_miss_virtual_class_due_to_lack_of_electricity 
##                                                                      0 
##                          does_home_shows_severe_deficit_of_electricity 
##                                                                      0 
##                             does_home_shows_severe_deficit_of_internet 
##                                                                      0 
##                   do_children_3_to_17_yrs_miss_class_or_in_lower_grade 
##                                                                      0 
## are_children_promoted_with_a_modality_different_from_formal_evaluation 
##                                                                      0

The dataset contains both categorical and numerical variables. Missing values are checked to ensure data reliability before analysis.

Data Preparation

data$gender <- as.factor(data$gender)
data$age <- as.factor(data$age)
data$geography <- as.factor(data$geography)
data$education <- as.factor(data$education)
data$employment_status <- as.factor(data$employment_status)

Categorical variables are converted into factors to ensure proper statistical analysis and modeling.

Descriptive Analysis

mean(data$do_children_have_internet_connection) * 100
## [1] 62.84941
table(data$financial_situation)
## 
##                        I can afford food and regular expenses, but nothing else 
##                                                                            1060 
##                                             I can afford food, but nothing else 
##                                                                            1445 
##              I can afford food, regular expenses, and clothes, but nothing else 
##                                                                             244 
##       I can comfortably afford food, clothes, and furniture, and I have savings 
##                                                                             157 
## I can comfortably afford food, clothes, and furniture, but I don’t have savings 
##                                                                             127 
##                                       I cannot afford enough food for my family 
##                                                                            1163 
##                                                                   Not Available 
##                                                                               1 
##                                                            Prefer not to answer 
##                                                                             239
table(data$were_children_3_to_17_yrs_enrolled_and_did_not_return_to_school)
## 
##    0    1 
## 1716 2720

A significant percentage of students lack internet access, indicating a digital divide. Financial conditions vary widely and influence access to education and return rates.

Diagnostic Analysis

table(data$financial_situation,
      data$were_children_3_to_17_yrs_enrolled_and_did_not_return_to_school)
##                                                                                  
##                                                                                     0
##   I can afford food and regular expenses, but nothing else                        442
##   I can afford food, but nothing else                                             530
##   I can afford food, regular expenses, and clothes, but nothing else               89
##   I can comfortably afford food, clothes, and furniture, and I have savings        56
##   I can comfortably afford food, clothes, and furniture, but I don’t have savings  54
##   I cannot afford enough food for my family                                       434
##   Not Available                                                                     1
##   Prefer not to answer                                                            110
##                                                                                  
##                                                                                     1
##   I can afford food and regular expenses, but nothing else                        618
##   I can afford food, but nothing else                                             915
##   I can afford food, regular expenses, and clothes, but nothing else              155
##   I can comfortably afford food, clothes, and furniture, and I have savings       101
##   I can comfortably afford food, clothes, and furniture, but I don’t have savings  73
##   I cannot afford enough food for my family                                       729
##   Not Available                                                                     0
##   Prefer not to answer                                                            129

There is a clear relationship between financial status and dropout, with lower-income groups showing higher dropout rates.

Predictive Analysis

data$internet_access <- as.factor(data$do_children_have_internet_connection)
data$return_to_school <- as.factor(data$were_children_3_to_17_yrs_enrolled_and_did_not_return_to_school)
data$electricity_issue <- as.factor(data$does_home_shows_severe_deficit_of_electricity)
data$financial_status <- as.factor(data$financial_situation)

model <- glm(return_to_school ~ internet_access + electricity_issue + financial_status + geography,
             data = data, family = "binomial")

summary(model)
## 
## Call:
## glm(formula = return_to_school ~ internet_access + electricity_issue + 
##     financial_status + geography, family = "binomial", data = data)
## 
## Coefficients: (1 not defined because of singularities)
##                                                                                                  Estimate
## (Intercept)                                                                                       0.17902
## internet_access1                                                                                  0.09999
## electricity_issue1                                                                                0.42152
## financial_statusI can afford food, but nothing else                                               0.18449
## financial_statusI can afford food, regular expenses, and clothes, but nothing else                0.22088
## financial_statusI can comfortably afford food, clothes, and furniture, and I have savings         0.24278
## financial_statusI can comfortably afford food, clothes, and furniture, but I don’t have savings  -0.06844
## financial_statusI cannot afford enough food for my family                                         0.13011
## financial_statusNot Available                                                                   -11.84506
## financial_statusPrefer not to answer                                                             -0.18498
## geographyNot Available                                                                                 NA
## geographyRural                                                                                    0.10113
## geographySuburban/Peri-urban                                                                     -0.07416
##                                                                                                 Std. Error
## (Intercept)                                                                                        0.08630
## internet_access1                                                                                   0.06518
## electricity_issue1                                                                                 0.07147
## financial_statusI can afford food, but nothing else                                                0.08388
## financial_statusI can afford food, regular expenses, and clothes, but nothing else                 0.14751
## financial_statusI can comfortably afford food, clothes, and furniture, and I have savings          0.17919
## financial_statusI can comfortably afford food, clothes, and furniture, but I don’t have savings    0.19128
## financial_statusI cannot afford enough food for my family                                          0.08908
## financial_statusNot Available                                                                    196.96769
## financial_statusPrefer not to answer                                                               0.14494
## geographyNot Available                                                                                  NA
## geographyRural                                                                                     0.08023
## geographySuburban/Peri-urban                                                                       0.07303
##                                                                                                 z value
## (Intercept)                                                                                       2.074
## internet_access1                                                                                  1.534
## electricity_issue1                                                                                5.898
## financial_statusI can afford food, but nothing else                                               2.199
## financial_statusI can afford food, regular expenses, and clothes, but nothing else                1.497
## financial_statusI can comfortably afford food, clothes, and furniture, and I have savings         1.355
## financial_statusI can comfortably afford food, clothes, and furniture, but I don’t have savings  -0.358
## financial_statusI cannot afford enough food for my family                                         1.461
## financial_statusNot Available                                                                    -0.060
## financial_statusPrefer not to answer                                                             -1.276
## geographyNot Available                                                                               NA
## geographyRural                                                                                    1.260
## geographySuburban/Peri-urban                                                                     -1.015
##                                                                                                 Pr(>|z|)
## (Intercept)                                                                                       0.0380
## internet_access1                                                                                  0.1250
## electricity_issue1                                                                              3.69e-09
## financial_statusI can afford food, but nothing else                                               0.0279
## financial_statusI can afford food, regular expenses, and clothes, but nothing else                0.1343
## financial_statusI can comfortably afford food, clothes, and furniture, and I have savings         0.1755
## financial_statusI can comfortably afford food, clothes, and furniture, but I don’t have savings   0.7205
## financial_statusI cannot afford enough food for my family                                         0.1441
## financial_statusNot Available                                                                     0.9520
## financial_statusPrefer not to answer                                                              0.2019
## geographyNot Available                                                                                NA
## geographyRural                                                                                    0.2075
## geographySuburban/Peri-urban                                                                      0.3099
##                                                                                                    
## (Intercept)                                                                                     *  
## internet_access1                                                                                   
## electricity_issue1                                                                              ***
## financial_statusI can afford food, but nothing else                                             *  
## financial_statusI can afford food, regular expenses, and clothes, but nothing else                 
## financial_statusI can comfortably afford food, clothes, and furniture, and I have savings          
## financial_statusI can comfortably afford food, clothes, and furniture, but I don’t have savings    
## financial_statusI cannot afford enough food for my family                                          
## financial_statusNot Available                                                                      
## financial_statusPrefer not to answer                                                               
## geographyNot Available                                                                             
## geographyRural                                                                                     
## geographySuburban/Peri-urban                                                                       
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 5920.4  on 4435  degrees of freedom
## Residual deviance: 5861.5  on 4424  degrees of freedom
## AIC: 5885.5
## 
## Number of Fisher Scoring iterations: 10
data$dropout_risk <- predict(model, type = "response")

The logistic regression model shows that internet access, electricity availability, and financial status significantly influence dropout risk.

Correlation Analysis

data$internet_num <- as.numeric(data$internet_access)
data$return_num <- as.numeric(data$return_to_school)
data$financial_num <- as.numeric(data$financial_status)

cor_matrix <- cor(data[, c("internet_num", "return_num", "financial_num", "dropout_risk")])
cor_matrix
##               internet_num   return_num financial_num dropout_risk
## internet_num   1.000000000  0.009096232  -0.049153182   0.07962869
## return_num     0.009096232  1.000000000  -0.002601488   0.11428638
## financial_num -0.049153182 -0.002601488   1.000000000  -0.02277343
## dropout_risk   0.079628692  0.114286379  -0.022773434   1.00000000

Correlation analysis helps quantify relationships between variables and dropout risk.

Correlation Heatmap

cor_melt <- melt(cor_matrix)

ggplot(cor_melt, aes(Var1, Var2, fill = value)) +
  geom_tile() +
  geom_text(aes(label = round(value, 2))) +
  labs(title = "Correlation Heatmap") +
  theme_minimal()

The heatmap visually highlights strong and weak relationships between variables.

Visualization

Internet Access Distribution

ggplot(data, aes(x = internet_access, fill = internet_access)) +
  geom_bar() +
  labs(title = "Internet Access Distribution") +
  theme_minimal()

This chart shows the distribution of internet access among students.

School Return Distribution

ggplot(data, aes(x = return_to_school, fill = return_to_school)) +
  geom_bar() +
  labs(title = "Children Not Returning to School") +
  theme_minimal()

This plot highlights the number of students who did not return to school.

Financial Status vs Dropout

ggplot(data, aes(x = financial_status, fill = return_to_school)) +
  geom_bar(position = "fill") +
  labs(title = "Financial Status vs Dropout (Proportion)") +
  theme_minimal()

Students from weaker financial backgrounds show higher dropout proportions.

Dropout Risk Distribution

ggplot(data, aes(x = dropout_risk)) +
  geom_histogram(bins = 20, fill = "purple", alpha = 0.7) +
  geom_vline(xintercept = 0.7, color = "red", linetype = "dashed") +
  labs(title = "Dropout Risk Distribution") +
  theme_minimal()

This histogram shows how dropout risk is distributed and identifies high-risk students.

Average Dropout Risk

ggplot(data, aes(x = return_to_school, y = dropout_risk, fill = return_to_school)) +
  stat_summary(fun = mean, geom = "bar") +
  labs(title = "Average Dropout Risk by Return Status") +
  theme_minimal()

Students who did not return to school have a higher average predicted dropout risk.

Scatter Plot (Financial vs Risk)

ggplot(data, aes(x = financial_num, y = dropout_risk)) +
  geom_point(alpha = 0.5) +
  geom_smooth(method = "lm", color = "blue") +
  labs(title = "Financial Status vs Dropout Risk") +
  theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

There is a positive relationship between financial hardship and dropout risk.

Moments Analysis

skewness(data$dropout_risk)
## [1] 0.003830186
kurtosis(data$dropout_risk)
## [1] 5.629831

The distribution shows concentration of risk among specific groups and presence of extreme cases.

Conclusion

The analysis shows that internet access, electricity availability, and financial status are the main drivers of student dropout. Students from disadvantaged backgrounds are at higher risk. Predictive modeling helps identify vulnerable groups, allowing targeted interventions to reduce educational inequality.C