Chapter 5 Results
5.1 Distribution of School Scores
Before we make any comparison between the NYC schools, we first have a look at the distribution of school scores given from students’, teachers’ and parents’ perspective. In order to do that, we make density plots of the scores faceted by five components (we drop supportive environment score because we know from chapter 4 that it has nearly 100% missing values).
We know from the plot that the distribution of school scores in these five aspects are not normally distributed. In fact, they are left-skewed, with long-tail data distributing in the left side of the plot.
5.2 Top 10 performance schools
5.2.1 Top 10 schools in five aspects
Firstly, we sort the schools according to the five aforementioned aspects. In this way, we made a leaderboard for top 10 schools with the most collaborative teachers, top 10 schools with the most effective school leadership, top 10 schools with highest trust score, top 10 schools with the most rigid instructions, and top 10 schools with the strongest family-community ties.
5.2.2 Top 10 Schools with the highest comprehensive scores
Sometimes it is necessary to evaluate the schools in a more comprehensive way. Therefore, we take all the five aspects into consideration and calculate a comprehensive school performance score by taking the average of all the scores in five aspects. Then we made a leaderboard of the “Best” 10 Schools in NYC.
The best 10 schools in NYC are:
## [1] "COMMUNITY SCHOOL FOR SOCIAL JUSTICE" "P.S. 321 WILLIAM PENN"
## [3] "THE BROOKLYN NEW SCHOOL, P.S. 146" "KENNEDY YABC"
## [5] "HELLENIC CLASSICAL CHARTER SCHOOL" "P.S. 253"
## [7] "P.S. 041 CROCHERON" "HS ARTS & BUSINESS YABC"
## [9] "P.S. 065" "P.S. 112 LEFFERTS PARK"
As we can read from this graph, some schools, like Community School for Social Justice, HS Arts & Business YABC ranked high in several aspects, thus have a high comprehensive score. There are other schools, like Manhattan Center for Science and Mathematics, that ranked high only in particular aspects.
5.3 Dependency Relationships analysis
Apart from the scores given by the Department of Education of NYC, we also evaluate the performance of each school from the perspective of students, teachers and parents based on their answers to the questionnaire directly.
In this section, we are going to look at the relationship of school scores given from different perspectives.
5.3.1 Do Teachers and Parents feel the same about Family-Community bond?
Both teachers and parents have answered some questions about their feelings on the family-community bond in their schools. For example, in the questionnaire for teachers, there are several statements like “teachers understand families’ problems and concerns.” Meanwhile, in the questionnaire for parents, there are statements like “School staff regularly communicate with me about how I can help my child learn.”. Parents and teachers are asked to give the degree in which they agree to such statements, such as “strongly agree”,“agree”,“disagree”,“strongly disagree”,“I don’t know”. In this way, we are able to analyze whether teachers and parents feel the same about the family-community bond in their schools.
In order to make our analysis easier, we firstly derive a family-community bond score for each school from parents’ and teachers’ point of view respectively. More specifically, we calculate the percentage of strongly agree,agree,disagree,strongly disagree,idk, and add +2 points for strongly agree, +1 point for agree, -1 point for disagree, -2 points for strongly disagree and +0 point for I don't know.
The scores given by teachers and parents are clearly positively correlated:
The correlation coefficient is:
## [1] 0.48121625.3.2 Do teachers and students feel the same on inclusion at school?
Teachers and students have answered some questions about their feelings on inclusion in their schools from their own perspectives. In this way, we are able to analysis whether teachers and students have a consensus on inclusion.
In order to make our analysis easier, we firstly calculate a student inclusion score for each school from students’ and teachers’ point of view respectively, using the formula mentioned in 5.3.1.
The scores given by students and teachers are also positively correlated:
The correlation coefficient is:
## [1] 0.4137645.3.3 Do teachers and students feel the same about aggressive behaviors?
Both teachers and students have answered some questions on aggressive behaviors in their schools. For example, they are asked to rate how frequent such aggressive behaviors happens, with response choices as “none”,“rarely”,“some”,“most”. In this way, we are able to analyze whether teachers and students feel the same about the aggressive behaviors in their schools.
In order to make our analysis easier, we firstly derive a score for each school from students’ and teachers’ point of view respectively. More specifically, we calculate the percentage of none,rarely,some,most, and add +2 points for none, +1 point for rarely, -1 point for some, -2 points for most.
The scores given by students and teachers are also positively correlated:
The correlation coefficient is:
## [1] 0.67651925.4 Do parents, students and teachers feel the same about teaching quality?
Students, teachers and parents have all answered some questions on teaching quality in their respective schools. Due to inconsistencies in answer choices, we have generalized the response based on degree of positivity(“strongly positive”, “positive”, “negative”, “strongly negative”, “i don’t know”). In this way, we are able to analyze whether parents, teachers and students feel the same about teaching quality.
In order to make our analysis easier, we firstly derive a score for each school from students’, parents’ and teachers’ point of view respectively. More specifically, we calculate the percentage of strongly positive,positive,negative,strongly negative, and add +2 points for strongly positive, +1 point for positive, -1 point for negative, -2 points for strongly negative.
The relationship between the score given by parents, students and teachers are plotted in the following scatterplot:
The score given by teachers and parents are positively correlated. However, the score given by students are negatively correlated with the score given by teachers and parents. Moreover, students tend to give lower scores to their teachers while teachers and parents tend to give higher score to teaching quality.
This is reasonable since students might have different ideas with adults about what good education is. They might dislike those teachers who impose stringent disciplines and assign a lot of homework. Additionally there could be subjective bias due to the positions that each of them holds.
5.5 The relationship between teaching quality and students’ performance
As we hypothesized, teaching quality would be positively related to students’ performance. Thus, we decided to create a scatter plot and look into the relationship between these two variables. Note that we have calculated the student performance score solely based on teachers’ perspectives, while the teaching quality is assessed by all three perspective (teachers, students, parents)
The result support our hypothesis mentioned above. The students’ performance score is positively correlated with the teaching quality score given by teachers and parents, while negatively correlated with the teaching quality score given by students themselves. It’s interesting to find out this negative relationship and made us wonder does students’ attitude toward teachers plays a role in students’ achievement.
We have also computed a average teaching quality score based on the feedback from all three perspectives and looked into its relationship with student performance.
## [1] 0.529755This averaged teaching quality score aligns with our hypothesis, such that teaching quality would be positively related to students’ performance.
5.6 The relationship between teachers’ trust/collaboration/respect with teaching quality
In this survey, teachers are also asked several questions about their feelings towards the trust, collaboration and respect between teachers in their schools. We believe that a healthy environment in teacher community is beneficial to the teaching quality. Therefore, in this section we investigate whether this hypothesis is true.
From the scatterplot above we notice that the trust, collaboration and respect between teachers are closely correlated with themselves, and are also strongly correlated with the teaching quality scores given by teachers themselves. However, such correlation is weaker for the teaching quality scores given by parents, and is negatively correlated with the teaching quality scores given by students.
5.7 The relationship between parents’, students’ and teachers’ feeling about teaching quality
Interested in the diversed opinions on teaching quality, we decided to look into this more by creating a parallel coordinate graph.
To make our graph easier to read, we have shorted the labels of the categories: st_v_n: student whose rating is very negative st_n: student whose rating is negative st_p: student whose rating is positive st_v_p: student whose rating is very positive t_v_n: teacher whose rating is very negative t_n: teacher whose rating is negative t_p: student whose rating is positive t_v_p: teacher whose rating is very positive p_v_n: parent whose rating is very negative p_n: parent whose rating is negative p_p: parent whose rating is positive p_v_p: parent whose rating is very positive