Behind the Data: Analysis and Visualization of School and Student Data
Engaging mathematics teacher candidates in critical dialogue about NYC schools with technical tools
By Nadia S. Kennedy
Note: Quotes from interviews edited for length and clarity.
GO BACK TO ALL SPOTLIGHTS
We are Dr. Nadia Stoyanova Kennedy; Associate Professor, Mathematics Education; Dr. Boyan Kostadinov; Associate Professor, Mathematics, and Dr. Ariane Masuda; Professor, Mathematics – City Tech faculty interested in enriching mathematics teacher education by including more versatile and contemporary approaches to mathematical modeling.
Dr. Kennedy has taught mathematics education courses and is interested in incorporating critical inquiry into mathematics teacher education and mathematics secondary education. Dr. Kostadinov has been exploring the use of data science, visualization, and computational modeling in undergraduate education, and Dr. Masuda has taught mathematical modeling and advised undergraduate research modeling projects.
The three of us teamed up to conceptualize the forms of computational thinking and modeling that are present or possible in the mathematics education program at City Tech.
“Computational thinking and modeling can help our prospective mathematics teachers engage their students with more authentic mathematics problem solving and modeling with more efficient and powerful technology tools.”
Our team’s “Why” for CITE
Before the CITE initiative, we had already embarked on computing integration by designing and piloting computational modeling projects with prospective mathematics teachers. Joining CITE helped us layer on computational thinking (CT) and get support from a diverse group of colleagues. Initially, we were exclusively focused on introducing teacher candidates to programming and coding.
The CITE initiative helped us reconceptualize CS integration as a larger domain encompassing not only coding and computational modeling but digital literacy and the use of digital tools as well, accompanied by a critical stance on technology, mathematics, and their uses.
“We think an expanded conception of CS integration would be much more valuable to prospective teachers, not only in terms of enhancing their mathematics teaching, but also in preparing them to use various technology tools critically.
CITE is ideal in terms of offering experimental space where our team can learn, create, discuss, and try out our ideas and artifacts.“
Our Team’s Context
Our artifact integrates computing into MEDU 3003: Microteaching. This is a required course in the program curriculum of the Mathematics Education undergraduate program at City Tech. The course has a practice-oriented component, which includes 60 hours of intermediate field school-based experience, lesson and unit planning, student assessment design, and instruction delivery. Dr. Kennedy taught this course.
The course participants are undergraduate prospective teachers in their second or third year of the undergraduate degree who have completed an initial round of school observations of mathematics teaching and learning. At the completion of the program, they expect to obtain initial certificates and teach mathematics in grades 7 to 12 as full-time mathematics teachers in public NYC schools.
“MEDU 3003 involves micro-teaching – teaching small segments of lessons in real classrooms – which provides an appropriate context for prospective teachers to do some exploratory work with school data sets and perform data analysis to learn more about the schools and students they will work with.“
The teacher candidates are invariably diverse in terms of race, ethnicity, education experiences, and age. A large percentage of these students have completed their middle and high school education outside of the United States.
“Teacher candidates have read about the “achievement gap” and pervasive inequalities in learning opportunities. This artifact, we thought, would offer them the occasion not only to learn more about their placement schools and their students but also the chance to encounter head-on the drastic difference in the learning opportunities that NYC schools do (or don’t) provide and reflect on them.“
Our Intentions
Ultimately, we wanted to encourage prospective teachers to learn more about and to raise questions about their field-work schools and students and to draw conclusions about the educational opportunities available to students. The artifact was also intended to challenge prospective teachers’ beliefs and conceptions about education and schools. We grounded our work in themes that included (in)equity, school segregation, (in)equitable school funding, and availability of educational opportunities.
“The team wanted the prospective teachers to understand the deeper social issues that affect schools, education, and learning outcomes.“
We thought that it would be helpful for teacher candidates to leverage both qualitative methods – conducting observations and reading articles about NYC schools – and quantitative methods – analyzing numerical data about Brooklyn schools’ funding, demographics, and other academic characteristics.
On the quantitative side, we wanted to support prospective mathematics teachers in developing data-analytical and critical thinking skills. For the purposes of this artifact, the team used open data sets retrieved from NYC Open Data and databases from Miseducation (ProPublica.org). The team also wanted to expose prospective mathematics teachers to “R” — an integrated suite of software for data manipulation, calculation, and graphical display– so that prospective mathematics teachers would experience “the power of R,” and be motivated to learn more about using R in the future.
We also hoped that prospective teachers would experience how data analysis and data literacy could put their concrete experience into perspective and that it would help them understand it in the context of large social and educational phenomena. Towards those ends, we conducted discussions in line with a pedagogical model called “community of inquiry,” which is a model for collective, egalitarian, democratic, and collaborative deliberation. We hoped that this approach would foster participant agency.
Our Artifact
Our artifact engages prospective mathematics teachers in using data sets to learn more about the specific Brooklyn schools where they are placed for their micro-teaching field experience. It includes opportunities for prospective mathematics teachers to read articles, explore data sets, wonder, pose and answer questions, and engage in critical collective discussions.
We implemented the artifact over four consecutive 2.5-hour synchronous virtual sessions held over Zoom. Assignments involved readings and a few homework tasks. During the first three sessions, Dr. Kennedy and Dr. Masuda engaged the prospective mathematics teachers in discussing guiding questions for each session and in exploring the databases. Prospective teachers investigated the demographics of schools and the educational opportunities they offered (e.g., whether high-level math and statistics classes were available, the percentage of certified teachers, the available technology, etc.). Dr. Kennedy guided discussions around data visualization, interpretation, and analysis, supporting students in making sense of the readings and of the contexts prospective teachers encountered in the schools and in drawing conclusions from the data. During the last session, Dr. Kostadinov offered an immersive workshop on the statistical package, R.
Activities In A Nutshell
Creation of school profile THROUGH data analysis and creating visualizations
Teacher candidates explored given education data sets and analyzed and visualized data to develop a profile of their fieldwork schools. They also articulated questions about their schools’ student populations and educational opportunities, and they analyzed and interpreted data to answer them. Each candidate developed a short presentation with graphs about their school and its students and presented it to their peers.
Engagement and inquiry WITH data to understand educational inequity
Faculty and teacher candidates discussed the data that had already been collected about schools and students. Teacher candidates interpreted visualizations from various databases to compare and contrast schools and educational services in different parts of the country and in New York City in particular, where they explored relationships between variables (test scores, demographics, grades, etc.) in order to become aware of issues surrounding injustice, inequity, and segregation.
Critical discussions and reflections THROUGH data analysis
Each session ended with a discussion about critical educational issues such as quality education for all NYC students; available learning opportunities, school segregation, school funding and its effect on achievement, repercussions of segregated schools for students and society, and potential remedies to address school segregation.
Engagement WITH coding and data analysis with R
One session was devoted to introducing mathematics teacher candidates to R and using it to sort and filter databases to answer questions and visualize results.
Talking back FOR and AGAINST particular uses of big data
Faculty also guided conversations about the potential of using educational data sets and data analysis in mathematics teaching and learning. There were also discussions with teacher candidates around the limitations of big data sets and the interrogation of assumptions that may have been made in data collection and visualization. Teacher candidates discussed the limitations of data, specifically what details of a community or characteristics of students cannot be captured by data sets.
Activity Highlights
Creation of school profile THROUGH data analysis and creating visualizations
Before class sessions, prospective teachers were assigned to use the interactive map of the United States in the Miseducation (ProPublica) database and explore the Civil Rights Data Collection and/or other databases of their choice. They were asked to check the “Opportunity,” “Discipline,” and “Achievement Gap” tabs, the tabs “Black” and “Hispanic,” and to search for the school and district of their field experience in the databases, making notes of what they noticed in the results and writing down their questions.
Prospective teachers were asked to prepare a one-page report on what they discovered about their schools and school districts. In the reflection, they were asked to include detailed results, graphs, and tables from the databases and to be ready to share their findings in class. The excerpts of candidates’ findings, given below, show some very different school profiles.
Excerpt 1
Excerpt 2
Engagement and inquiry WITH data to understand educational inequity
Student work example
The teacher candidates read journals and newspaper articles, listened to an episode of The Daily, and used the data sets to investigate relationships between inequity, segregation, school funding, and achievement. Dr. Masuda guided the candidates’ inquiries in the second session by focusing their attention on the explored variables and modeling a search through the data sets and data analysis. The candidates found that about 51% of the nation’s school students are in “racially concentrated districts,” where over 75 percent of students are either white or nonwhite. They also found that both NYC schools and others where they were placed for field experience reflected that reality. Data overwhelmingly supported the conclusions drawn by the group: Black and Hispanic students are several times more likely to get suspended than White students. White students have significantly higher chances of being in advanced placement classes than Black or Hispanic students. Schools with higher percentages of Black and Hispanic students are likely to have lower graduation rates.
Next, Dr. Kennedy asked the teacher candidates to explore the learning opportunities various schools and districts offered and to determine whether NYC students received the same quality of education. Based on their findings, the candidates commented that schools with predominantly Black and Latinx student populations offered fewer AP classes, had much lower percentages of students enrolled as well as higher percentages of inexperienced and absent teachers, and higher numbers of total days missed due to out-of-school suspensions. Two candidates found that their school did not offer any AP Mathematics classes at all and that students’ college readiness (measured by how many students graduate with test scores high enough to enroll at CUNY without remedial help) was well below the city average.
Below is one candidate’s work:
Critical discussions and reflections THROUGH data analysis
Teacher candidates concluded that school segregation nowadays is driven by systemic inequality, and existing residential segregation in NYC (and the US) results in schools divided by race and socioeconomic status. The candidates’ analysis led to the conclusion that segregation and inequity profoundly affect minority students’ learning outcomes and thus acted to limit their future educational and job opportunities. Dr. Kennedy asked the teacher candidates to make a case for what should be done — or not done — to make New York City’s public schools more diverse and inclusive. Below are excerpts from some candidates’ reflections.
“The current process of funding schools is outdated, not equitable, and perpetuates school segregation. The government must reformulate the way schools are being funded, for example, by using entirely federal funding. It is imperative for schools from low-income neighborhoods to receive sufficient funds in order to provide the necessary resources and supplies needed.“ – Teacher Candidate
Engagement WITH coding and data analysis with R
Dr. Kostadinov introduced candidates to R Studio and to using R to sort and filter databases in order to answer questions, as well as to visualize results. First, he guided candidates to download R and R Studio and create a free account. Next, he instructed them on how to load the NYC DOE Data from the NYC Open Data base. Then he guided them in using Tidyverse, which is a collection of R packages to be used in the data analysis.
Next, Dr. Kostadinov guided the candidates in filtering data.
Then he engaged the candidates in exploratory data analysis to model fitting. The question that was explored was, “Is there a relationship between student ELA proficiency and math proficiency?”
Finally, the candidates were guided in writing a code to select a certain number of schools and create a chart documenting the percentage of students with math proficiency.
Talking back FOR and AGAINST particular uses of big data
Several candidates agreed that all this would be useful when they started looking for jobs and deciding whether they would or would not want to work at particular schools. One candidate noted that learning these skills helped him make a more informed decision in choosing a middle school for his daughter. Dr. Kennedy asked the teacher candidates about the potential they see in using data sets and data analysis in their mathematics teaching. Candidates shared that using data analysis helped them how to further investigate and search for jobs and schools for their own children. Moreover, the use of data sets and data analysis further their own understanding and use in enhancing mathematic lessons, providing context and social justice lens to mathematics.
Dr. Kennedy also guided a discussion with teacher candidates about the limitations of data, specifically what aspects of a community or students cannot be captured by data sets. The candidates observed that often important aspects are missing as the data sets contain only information that the designers have decided to collect. As they reflect the interests and preferences of the data set designers, they may omit what we may consider important. One candidate noted that he wanted to find more information about extracurricular activities in the middle schools that he was reviewing and comparing, but this information was not available.
What did the team learn through implementation?
During the implementation of the artifact, we found that we needed to do more modeling of data analysis and question posing for the candidates. The next time we iterate on the artifact, we plan to devote the entire first session to familiarizing ourselves with the data set, posing a few questions, and working collectively to answer those questions.
A “think aloud” strategy can be used to help orient the candidates in analyzing and using the data sets. We have also determined that we need to designate more days for the immersive workshop with R. Again, with the next iteration, we plan to allocate two additional sessions for data analysis with R. We also plan to give an assignment at the end, which will consist of designing a data analysis activity to be used in a math lesson. Candidates will share their activity designs in class.
Where do they want to go next?
Next, Drs. Kennedy, Kostadinov, and Masuda plan to pilot computational modeling activities with prospective mathematics teachers. They are conducting a research study this summer as well as a computational modeling workshop for prospective mathematics teachers and are excited about the study.
References and Resources
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- EdBuild (2019). 23 Billion. Retrieved from https://edbuild.org/content/23-billion
- Futterman, K. (2020). Education and Equality in NYC: The Problem at Hand. Retrieved from https://polygonnews.org/2299/showcase/education-and-equality-in-nyc-the-problem-at-hand/ on August 7, 2022.
- Hannah-Jones, H. (2016). Choosing a School for My Daughter in a Segregated City, New York Times Magazine, https://www.nytimes.com/2016/06/12/magazine/choosing-a-school-for-my-daughter-in-a-segregated-city.html
- Lefty, L. (2021). The Long Fight for Educational Equity in NYC. Retrieved from https://www.mcny.org/story/long-fight-educational-equity-nyc on August 1, 2022.
- Lombardo. C. (2019). Why White School Districts Have So Much More Money. Retrieved form https://www.npr.org/2019/02/26/696794821/why-white-school-districts-have-so-much-more-money.
- Maragkidou, M. (2015). Segregation, bullying and fear: The stunted education of Romani children in Europe. Retrieved from https://www.amnesty.org/en/latest/news/2015/04/the-stunted-education-of-romani-children-in-europe/
- Mervosh, S. (2019). How Much Wealthier Are White School Districts Than Nonwhite Ones? $23 Billion, Report Says. New York Times, Retrieved from https://www.nytimes.com/2019/02/27/education/school-districts-funding-white-minorities.html
- Gould, J. (2021). New York’s Schools are Still the Most Segregated in the Nation: Report. Retrieved from https://gothamist.com/news/new-yorks-schools-are-still-the-most-segregated-in-the-nation-report on July 25, 2022.
- Miseducation https://projects.propublica.org/miseducation/
- NYC OPEN DATA https://opendata.cityofnewyork.us/
- Robinson, G. (2013). Class in the Classroom: The Income Gap and NYC’s Schools. Retrieved at https://citylimits.org/2013/09/25/class-in-the-classroom-the-income-gap-and-nycs-schools/ on August 1, 2022.
- Shapiro, E. (2019). Facing Segregated Schools, Parents Took Integration into Their Own Hands. It’s Working, New York Times, https://www.nytimes.com/2019/04/16/nyregion/new-york-city-school-segregation.html
- Shapiro, E. (2021). Lawsuit Challenging N.Y.C. School Segregation Targets Gifted Programs, New York Times,
- Surk, B. (2018). In a Divided Bosnia, Segregated Schools Persist, The New York Times, https://www.nytimes.com/2018/12/01/world/europe/bosnia-schools-segregated-ethnic.html
