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Math Class Meets the Real World:The Promise of Data Science Modeling
By Chris Bolognese, McElroy Master Chair in Math; Mathematics & Computer Science, Upper School, Columbus Academy
🎥 Video Interview: DS4E Communications Specialist Shea Stripling speaks with Chris Bolognese, McElroy Master Chair in Math; Mathematics & Computer Science, Upper School, Columbus Academy, about rethinking mathematical modeling through data science and empowering students to use data to investigate real-world problems.
Ask five different educators what “modeling” means, and you’ll likely hear five different definitions.
To a physics teacher, it’s a free-body diagram showing the forces acting on an object. To an English teacher, it’s a framework to deconstruct a persuasive essay. To a computer scientist, it might be a Unified Modeling Language (UML) diagram showing inheritance relationships.
As a high school mathematics and computer science teacher with over two decades of experience, I have found that “modeling” is one of the most heavily used buzzwords in education. Yet, its meaning shifts completely depending on the hallway you’re standing in. Moreover, modeling in school is often disconnected from how modeling operates in the real world.
Nowhere is this ambiguity sharper than in math education. The sterile modeling found in a typical math textbook is worlds apart from how modeling actually functions in our data-drenched society. While some might see this gap as a crisis, I see it as an unprecedented opportunity. Math teachers, and educators generally, are positioned to revolutionize how we approach modeling by introducing students to data science. By expanding our definition of what a “model” can be, we can help students use mathematics and data to investigate and address a broad range of issues in ways that are connected to our curricula and modern problem solving practices.
Traditional Mathematical Modeling: From Theory to Data
Traditional mathematical modeling is a top-down process that moves from theory to data. In my experience, classic classroom projects often attempt to bring mathematics to life, such as having students measure the height of a flagpole using right-triangle trigonometry—an activity I even assigned early in my teaching career. In traditional mathematical modeling, students begin with a known formula or theorem, such as ,
and apply it to solve a closed problem. The goal is simply to find the right mathematical tool to map onto a clean, oversimplified system. In this paradigm, the main objective is to apply an established mathematical relationship, such as an equation, and use that representation to model a well-defined problem.
However, it is often a dead end. In the flagpole example, students get an answer and move on. There is rarely an opportunity to iterate on the process, handle unexpected results, or discover a fundamentally different way to estimate its height. Moreover, what is the reason for measuring its height in the first place?
In essence, traditional modeling prevalant in many schools is modeling without agency: students lack choice in the context, the problem-solving methods, the tools utilized, the opportunity to iterate, or the way to communicate their findings.
Data Science Modeling: From Data to Theory
Data science flips this script entirely. It relies on a bottom-up approach: it moves from data to theory. Instead of starting with a rigid physical law, a data science model can begin with a question or data. Students don’t assume a particular relationship (e.g., linear or exponential) beforehand. In fact, they don’t start with an equation at all.
Consider a real-world data science lesson developed by the curriculum non-profit Skew The Script that I used in my own classroom: predicting student loan default rates. A traditional math approach might try to force a simple line of best fit between total debt and likelihood of defaulting. A data science model, however, considers multiple variables separately or simultaneously: zip codes, family income brackets, intended majors, tuition costs, and institutional graduation rates, to name a few.
The goal here isn’t to write a formula; it is to explore multiple relationships to determine which variables are most associated with student loan default rates in an attempt to make predictions about what types of students might default. This type of modeling can begin by examining the relationship between a single variable and default rates. From there, the analysis can progress to adding additional variables and even using computer software to investigate the effects of multiple variables simultaneously. At some point the process ends, but only after cycles of testing and refinement. If the goal is explanation, the process may result in a model with only a couple of variables, whose impact on the outcome can be interpreted. If the goal is prediction, the same process could produce a more complex model that produces accurate predictions, even if the effects of individual variables is less interpretable.
In data science modeling, students must make choices that are not predetermined by mathematical equations. This philosophy represented a significant shift in my own thinking during my master’s studies in data science and has continued to shape how I teach the subject today.
What This Means for Education
Embracing a data science modeling paradigm can breathe life into every subject area. My data science students partnered with English students to use computational tools to model the emotional arc of characters in Macbeth. Social studies students can move past static historical maps to build models that represent voting trends, exploring how shifting population dynamics can reshape the political landscape. In the sciences, students can develop models using live sensor data from local ecosystems, rather than relying solely on data collected in a classroom lab.
But I have found the most profound transformation happens when you bring data science into the math classroom, turning the subject into a launchpad for relevance. We no longer need to measure the heights of flagpoles just because a textbook published twenty years ago says so. Data science modeling empowers students to reveal and quantify patterns and trends in their own communities. In contrast to traditional modeling, students engaged in data science engage in modeling with agency: they decide the data sources, they make justified decisions about how to clean a dataset, they decide which visualizations best justify their questions, and they decide how to communicate their findings.
Defining the Shift
As another example of data science modeling in action, geographic information systems (GIS) data can be cross-referenced with healthy grocery store locations and unhealthy fast food chains or convenience stores in their community. Students can use this information to construct maps to identify local food deserts. Here is one for my home town of Columbus, Ohio:
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In traditional mathematical modeling, students would work from the top-down, such as by plugging in numbers into a tidy formula to calculate straight-line distances from a location to the nearest grocery store or fast food restaurant. But to build a map like this, students have to work from the bottom up. They start with messy, real-world data—layering supermarket locations (green triangles) alongside corner stores and fast food spots (red dots)—and let an algorithm draw the boundaries. Green areas highlight neighborhoods with strong access to fresh food, while red areas mark food deserts where unhealthy food access outnumbers supermarkets nearby.
Instead of searching for a clean equation, students focus on data-driven inference. They learn how to handle noise, spot potential bias, and validate their model against the actual lived experiences of local residents. The goal shifts from finding a singular “right answer” on a worksheet to uncovering real-world disparities in places like Olde Towne East. By trading modeling without agency for modeling with agency, math evolves from an abstract exercise in formulas into a practical tool for advocacy.
Empowering the Modern Student
If we limit our students to traditional math modeling, we are training our students for a world that no longer exists. We are conditioning them to expect clean inputs, static rules, and singular answers. But human society doesn’t work that way; it is multivariate, messy, and profoundly complex. Data science modeling offers a way to connect mathematics to the complex problems students actually care about in their communities. It doesn’t replace traditional mathematics, but scales it to meet the realities of the 21st century.
By teaching with data science modeling, we do something far more critical than simply preparing students for a data-driven workforce. We teach them a tool in the classroom that empowers them to be productive in society and in the workforce. The challenge before us is not whether students can learn how to model using data science practices. It is whether we are willing to make room for them in our classrooms.