It’s easy to assume that once something involves math, it becomes neutral. The numbers don’t care who you are. And the formula doesn’t take sides. But when it comes to building a model (and deciding how to represent something real and perhaps messy), it turns out the math can lean in one direction or another. But only if a human is pushing it one way or the other!

A math model isn’t just about putting numbers on paper. It’s a set of assumptions and decisions about how to bring order to something complex. That means someone has to choose which data to keep, which to ignore, how to assign relative importance to what is kept, and the end goal. Those choices shape the results. That’s where bias has an opportunity to enter the picture. Acknowledging that is part of developing a mathematical modeling mindset.

It Starts as Soon as the Math Modeling Starts

Modeling begins with a question, usually a broad one. How can we predict something? Improve something? Estimate something?

Before we even look at the data or relationships among different factors, there’s already judgment involved: What should this model focus on? What counts as relevant? What’s the most important context for reaching a solution? Whom is the model and answer for?

You might not realize it at first, but even in the early setup, you're filtering reality through a specific lens. And that lens reflects whatever assumptions, priorities, and limitations are a part of your thinking from the start.

A Commute Is Never Just a Commute

Let’s say you’re modeling how long it takes someone to get to work. You could start with distance and average speed. But that’s just one approach.

Do you assume the person drives? Takes the bus? Walks? Do you factor in today’s weather? Construction? Do you model a typical/average day or build in the occasional detour?

Two people could model the same commute and end up with completely different results, even using the same math, simply because they tackled the problem with different assumptions. That’s not a mistake. That’s how modeling works. But it also means we can’t treat the result like it’s the absolute truth. It’s a useful estimate, based on a particular version of the world.

If you want to continue the commute train of thought, check out this article from the Consortium on traffic flow.

Why the Details Really Matter 

The initial lens we use becomes more important when the stakes go up. Models are everywhere: in forecasting, planning, economics, logistics, research, and healthcare. And even in figuring out why a dozen roses costs what it costs! The more we rely on models to make decisions, the more pressure there is to treat them as airtight. But they never are.

Even the cleanest, most elegant model has a frame around it, a set of limits on what it’s meant to do. If we forget those limits, or never question them in the first place, we risk using the model in ways it wasn’t built to handle.

Sometimes, we may assume a model will work fine in a new context. Other times, we assume the model is unbiased just because it doesn’t explicitly include race, income, or geography. But bias doesn’t always show up as a bad variable. Sometimes it’s baked into the data we started with. Other times, it’s in the outcome we’re optimizing for. And often it’s present in our tacit assumptions and ways of thinking.

Models Simplify, But That Comes at a Cost

Models work because they ignore things. That’s a tradeoff. The problem starts when we forget that things were omitted.

Instead of asking: “Is this biased?” maybe we should ask: “What did we decide along the way?” And other questions like:

• Where did the data come from?
• What wasn’t included?
• How did we define success or accuracy?
• What assumptions might I have made that I’m not aware of?

From “Right Answer” to “Right Assumptions”

When students build a model themselves, they realize pretty quickly that the math isn’t always the hardest part. The hard part is deciding what to pay attention to in the first place. And once they’ve made those decisions, it’s a lot easier to go back and say, “Wait… what if we handled that differently?”

When students talk through the “why” behind their models, they’re building critical thinking and reasoning skills that serve them well beyond the math classroom.