Have you ever thought about how those two words, “What if?” can invite a million more questions and eventually change the outcome of the situation? Since many of us are diving into the back-to-school season right now, let’s take such a question: What if schools didn’t run on bells? 

You’re probably thinking about the chaos that would ensue or all of the classes that would be missed. But the idea that having a standard and structured school schedule is the best way for everyone to learn may not be completely accurate. Research has been saying for years that teens are wired to wake up later. So, for example, what if we shift the start of the school day to match when students are actually ready to learn?

Embracing the Chaos of "What If"

Well, it’s not that simple. Changing the start time of the school day would mean adjusting everything else (and really creating chaos!). Think about it. Bus routes might change, encountering different traffic patterns; staff schedules would have to adapt; sports teams would have to figure out a new plan for practice times; after-school jobs may be impossible; and even how families manage mornings and child care would all have to change. And that’s before getting into the logistics of staggered times across school districts.

The deeper you go, the more tangled it gets. But that’s exactly why it’s important to adopt a math modeling mindset toward the problem. And of course, another question arises: if we could actually figure out a way to make the school day fit how teens are wired to learn best, would they learn better?

Of course, we're not suggesting that the entire structure of a school day needs to be revamped. This is just a timely example of how asking the right question can lead to many different models and solutions. And with good modeling, perhaps there are marginal improvements to be found.

It’s the Everyday Variables That Make It Interesting

Some of the best math questions don’t come from textbooks. They come from wondering about the systems we deal with every day. The ones that sort of work, but not quite as well as they might. Think about grocery store checkout lines, for example. 

These are not clean situations with clearly stated problems or clean answers. They are layered, full of variables that interact with each other, and are shaped by human behavior that doesn’t always follow the rules.

To introduce students to mathematical modeling, consider using a familiar everyday context and focus on some of the “what if” questions your students raise about that context. If students are more invested in the questions, they will become more invested in the math.

Math Modeling Contests Embrace “What If”

In COMAP’s math modeling contests, students are asked to take on open-ended problems just like these examples. Contest problems are set in real-world situations with no obvious answers. Sometimes the challenge is figuring out what questions to ask before even starting the math. Sometimes the math points in one direction, but the real world pushes back.

We’ve seen students turn a problem on its head, just by saying, “Well, what if we tried this instead?” It may feel like you’re going down a rabbit hole because one what-if question usually leads to another and another and another.  But what students have discovered is that when they stick with it and keep working the problem from many different angles, the solution they get at the end is not only more creative, but often ends up being a better solution.

These are the kinds of skills students develop in math modeling contests and which will serve them well long after graduation. In that sense, the math modeling mindset isn’t just about solving problems. It’s about being willing to sit with a messy one long enough to make sense of it.

And often, it all starts with: what if?