Teaching the Meta-problem Mindset Can Empower a Generation of Confident Problem-Solvers

Author note. Over the past several issues of OR/MS Today, I have shared the meta-problem mindset as a tool for solving better problems. In this final article in the series, we explore how teaching the framework can help students develop the skills they need to thrive in our rapidly changing world. 

We rarely teach real-world problem-solving to students, yet it is the skill most likely to determine their future well-being and success (however you choose to define “success”).  

That same skill will also shape the future world that these students go on to build for us, our societies and our planet. It is our job to equip them for the task. 

That was the mission that drove me to develop the meta-problem approach. I felt there was something about the way I and other people in the OR/MS community solved problems that needed to be shared with the world.  

I remember taking my first optimization course and learning about the objective function and constraints. I recognized the way I already thought and decided to pursue a Ph.D. in the field. Still, over the years, I’ve talked to plenty of people who don’t see the world this way.  

The act of choosing which problem to solve is something we do intuitively because of our training. But the magic of OR/MS is that, with the language of optimization, choosing which problem to solve becomes just another decision to optimize.  

Eventually it clicked that the root of the skill gap lies in the way we teach students. We hand them neat and tidy problems with a correct answer. We tell them that by learning how to solve these designed problems using specific techniques, they’ll learn the skills they need for their future. But not everyone learns how to generalize those lessons.  

Decisions Shape Outcomes 

The earlier students start focusing on decisions and how they connect to outcomes, the sooner they can take their problem-solving skills to the next level. This has the added benefit of creating a sense of agency. 

Focusing on what they want from a situation is an empowering point of view. Jumping in with solutions when all someone wants is to be heard is frustrating for everyone. 

I have three kids in middle and elementary school. I talk them through the creative process of choosing which problem to solve all the time. Kids get it. If they’re fighting with a friend, you can focus on what outcomes they hope to achieve. If they are struggling with a topic, investigate what is standing in their way. If they don’t like their teacher, talk about what decisions they could make to have the best possible outcomes – given the situation. 

Adult students benefit from these same lessons. In college, one of my decisions each week was what process to use to finish my homework. I eventually noticed that as someone who sometimes picked the wrong method to try to solve a problem, I needed to take regular steps back to review where I was. My goal was to learn enough, get good-enough grades and not use up too much of my limited time on any one specific challenge. 

Weigh the Trade-offs 

Once you’ve made the shift to focus on decisions, you see the world differently.  

However, decisions are rarely all happiness and sunshine. We have alternatives to choose between, each with their own pros and cons. When deciding which problem to solve, we need a good understanding of the path each option sets us down.  

Students need to learn how the consequences of a choice flow from their decision of which problem to solve. Assumptions are also an important term to teach; I call them “guesses of what’s true” when I’m talking to younger students.  

People sometimes talk about problem framing to highlight how looking at problems differently can have surprising benefits. Seeing it as just a matter of perspective is a little too random for my tastes – how do you know which perspective will reveal a better option? 

In contrast, the meta-problem approach entails a disciplined clarification of goals and a rigorous, structured exploration of the costs and benefits of each potential solution before ultimately deciding which problem to solve. 

I encourage students to treat finding the best problem to solve as a chance to explore not only their options, but their preferences. While they might initially think they care about something specific, it can be fun and revealing to learn more about what they like or dislike. 

Designing Good Problems  

Deciding how to apply this idea to education is very much a research project. Still, there are some things that seem to work well while being an easy swap for parents and educators. 

If your student is struggling with a dilemma, ask them what they’re trying to get out of the situation. Instead of focusing on a single outcome, you can suggest some of the many competing objectives they might have in a situation. Then, you can discuss how they could pick the set of outcomes they like best. 

Teaching students how to design good problems also gives them more fluency as problem-solvers. With younger kids, we let them try writing their own math problems. Then, you can discuss what makes a good fraction problem compared with just another whole-number division problem. For older students, you might explicitly talk through the clues that make one method more appropriate than another. This strengthens their understanding of the methods they’re learning and of problem-solving. 

Inevitably, when you have students solving problems together, they will get different answers. In my opinion, this is the best meta-problem learning opportunity there is. To get different answers, you need to solve different problems. If one student missed a step, you now know the consequences for the outcome (solution) of that slightly different version of the problem. I treat this discovery as a bonus challenge – one that may be harder but is also more rewarding than just solving the problem correctly the first time. 

One other thing I have tried recently to save my students time and improve their understanding is not simply asking them to solve math or science problems. Instead, I ask them to describe which equations or methods they would use to solve the problem. This has been particularly valuable for college-level projects as I ask them to plan an analysis and then share why they crafted the plan they did. What outcomes do they expect to get? How might the systems they design change depending on what they learn? 

The Future is a Meta-problem 

The ability to adapt in a rapidly changing world requires flexibility and openness.  

If we want to do our students justice, we need to prepare them to live in that world. Fostering a mindset of curiosity and exploration related to problem-solving gives them a foundation to stand on. Build on that platform with specific skills to examine different problems and understand how they compare. Teach students to choose between their options based on the outcomes they hope to achieve.  

I encourage each of you to adopt this mindset in your own lives and with your students. Making this change will help us create future generations of critical, adaptable and curious problem-solvers.