Educators
How to help students problem solve with the meta-problem
Problem solving in the classroom usually means teaching students specific methods to solve specific problems. We rarely, if ever, teach them how to pick the right problem to solve.
The meta-problem method addresses this challenge, while also teaching the general skills that allow students to be better problem solvers. A meta-problem is about identifying the best problem to solve, knowing there is a tradeoff between the value of solving a particular problem and the effort it takes to solve that problem. For the full definition, click here.
Nuances matter
Thinking about the goals we have and the choices we can make is the way experts navigate virtually any situation. It’s easy to forget that the people you are teaching may not know what the goals could be. They also may not really know what options they have. And most of all, they are unlikely to be able to really compare the nuances of different options to choose the best one.
Those nuances can make a big difference. For example, a teacher who wants to teach her students about fractions might face these questions:
​
-
Which math problem should I give my students to help them practice fractions?
-
Which math problem should I give my students to help them practice recognizing if they should use fractions or not?
​
While they sound similar, those are two quite different problems, with quite different solutions. A skilled teacher needs to solve both problems – and many others – to ensure students learn what she intends. The meta-problem of how to teach fractions has many problems within it.
Similarly, a teacher trying to help his students explore the difference between opinions and facts, might face these questions:
​
-
Which text should I give my students to help them practice understanding the difference between opinions and facts?
-
What questions should I ask my students to check if they know the difference between opinions and facts?
​
Again, these are two very different but similar-sounding problems that fit into the meta-problem of teaching his students new skills and knowledge.
These dilemmas are focused on goals from the teacher, so you might wonder how it helps students be better problem solvers. The next step is the insight that makes the meta-problem such a useful framing
Classwork – what’s the purpose of the problem?
Students are rarely told why a problem has been set up the way it has, for example that multiple choice questions are designed to have wrong answers that are the most obvious mistakes. But if you think about why they are designed that way it makes sense: multiple choice questions are about making it easier to accurately grade many students, not about making it easier to pick the right answer.
When a student gets a “wrong“ answer, it could be because they did not understand the method, but other times it is because they did not understand the meta-problem. Suppose a student is asked how to divide half a pizza among four friends.
​
-
A student might miss that they started with only half a pizza and give a “wrong” answer.
-
If they think they are being tested on how to do long division and decimals when in fact they were being asked to practice fractions, they will give a “wrong” answer.​
If a student has made a mistake, educators can help them learn the process to diagnose their mistakes. Here are the two key categories to show how you could give your students a window into the meta-problem:
​
-
A student makes a mistake - support them by helping them find for themself where the error crept in. Did they miss that they needed to divide by 2? Did they multiply where they should have divided? What strategies can they use in the future to check their work? You can also put a more positive framing on the situation by pointing out that they just "solved a different problem than they meant to. And now we have a bonus puzzle / challenge to find the difference!"
-
A student uses the wrong method - support them by talking about how the methods are similar or different. What did they miss that was supposed to help them know which method to use? Which clues should they be looking for to know the right approach in the future? Are these clues only true in a classroom, or are they useful in the real world too? (Example: neat round numbers happen more in math class than in the real world).
When you are learning something, all your options often look the same until you learn the clues that set things apart. Teachers often present those clues, but it can take more exposures than you think to really see the differences.
Real-world problems – goals and choices
The meta-problem approach can help students with poor behavioral choices as well as academic problems. Talking about their goals and options can help:
​
-
A student is fighting with a friend – help them think about the difference between how they wanted things to go and how they actually went. What decisions can they make to improve the situation? Is everyone on the same page about what they are trying to accomplish together? This is the heart of the meta-problem, talking directly about what your goals are and what decisions you can make (i.e what is the best problem to solve) to try to achieve those goals.
-
A student breaks a classroom rule – what was their goal, and could they achieve it by making different choices? Did they think about the downsides of breaking a rule, or did they hope no one would care? Even if it would have been a little less fun to make a different choice, wouldn't that have been better than what's happening now?
-
A student is upset with a situation - support them by focusing on what is in their control and what isn't. In a lot of cases all we can do is change our own behaviors or how we talk to ourselves about the situation. Was a friend mean, or was that friend having a bad day? Should we demand an apology from someone who seems to be upset, or just take a break?
Understanding and talking about the goals and choices students have (i.e. the meta-problem) can dramatically shift their views.
If you work with students and are looking to incorporate the meta-problem into your classroom, or if you have suggestions to improve it, please use the Contact page to share your thoughts.