The term open-ended is frequently applied to problems that don’t actually have an open end, but rather an open middle. Here are two problem-based lessons I’ll discuss to make the difference clearer:
First, let’s consider how each problem ends. With the hybrid car problem, depending on the assumptions you make (cost of gas, miles driven, price of car, etc.), there are multiple correct answers for how long it will take to make a hybrid car worth the extra cost. That makes it open-ended. However, with the In-N-Out Cheeseburger problem, there is only one right answer, so the problem is closed-ended.
Now, let’s consider both problems’ middle. With both problems, there are many ways to solve them, so the middles are open. In contrast, something like “Use the standard algorithm to find the answer to 475 ÷ 25” is closed-middled because there is only one acceptable way to solve it.
Personally, I prefer problems that have open middles and closed ends. These problems all have the same answer (closed end) and allow for great discussions around the strategies students used (open middle). When the problems have open ends, it can be challenging to have discussions because you can’t readily compare how different approaches ended with the same result. Accordingly, the website Open Middle is a collection of problems like this.
To be clear, I am not saying that open-ended problems are bad and open-ended problems are good. What I am saying is that each have their own purpose and we should acknowledge the differences between them.
What do you think? Let me know in the comments.