My favorite problem-solving approach

One of the things that happens to us all, as learners, is that we find an approach to solving problems that works, and we try to stick with it. For me, that has always meant writing down my thoughts, and trying to use words to explain things to myself and others. I have long used this strategy in all areas, especially since I realized as a kid that if I could explain my thinking in words, then sometimes the teacher wouldn’t make me write the equation that they originally asked for. It often worked, and kept me from doing things I wasn’t comfortable doing.

I think that teachers were often surprised by my willingness to write like I was puzzling through the solution, even when it didn’t work out, and many times I got credit for things I probably shouldn’t have. What I see now, as an adult, a teacher, and a parent, is that by not making me solve problems in another way, many teachers over the years let me off the hook. I didn’t have to do the work that would have been uncomfortable, and a little more challenging, but that I would have learned more by doing.

Stronger problem solving with one question

As learners we might have a way that we prefer to solve problems. I know that it helps me to remember things when I write them down in words (the post-it note disaster on my desk, as we speak, can serve as proof). This doesn’t mean, though, that this is always a helpful approach to solving a problem. I’ve had to learn, as an adult, on the fly while teaching others, that it’s important to find the solution to a problem in multiple ways. I’ve had to learn to really consider which approach is best, and be thoughtful about what makes sense, rather than just applying my favorite approach, no matter what.

So how do we help our kids to solve problems in multiple ways? By asking them to. The you ask question can be super simple - it's some version of "How could you solve this problem another way?", or "How could you use solve this problem using a different strategy?". That's it. From there it's just a matter of what they come up with. I am often incredibly surprised (and impressed) by the results that I get out of this question because kids return with ideas and explanations that I never would have thought of, or that are far more efficient and elegant than their first attempt.

I always keep one important thing in mind when I pose this question to others. It's important to ask this question as a 'How could you...' question, rather than a 'Can you...' question. This is because if I say to my kids 'Can you solve this problem another way?' the question leaves them room to squirm off the hook by just saying 'Nope!'

What do we learn when we solve in multiple ways?

SO much! Let me make you a short list...

• Flexibility: Solving problems in more than one way helps us to become flexible thinkers. We begin to see that there can be more than one avenue to get to a solution, and it allows us the ability to try another road if the one we’re on isn’t working for us, or is a dead end.
• Critical thinking and efficiency: When I have to solve a problem in a couple of ways today, I learn things that will help me to be a better critical thinker and problem solver later. Seeing all of the different ways that a problem can be solved allows me to see patterns, to begin to look at problems with a more critical eye, and develop a sense of the kinds of approaches that might work better than others, given the type of problem being presented. Making good choices about how to approach a new problem helps to make me a more efficient problem solver.
• Connectedness: Seeing a solution in different ways - visually and then algebraically, for example - gives us a chance to start making connections between the various approaches. In its best possible form, this is when a learner begins to be able to actually SEE where formulas and algebra come from, or where learners begin to use symbols to represent pictures in their minds. That’s pretty powerful.

• Toolbox development: Teachers talk about helping learners to build a “toolbox” that they can reach into whenever they have a need. For problem solving, the tools are the various strategies, and solving problems in multiple ways helps learners to learn what to do with the tools in the box. Having a strategy is great, but not knowing when to use it is a problem in itself! When we’re asked to solve a problem in more than one way, or in as many ways as we can, we start to learn which strategies and tools work, and when.
• The value of process over product: Focusing on differing approaches to arriving at a solution teaches learners that the process matters. It places value on the idea that there is learning happening in the way that we reached the answer. Getting the answer is great, no doubt, but being able to explain the answer, in multiple ways, is amazing.
• Different doesn’t equal wrong: When we learn to solve things in multiple ways, we are reminded, maybe just subconsciously, that there is more than one way to do most things. This impacts EVERYTHING in life. If we can be a little more open to how we solve math problems, maybe we can start to be a little more open about solving other types of problems. Multiple approaches are a good thing. Learning that my favorite way isn’t the only way is freeing.

There are plenty more reasons where these came from, but you get what I’m saying. There are so many things that are learned from solving a problem in a number of ways, and the learning goes way beyond finding the answer. It’s almost always worthwhile to ask a learner “Hey, what's another way to solve this problem?” It may not be comfortable, but it will be worth it.

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