Have you ever been presented with a problem and just had no idea where to start? It happens to all of us; a challenge appears before us, or something strange happens, and you just freeze, and think: “What on earth do I do now?” This feeling recently arose when I woke up early on a Saturday morning to find it raining in my kitchen (and no, we don’t have a fancy outdoor kitchen), but the situation doesn’t have to be that dramatic. The dreadful feeling of not knowing where to begin can pop up without having your house fall in: many people feel this way simply when solving math problems. This is something I hear from friends, colleagues, and students regularly, and it goes something like this: “I looked at that problem on the (board/test/homework/worksheet) and didn’t even have the foggiest idea of where to begin. It’s so frustrating!” Have you had this feeling too? Even if you haven’t, it’s important to build strategies for what to do when you just don’t know what to do.
So, imagine you have encountered a problem and you don’t know how to begin. You’re stuck. You have no earthly idea what to do next. Now what do you do? Give up, right? Go do something else? Leave it blank? Of course not! Pause. Breathe. Give your panic a moment to subside. Now, return to the problem, read it again, a couple of times, maybe out loud, if you can stomach it! Start to take it apart. What do you know? What do you need to know? What is the question asking you to do or find out? Write those things down. Sometimes the simple act of putting pencil to paper helps to start everything moving forward.
Okay, so now you know what’s given to you in the problem, and what you need to figure out, but you are STILL stuck! The first thing to do now is actually the same thing we did before. Pause, breathe, and let the panic subside. Return to what you know about the problem, and begin to take tools, one by one, out of your mathematical toolbox. Is this a problem where a drawing might help? Great, draw something - anything to start, and see where it leads. Maybe there is information to organize. Super, bust out your favorite kind of chart or table, and start giving order to that chaos of information. Do you see any patterns? Maybe… if you do, that’s great - use them to your advantage - what do they tell you? Can you extend them to help you solve the problem? Still not there? Consider thinking backwards - can you begin at the end of the problem, and work your way back until you see how to reverse your steps? What else could you do? Well, you might make an informed guess, or choose another strategy that we haven’t listed here, since there are lots of other ways to approach a problem. The point we’re trying to make is not about the strategy you choose; what matters is thinking through the tools you have, and trying them out, to see what happens, and what actually helps.
The point is, choose a way to start. When it was raining in my kitchen, after I stood around and got rained on for a while, I started with buckets. Once you choose a starting path, evaluate it as you go. Stay on the path for a while… see where it leads. If you get to a point where it becomes clear that your path isn’t going to lead to the answer, then pause, breathe, and choose a different path. In my rainy kitchen, we quickly realized that our special sort of rain (mist really) wasn’t getting collected very well by buckets on the floor, 10 feet away from the source of the rain. So we got out the ladder, and propped the buckets right up at ceiling height - and the kitchen became functional (and less like visiting Niagara Falls) again. That’s the thing about solving problems - you aren’t married to any one approach. If one doesn’t work, put that tool to the side and try another. Then follow the path laid out by your new tool, until it either works, or doesn’t. If you still don’t have the right tool, try again, it’s okay. Going down the wrong path can teach us just as much (if not more!) than choosing the right path on the first try. And don’t be afraid. Sometimes the path to a solution is straight, and smooth, and painless. But not most of the time. More often the path is curvy, and strange, with unexpected bumps in the road. Stay with it. You’ll get there. So what if it takes a little longer? That’s how we learn, and learning is valuable.
Moral of the story? It’s okay if you don’t know where to begin. It’s normal. It’s actually kind of great (even though it doesn’t feel that way), because it’s a chance to experiment with your tools to see what they can do, and also to prove to yourself that you won’t be defeated by some silly math problem (or rainy kitchen). In the end, you’ll have learned something new. Maybe you’ll learn something amazing. Pause. Breathe, and start down a path, one step at a time.
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