If you have kids, or are ever around them, you might hear an adult say something like “No, no, you try it first, and then if you really need help, come back. But you have to try it yourself first.” Kids are often hesitant to do things themselves, or to try something new, or to experiment with something until it works the way they want. There are tons of reasons for this, and they apply to us adults too: new things can be scary; sometimes we’re not sure what will happen, and not knowing is also scary; we want to do things perfectly every time, so the prospect of something potentially not going as planned is (yup, you guessed it) scary. But those reasons don’t mean our kids shouldn’t try, and experiment. Our job is to help them learn that it’s okay to experiment in order to learn, even in the face of the (scary) unknown!
For the reasons given above, and lots of others, it’s not always easy to have kids experiment. To get there, sometimes we have to encourage (“I know you can figure out that puzzle, try it!”), other times it’s less a matter of encouraging and more a matter of the adults getting out of the way and allowing the experimentation to happen (“You want to make dinner yourself? Okay!”). No matter which version of experimenting is going on, it’s worth allowing our kids the opportunity to prove something, to figure something out, to see what happens when they experiment. Why? Because this is where confidence is built. This is where creativity shines. This is where logical and critical thinking skills are learned.
In a recent problem, we asked solvers, essentially, to play a game. The thing is, our intuition might tell us that we know how the game is going to work out, and then immediately move on to “Why bother?” Well, we bother because, as it turns out, our intuition often isn’t correct - and that happens a lot in math, and in life. Here, we might have to try the game to actually see what happens, not just make assumptions based on how we’re pretty sure it works. Double-checking our intuition can be scary to do, as human beings don’t necessarily love being proven wrong, or realizing that our intuition, which we trust so completely, might mislead us. But we still have to try it.
For me, the big question in a problem like this is how to help learners get over the scary feeling of not knowing where the problem is going, or of being unsure of what to do, and get them to just jump on in. One strategy is to jump in with them, and do your own experimenting - be the example for your learner of just how to begin! If you start to play, and keep track of your results (or do whatever your experiment requires), and acknowledge that you aren’t sure where it’s going, but that uncertainty is okay, then your learner will begin to see that it’s okay for them to do that also. The part where you acknowledge that you aren’t sure, but you’re fine with it, is a big deal - it will help your learner understand that it’s important to try even when you don’t know what will happen! It’s also important to acknowledge when you hit a bump in your experimentation, or get a result you didn’t expect (“Hmmm, that didn’t work the way I thought it would.... I wonder what happened.... What should I do next?”); this shows learners that even when the road curves, it’s okay to keep moving forward, thinking, evaluating, and trying again.
Learning to jump in, to try, to experiment, and to see what happens even when you are unsure of where it’s going, is a vital life skill. It’s one that allows us to meet new people, choose a new career, design the next big thing - to grow! And that’s one of the many reasons why we do math and solve problems like this - they help us all to grow, maybe even in ways that we didn’t expect!
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