Have you ever been working with your kid on a math problem and they just throw a number at you out of nowhere?
When this happens to me, I usually ask diplomatically, “Is that a guess?” or make the observation, “That sounds like a guess,” with a little smile.
The thing is, guessing is a super powerful problem solving technique – but most kids don’t realize that there are different kinds of guessing, and that certain kinds of guessing can move them forward confidently, while others can throw all of their hard work out the window.
Let’s break it down.
1. The first, and least helpful, kind of guessing is WILD GUESSING.
WILD GUESSING is NOT a helpful kind of guessing. It’s like if someone asks you what the capital of New Jersey is and you just open your mouth and name any geographical location that comes to mind. (“Poughkeepsie, Montreal, the Cote D’Azur…”)
Sometimes wild guessing happens at the beginning of a problem, when a student doesn’t know how to get started, so they just start doing random operations with the numbers in the problem. (“Hm, I have no idea what to do, there is a 5 and an 8 in the problem, let me multiply them together, then at least I have ‘done something’…”)
For some reason it also tends to happen when a student is almost done with the problem – usually almost at the very last step – and for some reason, instead of actually doing the tiny bit of work remaining, they’ll just throw a number out there.
This kind of WILD GUESSING – whether with guessing a number or just doing random operations – is important to recognize, because it usually means the student is not connected to what is going on in the math.
2. Another completely different kind of guessing is ESTIMATING. This is a great way to quickly predict an answer and then be able to confirm at the end of the problem whether or not you’re in the right ballpark, or if you made a calculation/computation error and are way off.
Frequently, estimating involves rounding the numbers and then making a mental calculation, before you dive into the nitty-gritty EXACT computation.
Estimating is a powerful tool and also a great way to practice mental math!
3. The third kind of guessing is DELIBERATELY TESTING A HYPOTHESIS.
This type of guessing is SUPER POWERFUL, and it’s something that professional mathematicians and scientists do all the time to move human knowledge forward!
For example, today I was working with a student on graphing a straight line.
She said, “What would happen if I flipped the xs and ys? Would they just be all over the place, or would they form a straight line?”
Though I knew the answer, I told her, “Why don’t you try it and see what happens,” because I knew that would be more impactful than if I just told her without her actually doing it.
Then she got to see that the points she was graphing DID still make a straight line – just a completely different line than the original one.
DELIBERATELY TESTING A HYPOTHESIS is also a great as a way to get started when you’re not quite sure what to do, but you have a hunch that you could try a particular approach, but you’re still not sure.
It is most helpful when there is some way to check your answer. Otherwise there’s no way to tell if your test was correct!
So guessing can either be a super powerful and savvy sophisticated tool – or the sign that a student is flailing and not yet connected to the meaning of material. That’s why it’s so important to know about the three different kinds of guessing, and discern between them.
Would you like your innovative, unique kid to experience math from the powerful position of being able to deliberately test out their own creative hypotheses? If so, I would love to talk to you!
To make sure it’s the right fit, I accept students into my magical tutoring programs by application only, and the application includes the extremely valuable opportunity to spend 90 minutes on the phone with me so we can getting super clear on what’s going on with your kid’s math and whether or not it would be a fit for us to work together.
Just send me an email at firstname.lastname@example.org, and we’ll get you started on your application for my private one-on-one tutoring programs!
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