This is the first follow-up post to a previous one aimed at parents and other non-math teachers, The Real Power of Studying Mathematics, about the significance of the Standards for Mathematical practice.
I was talking to someone once about this practice (MP 1, "Make sense of problems and persevere in solving them") and she asked me, "Isn't that just, like, doing math?"
Well, yes and no.
Yes, in that if you can't make sense of a problem, you're probably not going to get very far toward solving it. And if you can't persevere, you probably won't get to a solution even if you can make sense of the problem. In some ways, MP 1 is a kind of "Gateway Practice"; if you struggle to make sense and persevere, it's difficult to get much of any math done at all.
No, in that MP 1 is more of a starting point, a 'necessary' condition for doing powerful mathematics, but it is far from sufficient. You made sense of a problem enough to get started? Great! You're hanging in there and persevering? Also great! But there is a lot more to be said regarding how students are able to make sense of problems, and a lot to be said about how effective and efficient our perseverance is, and more yet to be said about what we do once we have solved a problem. All of that is what we get from the other seven practices.
Let us break MP 1 down into its two constituent parts:
- 1) Make sense of problems.
2) Persevere in solving problems.
Today we'll focus on what it means to make sense of problems; in the next post we'll come back to what it means to persevere in solving them.
So...what does it mean to make sense of a problem?
Ask any math teacher; if s/he had a nickel for every time a kid read a problem and threw up their hand to proclaim "I don't get it!," s/he'd have a whole lot of nickels.
To make sense of a problem means to read or look at a problem, comprehend the information that's being communicated, and be able to ask yourself, "What mathematics is involved in solving this problem? How will I know when I have an answer, and what will the answer mean?"