Word Search Heuristics, and Mathematical Problem-Solving
My son was doing this word search, and I started thinking about word searches. He is clearly a novice at word searches, having just learned to read. Experts must have strategies for doing word searches, go-to techniques or ways of approaching the puzzle that help them to solve it.
If he does enough word searches, he will no doubt develop some of these techniques on his own. Probably two other common puzzles that become much easier are crosswords and Sudoku: it’s not hard to find strategies for either, on the Internet.
Indeed, searching for “word search strategies” does yield some interesting lists.
Asking my Twitter network for their strategies yielded this thread:
I would call these word search heuristics. We could explicitly teach these strategies to kids, I think. A heuristic is a short-cut, or mental strategy for problem-solving. We use them all the time, in various avenues of our lives.
Thinking about how novices develop their heuristics could be useful for teachers.
My suspicions on how you move from a novice to an expert word search doer:
- do lots of word searches
- pay attention to the things that you do that make solving word searches easier
- use those things. Perhaps you always scan from left to right, AND look for double letter combos. Be aware of your own strategies.
Now, how do kids make the novice to expert move in mathematics classrooms?
I am tempted to use the same list:
- do lots of mathematics problems
- pay attention to the things that your do that make doing mathematics easier
- use those things.
This list looks weak all of a sudden. It looks empty. That’s because we need to learn and know lots of mathematics along the way. In doing word searches we don’t need to know what the words mean we are searching for. It is devoid of content. Mathematics is not. Kids need a robust toolkit full of things they know about to solve problems.
That said, we can help them develop their own heuristic approaches. We often fight about how best to teach through problem-solving, or whether it’s even advisable. The big question: can problem-solving skills be taught?
Again, I wouldn’t expect to be good at word searches without doing lots of them. I do suspect I would improve quite quickly, as would most kids. You get better at solving problems in math class by seeing lots of different problems, by experiencing them, and by having a chance to develop our own problem-solving heuristics.
George Polya’s How To Solve It is often presented as a problem-solving “method”. If we just trot out this four part model, and teach it to kids, the thinking goes, they will be able to solve problems.
- Understand the Problem
- Make a Plan
- Carry Out the Plan
- Reflect On The Plan
See the problem here? #1 is everything: if you don’t understand the problem, you can’t start. Further, this list is generic enough that it could be about solving ANY problem. Actually, this list alone is too generic to be a good enough heuristic for word searches!
This list describes a general heuristic approach to problem-solving, but we need to use more specific heuristic approaches to problems when we do math.
We need to get specific about ways to approach mathematical problems. These are things we can explicitly show kids. Polya does go into many in his book. Perhaps the most powerful one is a weapon used at all level of mathematics: solve an adjacent or simpler problem.
Kids can be taught to break things down into smaller pieces. Consider if I asked you the classic question, “what’s the sum of all integers from 1 to 100?” Is brute force the way to go, or would summing 1 to 10 to start help?
Solving a simpler problem is a big time weapon in our problem-solving arsenal. But what happens when kids can’t think of a simpler or related problem to start with? Sometimes they don’t know enough to make connections.
Solving a simpler problem is just one weapon. We must teach kids to bring their mental models into being (no, “draw a picture” , is not enough). We must teach them ways to represent mathematics on the page. Explicit and careful instruction is necessary. Models and manipulatives need to be deployed for good reasons.
Most of all, we must talk about how we solved problems, and how our solution paths are alike and different. Teachers must talk to kids about their thinking on a regular basis, or they won’t get better at problem-solving.
Recognizing that there is no magic method is a good start. If we recognize that, we can get kids to work on monitoring their own thinking about mathematics. We can teach heuristics, and watch them develop their own methods.
When you put it this way, isn’t it true that teaching through problem-solving requires more explicit instruction than you thought?
