A while back, Justin Tolentino had a post asking how others might go about teaching problem solving strategies. Great question. I have started and scrapped a couple of responses to his post as well as a posts of my own on this topic. I think the easiest way for me to describe it is in the question I gave my 7th graders this morning.
A man lives on the 10th floor of a building. Each time he leaves his building, he will take the elevator from the 10th floor to the 1st floor. However, when he returns, he will take the elevator to the 7th floor and walk the remaining three flights to his apartment. Why does he do this?
I am sure that many of you have heard this lateral thinking puzzle before and may wonder how it belongs in a math class. I realize that this problem has nothing to do with math, but in my opinion, neither does problem solving. We use math as a vehicle to teach students how to take information they are given and then discern that which they can use and that which they must refuse. From there they can ask questions to gain any new information they need in order to solve the problem.
The only requirements I give students the first time I ask them one of these puzzles is that they ask "yes or no" questions. I also tell them that my answer to their questions will either be "yes, no or irrelevant." Then I turn them loose.
They start firing random questions like crazy.
"Is he afraid of heights?"
"Does the elevator work?"
"Does he need the exercise?"
These questions come in all shapes and sizes and many of them are very specific. After about 10 questions, I tell them I'm only going to give them 21 questions and I make a mark on the board after each question. At first, it doesn't deter them. They keep at it, often times repeating a question that was already asked. Then they get to about 15 and someone suggests that they slow down a bit and start thinking about what to ask next. Today, we got to 21 with no resolution and I was about to walk away from it when one of the kids who knew the answer asked if he could ask a question.
"Does he have to walk the remaining three flights?"
"Yes he does. And if you guys would have asked this question in the beginning, it would have kept you from having to waste some of your other questions."
This brings us to a great discussion on how we can look at a problem and ask general questions that eliminate the need to ask other more specific questions. As we carve out large chunks of potential questions, we begin to narrow our focus and become more specific.
I really like what I see when I present these puzzles to my students. Kids who won't normally offer much in a class discussion, will often times ask really good thoughtful questions. They feel safe to do so because the given information is so limited, there is no way to feel "stupid" for not knowing the answer. In fact, the entire process assumes that no one knows the answer.
This leads me to ask: How can we get students comfortable with what they don'tknow? How do we convince them that being educated isn't about knowing all the answers; it's about asking the right questions?