Solving Problems

My awesome partner loves to test my brain sometimes. At one point he was reading the book How Would You Move Mount Fuji, a book about the problem solving interview questions that companies like Microsoft and other big companies would use to “test” their potential employees. Now, it’s not always about getting the correct answer, but also about the thinking process that the interviewees used to achieve their answer.

There was one problem in particular that I remember being asked…

There is a row of 100 lockers in a school hallway; all of the locker doors are closed. A first whistle blows, and all the doors toggle — meaning if the door is open, then it will close, and if it is closed, it will open.  On the second whistle, every two locker doors will toggle.  On the third whistle, ever three locker doors will toggle. On the fourth whistle, every four… and so on, until the 100th whistle blows.  After the 100th whistle, how many locker doors will be open?

Now, I’m sure there are many people smarter than me that will solve this almost instantly. I didn’t. But that’s not my point.  What I did do is something is resort back to what I do know … using my fingers. It may sound kiddish, but it worked. I made the problem into a much smaller problem, thinking of only the first ten lockers and the first ten whistles (since I only had ten fingers), then used my fingers to track what happened until I noticed the pattern. From there, the solution made sense both logically and mathematically.

So, I guess my question is this. How do we teach this type of thinking in our classrooms?

I say this a lot in my classroom, and I remember reading it on another post from samjshah.com… “Take what you don’t know, and turn it into what you DO know.” I feel this concept of thinking and learning is more important than any content math standard being tested, because this is what matters. Everyone eventually forgets the much of the math they learned. But learn to think like this, and math will suddenly have purpose.