Tuesday, October 30, 2012

Why take the road less traveled?

I love being in the woods. It is nearly always an adventure. Even if it's a path I have been on before, the possibility of a surprise around the next bend is exciting to me. I never know for sure what I will see or hear. That's not to say that I am always comfortable with this state of uncertainty. A few weeks ago, I heard two coyotes howling up ahead as I was walking on a logging road in the Upper Peninsula of Michigan. Or there was the time I encountered an overwhelming smell that I can only describe as wet dog as I walked alone along the nature trail at Seney National Wildlife Refuge. In cases like this, I try to find a big stick to "support" me as I walk.

What keeps me coming back to these roads less travel are the sights and sounds that come from exploring something new. For example, while walking down one of the access roads at Seney, I came across this beautiful Trumpeter Swan that, true to its name, announced my presence to others in the area.

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I have found that this metaphor of taking the roads less traveled also applies to my teaching practice. When I first began asking my middle school students how they would solve a problem before showing them the right way, I was quite uncomfortable with the idea that they might share something new - something for which I was unprepared. Fortunately, I had mentors that assured me it would be alright and encouraged me to explore.

The first time I recall letting my eighth-graders lead the way was when we began a section on dividing fractions. I put three-fourths divided by one-half on the board and asked for a volunteer to share how they thought we ought to calculate the result. Here's essentially what happened:

 

Because the student had not used "invert-and-multiply" to calculate the quotient, I considered the effort incorrect and tried to determine what went wrong. First, the student was finding common denominators, so there was a chance the student was confusing this procedure with the one for adding and subtracting fractions. Then the student divided across, which resembles the procedure for multiplying fractions. Clearly, the student was mixing up the various rules for fraction computation and I would need to be explicit about the differences. But something was bothering me. The answer the student came up with using this mish-mash of methods was correct. I attributed it to the numbers I had selected and decided to try the method with another pair. It worked again. I was at a loss.

I don't remember what I did with the students, but I do remember exploring this approach more and finding out that it always works and why. This experience hooked me. Now I am not suggesting that the student was doing anything other than trying to apply various rules and happened upon a solution.  But I might not have ever heard or seen this approach if I had not been open to following this unfamiliar path.

If you are still uncomfortable with exploring the "wilderness" with your students, then take solace in knowing that you do not need to go too far off the regular roads to experience something wild. Simply being alert to students' thinking while covering familiar ground can allow for new ideas to be uncovered. Just like when I was able to film this Peregrine Falcon on the bike path near our house, it only takes being aware of something new and prepared to see where it goes.

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