That really is the question posed by Dan Meyer in his opening keynote speech at the NCTM Reasoning and Sense Making Conference Institute. Honestly, I had never heard of Clever Hans, and unless you are a fan of esoteric German animal trivia, you might not have heard of him either. Clever Hans was a horse that had amazing powers of reading the people around him. The horse could do any math the audience could do.
I won’t bore anyone with the story, especially since Lisa Henry did such a great job explaining it on her blog, and Wikipedia and other sites have thoroughly explained it as well. The story is extremely relevant to math education today, and more importantly, important to the practice of math educators today.
As I was listening to Dan, I recalled a comment a learner made to me. I had just asked a learner, “Why” when she gave me an answer to something. The learner tried to explain, and couldn’t. Another learner came to her defense, and together they figured out she was correct, and they explained why. At that point, Learner 1 turned to me with a very angry look on her face (all made up, she is a great actress) and said, “Mr. Waddell. You tricked me. You are only supposed to ask why when we give wrong answers.” The class then went on to tell me that I have a great poker face, and that I am supposed to let them know when they get something right by smiling or something.
I had just accidently stumbled upon the Clever Hans Effect, and didn’t know it. I just wanted to know if the learner understood the problem.
Imagine that. The learners in the class understood the issue better than I, the teacher did. They were instructing me when it was okay to ask them if they were sure, and how to non-verbally communicate with them when they are supposed to stop
clomping their hoof guessing the correct answer. Thankfully I ignored them.
I didn’t have a name to describe what occurred that day, but I do now, and Clever Hans will now and forever be in my first day of class discussion.
But of course, the keynote was far more than just a talk about a horse. It was about how to take a boring, dry, and thoroughly massacred problem, and turn it into something that might actually have some interest to learners.
Dan breaks his problem solving process into 4 steps.
Of these, I personally find the Verbalizing of the problem the most important. Verbalizing a problem is asking the truly relevant and interesting question in just a few words. Taking a long and boring question from a text book (how about the “which cell phone service should I get that is now de rigour for textbook companies) and turning it on its head.
The new question should be something along the lines of:
1. What cell phone plan would you buy?
2. [insert some image of local cell phone advertisements here] Make the insert local, relevant, and complete.
3. And this is probably the most important part as a teacher. WALK AWAY for a bit and let the learners abstract the question. You see, the textbooks do that for the learners. They break the problem down into nice, clean, manageable chunks that are easy to digest. We need to let the learners look at the actual ads, the actual, messy, ugly details of the ad and decide for themselves what is important.
4. After that, then they will decompose the question and figure out an answer and then justify the answer.
Guess what, some may choose a plan I would not. The real question at that point is, “Why?” Did the learners overlook something, or did they just think the 2 gig plan fit their needs better than the 5 gig plan?
Why do I need to always decide for them?
And that is a great way to run a rich question with Reasoning & Sense Making. I will have more to say on this later. Right now, I am in Orlando, and some fun beckons.
After all, it is not always about the math. (yea, right!)