[PT] Pseudoteaching: Hunting Monkeys
I’d like to begin this post with the coining of a new term: Pseudoteaching. This term was inspired by Dan Meyer’s pseudocontext, which sought to find examples of textbook problems that on the surface seemed to be about real world problems and situations, but actually were about make believe contexts that had little connection to the real world, other than the photographs that framed the problems.
After reading many of Dan’s pseudocontext posts, Frank Noschese and I had the idea of pseudoteaching [PT] which we have defined as:
Pseudoteaching is something you realize you’re doing after you’ve attempted a lesson which from the outset looks like it should result in student learning, but upon further reflection, you realize that the very lesson itself was flawed and involved minimal learning.
We hope that though discussion, we’ll be able to clarify and refine this definition even further. The key idea of pseudoteaching is that it looks like good teaching. In class, students feel like they are learning, and any observer who saw a teacher in the middle of pseudteaching would feel like he’s watching a great lesson. The only problem is, very little learning is taking place. We’re hoping that Pseudoteaching will become a valuable lens for critically examining our own teaching, and that the idea will spread to other teachers as well. Frank is keeping a collection of pseudoteaching examples at his blog, Action Reaction, on custom Pseudoteaching Page. We hope you’ll contribute some of your own examples of pseudoteaching as well.
Scene: Hunting Monkeys and Pseudoteaching
My example of Pseudoteaching is super fresh. This week, I decided to do an exercise where we explored the famous monkey hunter problem. In case you haven’t seen it, here’s the basic setup. A monkey is hanging from a tree, a height above the ground. It’s a nervous monkey, and so it will drop from the tree at the same instant it hears any disturbing noise. You’d like to shoot a banana at the monkey (yes, this problem has been sanitized from its previous monkey hating roots), and you are a horizontal distance away from the the landing spot of the monkey. You wonder how you should aim at the monkey if you want to hit it with the banana. Should you aim at the monkey, below the monkey, or above it?
The unintuitive answer from physics is that you should aim at the monkey, since both are falling, even through the banana is traveling “upward” on its way to the monkey.
Being the masochistic teacher I can be, I thought this presented a great opportunity to dust off our algebra skills and prove, once and for all, that you should aim at the monkey.
From these graphs, I ask the students to write the equations for the x and y positions of these objects, assuming an origin at the starting location of the banana.
Then I ask what must be true if the banana is to hit the monkey, and the students tell me that the x and y positions must be the same at the time of impact, . So we write
They also see that the last equation can simplified to
Now we have two equations that relate describe the motion of the banana
With some coaxing, my students see you can solve the first equation for t_i, to get , and this can be substituted into the second equation to get
Which rearranges to
We stop and puzzle here, since this seems to be relating the horizontal and vertical components of the velocity to the intial height and distance of the monkey. I say, “to a physicist, this says ‘aim at the monkey!'” How can we see this? I get them to draw a triangle for the initial velocity of the banana and its components:
Soon my students see that the ratio and are just the tangents of and must be the same:
And the only way this can be true is if , so you aim at the monkey!
Breakdown: Why this is Pseudoteaching
After the lesson was over, I felt great. I’d basically run through this on the fly, and everyone seemed to be participating and understanding. I stopped along the way to make sure everyone was following the discussion, and to pick apart the particularly difficult parts. Courageous students asked good questions when they couldn’t follow, and I was sure that I’d made my former professors proud.
Then the next day, I decided to see how well my students could do this same derivation on their own. So I gave them this:
And as soon as they started working on it—I head the questions start rolling in:
“Wait, what are we supposed to be doing?”
“I don’t get it.”
“How should we begin?”
And boom—it hit me. Yesterday’s great lesson really wasn’t much more than me showing off my algebra skills. Students were saying the right things when I paused long enough and gave them enough hints to get to the right answer like Clever Hans, but there’s no way they were learning this to symbolically reason through a challenging problem, which was my goal.
Pseudoteaching rears its ugly head right in my classroom. Ugh.
This experience taught me a vital lesson. If I want my kids to be able to reason their way through difficult problems, using symbolic reasoning, I can’t teach it to them by walking them down the narrow road of my “enlightened” physics understanding. Since this is how almost all of my physics classes were in high school and college, and I turned out ok, I thought this would be a great way to learn from time to time. Of course, I forgot how poorly I understood physics when I graduated from college and started teaching. I didn’t figure out most of these things until I was forced to puzzle through them on my own as a teacher.
I need to make time and space in my teaching for students to take on challenges like with this, struggle with them, get lost, fail, and keep going until they get to the solution. So that’s what we did. My classes worked on this for more than half an hour. A few got right to the finish, and were able to then try to figure out how high off the ground the monkey would be when it got hit. Others really struggled to figure out how to interpret their graphs to get equations, but got there in the end, and a few never finished, and I need to find a way to give them more opportunities and scaffolding so that they, too, can see success.
Read more examples of pseudoteaching at Frank Noschese’s Pseudoteaching Page.