The other day, a colleague shared this story with me about an interaction with a student:
Students in her class had a project in which they were to create a dartboard. Among other specifications, students were to construct it such that a randomly thrown dart had a less than 10 percent chance of hitting bullseye.
At the beginning of class on the day it was due, a student who had struggled in her class approached her with a completed dartboard. Before turning it in he asked, “My bullseye probability is equal to 10 percent, is that right?”
This situation is relatively common for math teachers, particularly at our school where most assessment occurs through performance-based, non-routine problems: a student has worked hard in a problem solving context yet landed on a solution which isn’t fully correct. What is a teacher to do?
My general stance on this situation has been to err on the side of praise for student ideas and problems solving they did do over strict adherence to “correct answers.” Of course, a probability equal to 10 percent is not the same as a probability less than 10 percent. But the young man has a dartboard, he’s got a sense that there’s different chances for different regions, we’ve got some stuff to work with here, right?
Given the timing of the student’s question, the teacher did not feel like she should engage in a dialogue and delay the start of class for the rest of her students. She recognized that there was some stuff to unpack and noted to herself that they would need to have a longer conversation at some point. Yet, here was the student wanting a “yes” or “no” answer in the moment, didn’t show owe him that?
She felt she did, so she gave him the honest answer: You got it wrong.
She briefly reminded him that she would grade his project using our department rubric, on which one can make minor mistakes and still earn a passing score. She assured him that he would get more detailed feedback. But — perhaps most importantly — she gave him the straightforward/unambiguous answer to his question.
For decades educators, policy-makers, and academics have debated the philosophy at work behind this interaction. Is math about a problem solving mindset or about getting an answer? (This post from September 2015 is a nice reminder of some of the ideas at play in this debate, the piece and the comments are worth the read/re-read if you want a refresher).
I find the neuroscience about shifting emphasis from answer to process to be compelling. I have evidence for the strength of this shift from my own career — interactions with the young people I have taught (including those who are now scientists and engineers after graduating college).
But recently I’ve become more wary of my process-focused approach and the problematic aspects of this orientation.
“Alternative facts” existed before January 2017, but I think many of us are more keenly aware of the way one’s political ideology can influence one’s perspective on “truth” today than we were at this time last year.
The rancor of partisan debates about everything from inauguration crowd sizes to immigration policy serve as a reminder that we all ought to be honest and straightforward when we come across a wrong statement.
One’s perspective inevitably influences one’s understanding of the world. The process that you use to get to a solution is interesting, useful, and should be explained/understood; however, this doesn’t mean that everything is up for debate. We can and should identify right and wrong claims even in a complex problem or world.
I’m committing to try to be more like my colleague in interactions with the students I teach and adults I debate.
When someone suggests that 10 percent is the same as less than 10 percent: no, you got it wrong.
When someone tells me that the murder rate today is the highest it has been in 45 years: no, you got it wrong
When someone proposes a health care reform plan that creates new requirements for insurance, then claims “if you like your health care plan, you keep your health care plan:" no, you got it wrong.
“You got it wrong” should not be an end point. This feedback might prompt us to re-examine assumptions, communicate with greater precision, or re-evaluate our process. It should allow us to defend those things about a process that did work even if the end result doesn’t.
But wrong is still wrong. We cannot expect to have honest conversations with our students, fellow citizens, or leaders unless they start with clear identification of false claims.
How do you name and address wrongness when you encounter it? Please share strategies that work in and out of your class in the comments or on Twitter.
Photo by LincolnGroup https://pixabay.com/en/wrong-way-sign-road-caution-167535/
The opinions expressed in Prove It: Math and Education Policy are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.