I would argue that no three words give more angst to students in mathematics than, “Show your work.” In countless situations, a student believes he/she has grasped a concept and can produce solutions to a given problem, then the teacher suddenly wants more than the answer. Those dreaded three words: show your work.
So what is it about being asked to script the process used to navigate from the problem situation to the solution so stressful? Here’s the rub: it’s how the prompt, “Show your work,” is being loosely translated in the teacher’s mind too often as, “Show my work.” In other words, the teacher is looking for the student to mimic his/her thinking and replicate the process he/she took to solve the problem.
And, this is where the dramatic irony comes in to play. In theater, dramatic irony occurs when the audience knows more about a particular situation than the characters in the play. In the math classroom, the teacher is the audience in this scenario and the student is the character. The teacher knows the process to solve the math problem and waits with bated breath for the student to discover what the teacher has known all along. This doesn’t sound problematic at first, instead it sounds like the type of success we are aiming for: the student to demonstrate the same level of mathematical fluency that the teacher possesses. It’s not that simple. There is a long, arduous path to get from initial experiences with numbers to the fluency of an adult. It’s not like a light switch that suddenly comes on and the student is fluent.
‘Show your work’ should be used to pull out of the student’s brain what he/she is thinking in order to interpret exactly where on this learning continuum the student is located, so that forward movement can be nurtured.
So how to we get past this rigid imitation of math rules and foster a true sense of problem solving? How do we utilize a growth mindset that regardless of where the student is on the progression of learning mathematics, the goal is for him/her to continue to move along to more and more efficient methods of solving? Wouldn’t it be great if the teacher could pinpoint exactly what the student does know so progress could be made? That’s why we don’t want the students to hear, “Show my work,” but rather, “Show your work.”
I recommend reading Robert Kaplinsky’s resent post Never Ask a Question a Horse Could Answer. Not only is this an interesting story, it hits home with a connection to his Questioning Scenarios that can be used to practice questioning with teachers in professional learning. With Robert’s resources, teachers form groups of three with one playing the role of teacher, one in the role as the student, and the third as the observer. The teacher and student receive scenario cards and proceed to enact a mock classroom questioning situation.
These questioning scenarios reflect the dramatic irony of the classroom and also the exciting challenge on the part of the teacher to solve the mystery of what the student understands. Using this information, the teacher is then able to determine what learning experience the student should encounter next in order to progress along the continuum of learning.
Within Article IV: Accountability for Learning of the Visioning Document, we guide teachers to ask: How are my assessments designed to intentionally gather evidence of understanding that direct my next steps of instruction? This question does not read: How are my assessments designed to intentionally guide my students to replicate my thinking?
One final thought regarding questioning: I challenge classroom teachers to never ask a question to which you already know the answer. Rather, ask questions with sincerity to uncover student thinking, remove the 4th wall of the theater, and consider dramatic irony in the classroom.
Read more about showing your work in Pam Harris’ book, Building Powerful Numeracy.