“Find the right in the wrong.”
As a student teacher, my mentor teacher gave me this advice. It stuck. For 15 years, it’s been a helpful mantra. A reminder to:
- focus on what students are able to do when solving multi-step equations,
- recognize some mistakes as being overgeneralizations (e.g., a negative plus a negative is a positive), and
- think of contexts in which math mistakes make sense (e.g., 1/3 plus 2/5 does not equal 3/8, except with at-bats in baseball, or powerplays in hockey, or marks in math class, or …)
“You assign grades. Your gradebook offers suggestions.”
Advice given to me as a first year teacher. It stuck. Not helpful day-to-day but invaluable on certain days (i.e., when marks are due). Over the years, remembering this gave me permission to consider other evidence of what a student knew (e.g., classroom observations and conversations with the kid) and assign a higher letter grade when appropriate. Obvious to me now, but as a beginning teacher? Not so much.
Also, it helped me take the top-down policy of “No 46s to 49s” in stride. Bent out of shape, some colleagues took this to mean “45 is the new 50.” Others reacted like a Tim Horton’s franchise owner facing the Canadian government’s phasing out of the penny: rounding down 46s and 47s, bumping up 48s and 49s. Most teachers felt compelled to call students in to finish just enough missing work to reach the magical 49.5. I avoided the silliness. Marks were my decision. Always were. Now I just had fewer options.
“I ask my students to explain their thinking, and they automatically reach for the eraser.”
Not advice but an observation made by a colleague earlier this year. It stuck. I’ve been working on consistently asking “Why?” both with students in classrooms and with teachers in workshops. It’s easy when students (or teachers) give incorrect answers. Hence the association, built up over time, between “Can you explain?” and the eraser.
It’s also easy when students (or teachers) present an unexpected solution method. But even “I’m curious. Can you explain?” is met with skepticism. “It must be a trick, I must be wrong,” the thinking goes. My reaction to seeing the hand reach for the eraser is often something like “No, it’s right! I just don’t know how you got it. Can you help me make sense of it?” That first part feels cheap. Reassuring the student/teacher may lessen his/her anxiety, but it frees him/her from having to construct a viable mathematical argument. It’s disempowering.
Tougher, for me, is asking “Can you explain?” when I instantly recognize the solution method (e.g., Group A, lowest common multiple, check. Group B, proportion, check. Group C, unit rate, check). But not asking “Why?” here creates the reaction described above.
“How often do you see a student reach for the eraser?” could be another.
Each sticky quote above (< 140, btw) is probably long forgotten by the speaker. Certainly, they would be surprised to learn that I remember. I’m curious, what are your sticky quotes?