**“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 â€¦)

**“ 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.Â 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?

I like “find the right in the wrong.”

“Be fast, fair, firm, friendly, and funny.” Not necessarily in that order.

“It’s not about you.” For me, this is good for teaching and just being a human.

I have a habit of staying quiet after a kid shares something, maybe just a nod, and he/she knows that we’d like to hear more. Thanks, Chris.

Thanks for commenting, Fawn. At least 4 of those F’s come through when I read about your classroom on your blog. The staying quiet thing is great advice. There’s an uncomfortableness with silence. You just gotta outwait ’em.

I think you are right on about normalizing the “can you explain?” One phrase I like that almost seems more affirmative while still asking them to explain is “How do you know that?”

You’re right, Bowman. I like “How do you know?” better. It is more affirmative. I was using “Why?” and “Can you explain?” as generic placeholders for this family of questions. For me, I still think it comes down to consistency.

“Can you explain?” is a good question. I hope I’ll add it to my routine next time I teach.

Reblogged this on Shade Tree Math Teacher.