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"Yes, and" instead of "yes, but" in math teaching?

+2 votes

This morning I heard a report on the radio about business school students taking an improv course in order to improve their deal-making skills: They key point of the improv training is to learn to shift from a "yes, but" response to someone's idea to "yes, and." The beauty of "yes, and" is that it draws the person in rather than dismissing their ideas. 

A shift from "yes, but" to "yes, and" should be a useful tool in teachin math too. Now I can imagine this response: "yes, but in math there are wrong answers and incorrect arguments, and we must correct these." Yes, and we must accept our students where they are and help our students revise and stretch their thinking.

This reminds me of a posting on the blog of middle school teacher Jose Vilson at Mr. Vilson says he rarely uses the word "wrong." Interestingly, he also refers to improv.

Perhaps also related, there is an interesting experiment from psychology about the value of affirming self-worth in the face of errors,

"What the researchers found was quite interesting. Not only did folks who affirmed their self-worth beforehand make less errors than those who did not, but their brains seemed to be especially attuned to the mistakes they had made. It was almost as if self-affirmation allowed folks to be more receptive to their errors and correct for their mistakes.

The take-home? When faced with information about your failures, affirming your self-worth may help orient you to your mistakes. When you face your blunders head on, it seems that you are more likely to learn from them and do better the next time around."

What I would like to learn about and think about is how to take a "yes, and" approach to teaching math while also acknowledging errors as such and giving grades that accurately reflect my honest professional judgement about how well students understand the course material. Are these things in conflict or not?  Thoughts? Advice?  



submitted 3 years ago by Sybilla (9,780 points)
edited 3 years ago by Sybilla


0 votes


The hardest lessons for me to learn as an instructor is "It's not what you say to students as much as how you say it." There are no magical phrases that always "work" and are no magical phrases that always "fail." 


There are ways one could make "Yes, but" something other than dismissive, just as there are ways one could make "Yes, and" non-encouraging. For example: "Yes, but keep going…." (a fairly encouraging use of "yes, but"). Here's another example: "Yes, and then in the next line we see 0=1 and something went wrong." (a fairly dismissive use of "yes, and").


My overall immediate response to using "Yes, and" vs. "Yes, but" is that it is yet another attempt to (i) script teachers even more than they already are (ii) create a magical formula for making a math class "successful" and (iii) emphasize that students must be coddled with "A's for effort" in order to keep their interest in a subject.


Having said all of this, I think there is quite a bit to learn from improvisation. In a move towards a more "active" classroom audience, teachers must be prepared for students to ask various questions, suggest various correct and incorrect answers. Teachers must even be prepared for the class to request "one or two more examples" of a given technique--even when all the examples in the textbook have been covered. All of these scenarios require that a teacher think on her feet.


Another general comment is that what appears to be an issue is the student logic of "I cannot make a mistake." We also seem to think that once students have been told they are wrong, they "zone out" and immediately become uninterested. We must encourage our students to speak up--even with incorrect answers. We must teach students that it is not the end of the world to make a mistake. And these lessons have nothing to do with vocabulary. 

commented on 3 years ago by Kate_Thompson (3,050 points)

I see what Kate is saying about simple scripts not being very effective.  She also points to the bigger issue Sybilla is raising. Namely, as Kate points out, since we are asking teachers to open up the classroom to student discussion, we must be mindful of how we are going to handle the psychology/emotions of students making erroneous statements.  I think the key idea here is in the Standards of Practice #3: construct viable arguments and critique the reasoning of others. If the teacher can help create an atmosphere where students regularly take contrary positions and critique each other's reasoning, until a consensus eventually emerges, then being wrong loses its sting over time.  I've often noticed when working in collaboration with other mathematicians that one of us will take a position even before (or even without) fully believing it, just to prod the others into proving the position false (or deciding that it was true after all).  In other words, it's ok to be wrong - it's all in the name of progress for the whole group engaged with the topic.  In classrooms I've seen  where students are allowed and even encouraged to critique each other's reasoning, the teacher is less frequently called in to declare a statement true or false, but also when she does, it's not that big a deal because it's something students do on a regular basis.

I wonder if anyone can point to work that's being done on analyzing classrooms where student reasoning is the main driver of instruction.  It's really amazing watching third graders debate mathematical ideas the way mathematicians do.  What are the teacher moves that help create such an atmosphere in the classroom? How can we support teachers who start experimenting with this mode of instruction?



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