**Listen to Your Students**

Teachers are busy—so busy we often don’t hear what students say. Sometimes we hear things that students don’t say. I’ll make a case for the importance of listening carefully to students of all ages. I’ll encourage you to make time to listen more carefully, and I’ll give you some simple strategies for doing it.

**Call to Action**

Try this 3 times: When a student explains something or makes a claim in the regular course of class, and you believe you and the student have a shared understanding, ask a follow-up question. Listen carefully to the response. Make a note of any differences between what you expected to hear and what you heard. Share one instance where these differed by briefly describing: (1) The initial student explanation or claim, (2) Your follow up question, (3) What you expected to hear, (4) What you did hear, and (5) Your reflections on what this difference means for your class.

**About the Speaker**

Christopher Danielson is a curriculum writer, educator, math blogger, and researcher bringing cutting edge ideas from mathematics education research to parents and teachers across the country. He teaches at Normandale Community College in Minnesota. He has written Common Core Math For Parents For Dummies, which came out April 2015. He blogs at Talking Math with Your Kids and Overthinking My Teaching. Find him on Twitter: @Trianglemancsd.

**Updated 2015 Apr 21: Livetweeting**

Check out the collection on Storify.

Students were working on a problem that involved 2/5 x 7/10 and I was walking around the room observing their work. Glanced over a student’s shoulder and saw “Doubling and Halving” written with the correct answer. Assuming it was doubling/halving in the sense of doubling one factor and halving another factor, I was excited to see the use of the strategy.

Then, I asked her how she did it and it was not at all like I had imagined.

“I halved this numerator and doubled this denominator [points to 2/5] then I doubled this numerator and halved this denominator [points to 7/10].” I asked her to write the fractions she ended up multiplying she said 1/10 x 14/5 and got 14/50. Ok, now THIS is much different than I thought!!

Listening to her explain her correct answer and strategy name made all the difference in the way she was truly solving the problem!!

Wow! This is a sharp example of how we think we know what students are thinking even when we do not.

And now I want to ask that student,

How did you know to do that?And I need to go play around with this strategy to really get a handle on what’s going on. It is definitely something I haven’t thought about before.Thanks for sharing it!

Very nice compact talk, Christopher. I question whether you necessarily “heard” the student say that he’d memorized 12 x 5 = 60 so much as that you didn’t question how he knew and simply accepted the fact. I’m wondering if the sin of omission here is assuming that he’d learned/memorized multiplication facts up to 12 as much as just not wondering about it at all given that the focus was how he got to 12 x 6 = 72. Sometimes when interviewing about mathematical thinking, it can be a tough call whether to just make a note of a “subquestion” that arises like this one (“How did that intermediate step get done?”) and come back to it if possible or to interrupt a train of thought by going for an immediate answer to a point that arises as part of a bigger explanation/answer.

The above almost feels like the third student you mentioned who was deeply concerned with determining significance. It’s hard to listen, think, question, make notes, anticipate, and any number of other things that go into this sort of interviewing, and that’s if you have the discipline not to interject a lot. This all starts to get very “meta” when you then put it in the context of interviewing student thinking about their own thinking about doing math and (sometimes) having to do one’s own thinking about that math while juggling all the balls mentioned above, even though the math is, ahem, elementary.

And then, of course, there’s the metacognition involved in being a student in mathematics trying to follow a lecture or classroom conversation about mathematics that one is trying to learn while still being aware of some of the issues of teaching and learning that are present in the room (or on the YouTubed lecture, as is so often the case with me these days). You really haven’t lived until you’re watching something on, say, category theory and trying to grasp the math and somehow still attending to all these pedagogical and metacognitive questions.

Not just in class where we hear things that aren’t said and don’t hear things that are. I know some couples who have been together long enough that most of their interaction is based around these two communication errors!

Absolutely right,

Joshua! Listening is such an important skill in all areas of human interaction. Do you think I should hit the self-help and marriage counseling circuit?I loved your talk and sent it out to all members of my department. I think your “Which one doesn’t belong” is a great way to get students to make a decision and use evidence to justify it. As with Common Core modeling, there are times when there is “no one right answer” and we just want insight to their thought process to be able to see what they are seeing. I love this idea and hope to create some examples for each class I teach.

When teachers attend conferences, we are often inspired by the lecture and want to incorporate the call to action, but then the time and demands of our daily lives take over and it gets lost. I think the shadow con web site is a great idea and would love to see teachers post their “Which one doesn’t belong” so we can share and not have to re-invent the wheel. Having a web sites like Estimation180, Daily Desmos, Graphing Stories and http://www.101qs.com/ with these kinds of questions already built would be amazing!

Good news,

Nancy!Mary Bourassa started a Which One Doesn’t Belong? website: wodb.ca.

Also, a version of my

Which One Doesn’t Belong?shapes book is coming—together with a Teacher’s Edition—from Stenhouse in spring 2016.SOOO Awesome -thanks for sharing this!

Your call to action is gaining legs, and we are off and running!