In my first few years in the classroom, I held the notion that the best way to improve as a teacher was to **hone my explaining skills**. I figured that if I could explain things more clearly, then my students would learn more.

It only took me a few years to realize that this philosophy of personal development was woefully incomplete. (Quick learner, right?!) So I turned my attention to a more noble pursuit: **engaging my students**.

In version 1 of this approach, I tried to find ways to get my students to pay more attention to my *better-than-they-used-to-be* explanations. The net result? Nothing much changed.

In version 2, I put my energy into engaging students not with *explanations*, but with *mathematics*. I tried—and still try—to create opportunities for students to engage productively with a problem or a concept. As with everything else in my life, it’s a work in progress. But I’ve seen some promising results.

Last week at NCTM, these percolating thoughts combined with several tweets, sessions, and conversations and led to this thought:

*The best way to grow as a teacher is to develop my capacity to listen, to hear, to understand.*

(Quick aside: I suppose I might replace the word teacher with husband, father, neighbor, colleague, or stranger, and the statement would still hold.)

This doesn’t mean that I’ll stop working on those other skills. But it does mean I have a new passion for learning about listening—really listening—to students and their thinking.

If you know of any books, articles, or blog posts that might help me along, please share them in the comments. Or maybe you disagree with my thoughts above as some combination of wrong or incomplete? I’d love to hear your pushback in the comments as well. Thanks in advance!

## Comments 9

I would say listen like you have all the time in the world for a student to understand. I began my career teaching students with disabilities at a non-public school. We used a competency based curriculum and it was self-paced. If a student took 1.5 years to get through algebra…that was fine. I learned the skill of listening through those students.

This is one on the tenants of Dale Carnegie…seek first to understand then to be understood. Classic advice that we all need to be reminded of regularly. Thanks. I need that!

I totally agree. The best way to tutor a student is to sit behind her while she works problems at the board and ask her to explain her thinking out loud as she works. There are times when a student will do the right thing for the wrong reason, but I would never know unless I asked her to think her thoughts out loud.

Yes! My first few years of teaching, I thought that I was a great “explainer.” My students even told me that I was good at explaining difficult topics, so this reinforced the notion that I was doing a good job at teaching. It probably took me longer that it took you to realize that my job was to listen. (Although, I think that explaining has a good place in dialogue – that is, one-on-one talking with ONE student, like in a tutoring situation. It’s easier to ensure that one person understands and the task of listening is more likely to be assumed by BOTH parties.) But classroom situations are different. I finally learned listening when I went through National Board Certification and had to orchestrate REAL classroom mathematical discourse on video. I had to WATCH myself teach on video – YIKES! – several times before I got it. And, this brings to me one of my points – how powerful teacher reflection can be when they watch videos of themselves teaching. It’s essential that teachers listen to what students say when the teacher is responsible for orchestrating real math discourse. The point is to get all students to listen to each other, so teachers have to do it in order for anyone else in the classroom to. In the past several years, I have conducted video clubs where teachers examine their teaching, but the focus of the clubs had been on *student thinking*. That prompt alone changes the focus from teacher moves to students’ ideas. This takes some of the pressure off of teachers to perform/explain and tacitly provokes them to elicit student thinking in the class. Then in the video club, we can unpack the student think as a group. That practice of unpacking translates to better noticing and attending to student thinking in subsequent teaching. Basically, reflection via videos and video clubs can be a powerful tool to change teachers to listeners, instead of explainers. Shameless plug: I collaborated with some colleagues on a Sept 2014 Mathematics Teacher article: “Lenses for Examining Students’ Mathematical Thinking.” Perhaps those lenses will help with listening.

Listening is very important! But the idea comes about of how do you get students to speak, and more specifically speak on topic. My belief is that this comes from questioning. Developing GOOD questions and activities that lead to discussions which are guided by the teacher but led by the students are integral in a mathematics classroom. I have recently spent time thinking about the correct questions to ask, so that the students can discover the math on their own and have discussions with one another. When students are stuck on a problem I try to use a Socratic Method technique of asking questions to lead them in the right direction. If I HEAR something I don’t like, I ask other questions to get them back on the path.

To make a connection to a previous post, I think these questions we ask students (which lead to them discussing and we as teacher listening) are easier to create with a high level of content area knowledge. I great lesson to me is where I design activities and discussions, and students work with one another and guide one another to the correct techniques and solutions.

Do we really have to move “beyond explaining”?

Are there principles for giving good mathematical explanations? Granted, there’s more to teaching than explanations (a lot more). Still, it doesn’t seem to me like the MTBoS is brimming with pieces thinking about what it takes to give a good explanation in math. In fact, I’ll bounce your question back — if you know of any good pieces on how to give good mathematical explanations, I would love to read them!

As far as listening goes, though: absolutely! It’s so important.

One thing that I’ve learned that listening isn’t just about “listening.” Part of what helps me listen more carefully to my students is understanding more about their thinking. The model for me, here, is Cognitively Guided Instruction. I think of CGI as a theory of how students think about arithmetic word problems.

Max Ray-Riek distinguishes between listening

foran idea and listeningtoour students. In that sense, CGI helps me listen for different sorts of thinking, but that opens up space for me to listen to my students in more patient ways. I think it’s because having a mental model of student strategies helps me listen to those strategies, instead of just listening for correctness/incorrectness.I’m excited to see where an orientation towards listening takes you in your work as a curriculum designer.

Author

Michael: Thanks for the comment and the great questions.

Do we really have to move “beyond explaining”?I think so. Not in the sense of “leaving behind,” but rather “progressing beyond.” In my early years, I relied pretty heavily on explaining. I figured that honing my skills here would be a (the?) major ingredient in boosting classroom success (as measured by student learning).

That being said, I appreciate your encouragement to think more carefully about what it takes to give a good explanation in math, and how explanation fits into a teacher’s overall skill set.

Side note: I think it’s time for me to learn more about CGI. What I actually know about it is pretty limited. Is

Children’s Mathematics(Heinemann) the best place to begin?I love Max’s distinction between listening

forand listeningto. So good.I’m excited to see where an orientation towards listening takes you in your work as a curriculum designer.Me too.

Children’s Mathematicsis a great place to start. A few years ago I wrote the CGI page on Raymond’s Math Ed Wiki (here), which might be helpful to start. I think a lot of the CGI papers are pretty readable and give you a decent sense of the project.As far as “moving beyond explanations,” I can totally agree that we should move beyond seeing explanations as the key component of math instruction. But it still seems to me that explanations are a pretty significant piece of what we do to help students learn math, and I have no reason to believe that it’s a particularly well-understood aspect of teaching.

(A trick that some teachers pull off is to avoid offering teacher explanations and instead creating situations where students provide explanations to each other. It seems to me that it’d be a mistake to say that this is moving beyond explanations.)

Teaching is a deeply interconnected activity. If you listen differently, you explain differently. So I think we can’t move beyond explanations, any more than we can move beyond classroom management. My experience has been that once I started listening and learning more about how kids think about a topic I’ve been able to more accurately understand what my students limitations of learning are. This allows me to point out and explain in new and (yes) exciting ways. And all this requires slightly differently classroom structures and management techniques, etc.

Teaching is one big knot, and I’m all for focusing on just an aspect of the work at a time. But if we’re moving “beyond” anything, I think we have to move “beyond” placing one aspect of teaching above any other. It’s all connected.

(related: Nothing Works)

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