Classroom Questioning – A Portrait of a Math Teacher as an Aging Man

Questions about Questioning

I feel I am long overdue to write this blog post. In part, this is due to, you know, life getting in the way. In part it is because I have about three posts swirling around in my head right now. Next week our students are taking term finals so I will have a little more unstructured time and I may finally get around to writing more. That is, if I get around to writing plans for the short stint between thanksgiving and winter holidays.

Today, I am going to try and make sense of a fantastic post by Mark Chubb (@MarkChubb3) that can be found here. In the post (which you DEFINITELY should read) Mark raises important questions about the questions we ask our students AND the purpose, the goal, of those questions. I often tell a story about a student who graduated back in 1993 named Ashley. I had the privilege of teaching Ashley for four years in a row up through Calculus BC. The week before her AP exam I asked her how she was feeling. She told me that she was not worried at all because she knew that if she got stuck on a problem she would hear my voice in her head asking her what that problem reminded her of or what have we done in the past when we have seen this. I was flattered that she had internalized some of the strategies we had worked on together and I felt good that she felt comfort in my leading questions that I had been asking her over the years. She was also a tremendous student who was in a group of talented kids who pushed each other over that four year span. Since then, however, I have begun to question myself about the sort of questions I pose. I still believe that most of my students would be able to effectively work through problems they are presented if they can have an internal monologue that is similar to the conversations we have as a group. What I worry about is whether my guided questions are taking away their agency, their ability to discern what they think is important in a problem. I made it through high school math pretty successfully and I have confidence that I can guide students through this journey. But posts like Mark’s, and conversations I have had through this blog, in conferences, through twitter all push me in the direction of making my voice less central in my class. I have taken great strides in this direction in the past few years, but I still feel that I talk too much, that I initiate conversations and lines of questioning too often. That I impose my sensibilities about what to notice and what to wonder about on my students. The trouble is that many of them are happy to have me, and their other teachers, take on this burden. It is easier, it feels more stable and safe to hear the expert in the room direct the conversation. I know that this is not the best strategy but I too often fall into this trap.

I am going to lift a portion of Mark’s post here to draw attention to the central question about questions that I think he was trying to raise.

Funneling vs. Focusing Questions

As part of my own learning, I have really started to notice the types of questions I ask. There is a really big difference here between funneling and focusingquestions:

Think about this from the students’ perspective. What happens when we start to question them?

After reading this and playing back a number of classes in my head, classes that I was really proud of, classes where I felt that my students had made some major breakthroughs, I realized that I do FAR too much funneling and not enough focusing. An easy excuse is that my students struggle in metacognitive processes, so it is more painful and time-consuming to do this. And, just like my students want the more comforting path of me telling them what is important, I am prone to take the comforting role of the guiding questioner. But my students are not going to get better at monitoring and understanding their own thinking this way. They are not going to take ownership of what they feel is important in a problem this way. They can get to be better mathematicians and be more successful at high school math, but I fear that I am training students to be mini mrdardys instead of being better high school mathematicians as themselves.

Our school is moving to a new schedule model next year. We will be on a seven day cycle where in each rotation we meet four times for 50 minutes and one time for 90 minutes. This will force us to re-examine how we run our classes, how we will value and plan for our time together with students. There are many layers of what we will have to examine but for myself, I think that I will be going back to Mark’s post over and over, I’ll be looking at a few classes that I have had videotaped and I will be working out how to hand ownership of ideas to my students. I will be working on how to make sure that the classroom and the class time we spend together is not so dependent on my point of view and my insights into problems. I want my students to leave my class better high school mathematicians, that is absolutely true. But I want them to be better models of themselves as high school mathematicians, not imitations of me. As Ben Folds sang once, I do the best imitation of myself. I don’t need my students to be imitations of me.

TMC Reflections, Part Three

In this post I want to concentrate on a couple of the afternoon sessions I attended. The TMC program (you can find it here) was filled with so many interesting opportunities that I kind of agonized over some of the choices. One that I knew I would attend was the session run by Danielle Racer (@0mod3) discussing her experiences in implementing an Exeter-style problem based approach to Geometry this past year. Danielle and one of her colleagues (Miriam Singer who is @MSinger216) came back from the Exeter summer math program (it is called the Ajna Greer Conference and if you have never been, I suggest that you try to change that!) all fired up and ready to reinvent their Honors Geometry course. Danielle spoke eloquently about their experiences and shared out some important resources. We had a great conversation in the session about the benefits and struggles of problem based curriculum. This conversation tied in to another session I saw as well as some thoughts and conversations I have been having for years. First, the afternoon session that I think linked in here. Chris Robinson (@Isomorphic2CRob) and Jonathan Osters (@callmejosters) are colleagues from the Blake School in Minneapolis. Chris and Jonathan spoke about a shift in their assessment policy that centered around skills based quizzes using and SBG model and tests that were more open to novel problem solving. I am simplifying a bit here for the sake of making sense of my own thoughts. I thought that their presentation was thoughtful and it generated great conversation in the room. Perhaps we (especially I) spoke out more than Chris and Jonathan anticipated and we ran out of time. Another sign of a good presentation, I would say. When there is more enthusiasm and participation than you thought you’d get, it probably means that you are tapping in to important conversations AND you have created a space that feels safe and open.

These two sessions had me thinking about some important conversations we have been having at our school and I am totally interested in hearing any feedback. The first conversation I remembered was with a student who had transferred to our school as a senior and was in my AP Calculus AB class. She was complaining about my homework assignments which were a mix of some text problems and some problem sets I wrote. She said in class, ‘You seem to think that AP means All Problems.’ A little probing revealed that she saw a difference between exercises and problems. A brief, but meaningful, description I remember reading is that when you know what to do when you read the assignment then it is an exercise. If you read it and you don’t know what to do, then it is a problem (in more meanings than one, I’d say). The next conversation I recalled was with a colleague who has now retired from math teaching. We were talking about homework and the struggles with having students persevere through challenging assignments. He also used this language making distinctions between exercises and problems and he suggested that HW assignments should have exercises and problems should be discussed in class when everyone was working together. He felt that the struggle and frustration of problems when you are on your own would be discouraging to too many students and would likely lead to less effort toward completion on HW. A similar conversation came up with another former colleague who was frustrated with some of the problem sets I had written for our Geometry course. She did not want to send her kids home with HW that they would not be able to complete successfully. I recognized that this was coming from a fundamentally good place. She did not want her students to feel frustrated and unsuccessful. However, I firmly believe that real growth, real learning, and real satisfaction are all related to overcoming obstacles. I have witnessed this recently with my Lil’ Dardy who just became a full fledged bike rider this summer. I heard it from my boy, my not so Lil’ Dardy, who made the following observation recently, ‘You know, I find that I like video games much better if they are hard at first. Why do you think that is, dad?’

I know that we can anecdote each other to death on these issues and I also know that there is not ONE RIGHT WAY to do this. But I am in the process of trying to make coherent sense out of my inherent biases toward problem based learning. I want to have deep and meaningful conversations with students, with their parents, with my colleagues, and with my administration about how to approach this balance and about what a math class should look like and feel like in our school. While I have been writing this I was also engaging in a meaningful twitter chat about some of this with the incomparable Lisa Henry (@lmhenry9) and with one of my new favorite people Joel Bezaire (@joelbezaire) so I know I am not the only one struggling with these questions. Please hit me up on twitter (@mrdardy) or start a raging conversation in my comments section sharing your successes/failures/theories about how to strike a balance between exercises and problems between challenging students while making them feel safe and successful and between running your own classroom with your own standard and fitting in with a team at your school. These are all big questions and I wrestle with them all the time. I want to thank Danielle, Chris, and Jonathan for sparking them up in my mind again and for creating lovely spaces for conversations in their afternoon sessions.

Coming soon will be my last entry in this series where I think out loud about the amazing keynote delivered by Tracy Zager (@TracyZager)

Thinking About Work and about Homework

I took my mom to the airport this morning which means I have one less reason to start thinking about work again. We start back on Jan 5 – as many of us do, I am sure – and I have a pile of papers to grade and some class planning to do. As I have written before, we are working with a new Geometry book that I wrote last summer. You can find a dropbox link to it here. I have also posted a folder of the HW assignments we’ve written for it here. I’ll be updating the HW folder regularly. I have been compiling a list of edits for the text and I’ll be doing the updating work this spring.

As I think about our next Geometry unit I have really been wrestling with the role of HW and how to incorporate it into my classroom routine. I’ve been mostly teaching AP classes the past few years and I have definitely adopted an attitude that HW is assigned but not graded. I’ll discuss it in class when someone asks a question, but I don’t plan around that activity. These questions from my students pop up on quiz days or on test review days but not too often otherwise. I am under no illusion that the students are doing all of what I ask from them, but their performances indicate that most of them are doing enough to get a grasp of the material. I believe that their understanding and mastery of the material would be deeper with more practice. I also believe that they would practice more diligently if I incorporated HW into my grading system somehow. What I have seen is that any way that I have tried to include this into my grading system encourages copying and shortcuts that are frustrating to me and reward bad behavior. This year, however, I am working with younger students again in the Geometry class. These students pretty clearly crave much more attention to HW than my older kids seem to want/need. Days when I post the last HW on my AppleTV and spend time directly addressing it are clearly appreciated. What I am wrestling with is the feeling that these days also lack some of the creative problem solving feel of days with more open-ended questions driving the conversation. Am I wrestling with the balance between what motivates me and what motivates my students? I know that there is a cliche that most of us become the teachers we had. I certainly think about some of the inspirational teachers I had and try to capture some of that magic. However, I also find myself thinking at least as much about the experiences that were NOT inspirational and try to avoid those scenarios. For me, many of those uninspiring days centered around 20 – 30 minute conversations about last night’s HW. Days where we seemed to be spinning our wheels. I know I was not the only student who had completed the HW from the night before and did not need to have most of those problems reviewed right after completion. I know that I have students who drift away from being engaged when we are going over problems they have already thought about and completed correctly and confidently. I am really struggling with how to best strike a balance between what some of my students crave and what I think is best for them. I think that our time together is best spent on open questions that push our understanding forward, problems that would be a real stretch for them on their own. I want to include those (periodically) on HW assignments and concentrate on THOSE problems when we are together. Given that a number of my students seem to crave the comfort of the routine of doing HW and then going over it together, I need to find comfortable ways to incorporate that without stalling other routines. One way I am thinking of – and I know that this is not original at all – is to have answers posted at the beginning of class and asking students to take the lead on any review questions that pop up. I can have a few kids up at once and cover this material more quickly and in a more student-centered way. This way, we can get to the more challenging questions together more quickly and I can respect the desire to have space for HW review. Since we are writing our own HW assignments, the students have no answer page to look at and this may be an important source of the difference in HW attention desired. My older kids have standard texts with answers in the back of the book for reassurance.

I’ll report back soon after we start again and I’ll write about how this works. In the meantime, as always, I welcome wisdom in the comments section or through my twitter @mrdardy

Questioning Questioning

At our school’s whole faculty meeting yesterday morning (we see our kids on Monday for the first time) we had an interesting PD session on listening/counseling/advising and I have some ideas rattling around the cave of my mind that I need to air out somehow.

We had an exercise where we were to pair up with someone that we do not know well. Our school has two campuses separated by 3 miles – so the pairing generally was one upper school member with a lower school counterpart. We were to then take turns talking about something important to us for 8 minutes and then switch speaker roles. When it was not our turn to speak we were to listen – not to ask questions, not to comment, just listen. After the activity the guest speaker – a therapist from the Stanley H King Counseling Institute – was gathering reflections and impressions from us about this exercise. One of my colleagues commented that he found it difficult to listen without asking questions and the therapist remarked that it is difficult to simply let another person’s thoughts go where they want to go rather than influence them to go where we want them to go.

This got me thinking about my questioning habits in the classroom. I have long thought that one of my strengths as a teacher is my willingness to trade telling for asking in many situations. After this conversation yesterday I am now wondering how much I need to try to trade asking for listening in classroom discussion situations. Am I just fooling myself into thinking that my asking is any less monopolizing an activity than telling is? I need to ponder this and I’d love to hear any reflections from the world outside my head.