We haven’t started school year. But last week and this week I’ve done some brainstorming about things I intend to do this school year (which *ahem* has some aphorism involving a road and hell associated with it, right?), and so I thought I’d pull out those few concrete little bits that deal with questioning that I want to do this year.
- If your group has a question, everyone in the group must raise their hand to call me over… This is how I started the last couple years of precalculus (all my kids work in groups). The idea was that if a kid had a question, they needed to first talk with their group so that the math teacher (me!) was not the sole mathematical authority in the classroom. I quickly added on … and I will call on one of you randomly to ask me the question. That way everyone in the group had to be comfortable asking the question, and that it was a real group question and not just an individual question.Last year, for some reason, I didn’t keep up with this practice, and started answering individual questions. I need to remember to keep up with this practice, because it’s awesome and it works to get kids really talking and explaining without you.
- I taught calculus for seven years, and when I started standards based grading, I used to put after each question testing each skill a little box:
It was useful when I met with students to discuss their tests. If they felt shaky and did poorly, that meant one thing to me. If they felt confident and did poorly, that meant another. If they felt shaky and did awesome, that meant something totally different. It led to some good conversations, and got kids to be more meta-cognitive. It also led to some interesting written feedback on the tests (even if I didn’t meet with the student).But I only ever did that in calculus, and I don’t teach calculus anymore. So I want to incorporate this on my assessments in my other classes — at least geometry and precalculus. When I’m asking a “mathy” question, this is a sort of different additional question that helps me put their response in some context. - Questions can have different purposes for me, even though I don’t (in the moment) think of them this way. Mostly they are to either (a) to get a student to go from a place of not understand to understanding (through asking questions to get them to think and make connections), or they are (b) to help me understand what a kid (or my class as a whole) is understanding.If I’m asking a question to the whole class, and my purpose is to figure out what my kids understand and what they don’t, I’m not going to have my kids raise their hands anymore. I got to the point where sometimes I would call on kids with their hands raised, and sometimes not. I mean: if the kids all raising their hands to answer a question feel they know the answer, then why am I calling on them? Instead, I am thinking of stealing an idea from a friend who taught middle school: THE POPSICLE STICKS OF DESTINY. I am going to have my kids’ names written down on popsicle sticks and pull them out of a mason jar (because I’m such a hipster!) to randomly call on someone. Yeah, index cards work too, but INDEX CARDS OF DESTINY is way less fun to say dramatically.
If I do this, however, I need to make sure that the kid who doesn’t know something or is confused feels like the classroom is a safe space. This year I’ll be teaching the advanced sections, so there is a lot of insecurity that these kids have about “being smart” (*cringe* I hate that word) and “appearing dumb” to their classmates. I have to brainstorm how I’m going to publicly reward kids for having good questions or being confused but doing something about that confusion or for being wrong but for owning it and saying “I NEED TO GET THINGS WRONG IN ORDER TO FIGURE OUT HOW TO BE RIGHT. AND I’M AWESOME FOR KNOWING THAT.” Heck, maybe I’ll have a poster made which says that, and have kids read it aloud occasionally when they’re wrong. And I should point to it and say it when I am wrong. Or maybe that’s dumb. I don’t know.
That’s about it for now. Hopefully more to come as I figure things out!
[cross posted on the betterQs blog!]
Continuous Everywhere but Differentiable Nowhere 
I love “The Popsicle Sticks of Destiny.” I am going to call mine that now.
– Elizabeth (@cheesemonkeysf)
Sam, I love the popsicle sticks idea, even in high school. Within a few weeks of the start of the term, it is clear who will be raising their hands to answer questions most of the time in Algebra 2, even with extended wait time. So how do you randomly call on students without shaming them – those students who struggle (if you are not teaching honors) – using the PSOD? (I’ve created an acronym for you!) As I am typing this, I am wondering if I create the sticks rather than the students I can color code them – there are rainbow colored popsicle sticks available, I think. Do you have any thoughts about this?
“So how do you randomly call on students without shaming them – those students who struggle (if you are not teaching honors) – using the PSOD? (I’ve created an acronym for you!)” That is exactly the question I’m grappling with. I want to create a culture where not having the right answer, but talking about what they do know or something specific they don’t understand is really celebrated — process! growth mindset! But I’m not sure yet… I think some of the commenters below talk about it though.
I really like #1 and #2. But I do not feel so great about #3 (other than its name!).
My thinking is that one of the important (difficult) tasks for an instructor who teaches in a way that incorporates participation as a cornerstone is to determine who to call on. I do not think that randomness is the best approach (even in the whole class setting specified here).
As one small example: If I have a question that I think might determine how well the students are progressing in their understanding, I’ll pose it, and ask that everyone take a moment to give it some thought. Then I’ll ask for someone who is not so sure about their answer/idea to share it out. (This requires establishing certain norms around mistake-making, as alluded to towards the end of #3.) And then I’ll ask for other answers and ideas before deciding which one(s) to explore (and how).
…Just a thought to be taken with a grain/pillar of salt.
MQ
If you consistently ask those who are not sure to share, you’ll make everyone pretend to be sure, even when they aren’t. You’ll also make some of the students feel that you are picking on them. Better to be obviously random—but do ask the question and pause before picking who to cold call.
“If you consistently ask those who are not sure to share, you’ll make everyone pretend to be sure, even when they aren’t.”
This has not been my experience. Rather, students have been quite willing to share incorrect answers, different answers from others, ideas that didn’t work out, misinterpretations of questions, and so forth. There are also some students who are frequently correct, but harbor enough self-doubt to consider themselves unsure; if that particular issue arises, it can be addressed separately.
“You’ll also make some of the students feel that you are picking on them.”
I do try to keep a mental log of how often students are speaking. So, if I notice that some haven’t spoken up, I’ll call on them later on.
E.g., GasStationWithoutPumps, we haven’t heard from you today. What do you think about … ?
I don’t believe it is beneficial “to be obviously random.” (Note, by the way, that a “random” method such as using popsicle sticks will lead to some students being called on multiple times in a row; although random, this will probably induce the exact concern you have about feeling “picked on.” This can be modified by removing the stick from the jar or a similar alteration, but that can disengage those who have already spoken – somewhat akin to those who try to speak early on in a discussion in order to avoid being called on later!)
Anyway: I believe strongly that the teacher should draw from her own pedagogical expertise in calling on students to facilitate discussion; on this matter, we may well diverge.
Yes, I’ve asked students who are *unsure* to share their thoughts, and that has worked with varying success. Maybe I shouldn’t have a blanket “popsicle stick for questions to let me know what the students are thinking,” but I do think there is something very egalitarian and visible (and let’s every kid know they are accountable for sharing their thinking) that I like about it. I must think on this some more. Thanks for sharing your thoughts (pillar!!! of salt).
When a student asked a good question in my class, I make a big deal about how lucky that class is to have that student in it because he or she is not afraid to ask questions and so the whole class is going to learn more. I do the same thing when someone makes a mistake. It does seem to establish a positive culture for being willing to stick your neck out and take a risk for the good of the whole class.
Thanks. I’ve been thinking a lot on these lines. I just need a way to remember to do this consistently — some sort of visible reminder/structure to help me with this!
My experience may differ from Maya’s because I’m mainly teaching 10-week classes at the University. There are not 180 days to establish a class culture, and many students are often quite reluctant to say anything in class (something like 1/3 of our students are first in family to go to college and suffering from “imposter syndrome”).
I used to rely on “pedagogical expertise” to choose who to call on also, but I read a number of papers about how teachers’ unconscious biases lead to systematic inequities in who got called on, and I read the advice in “Teach Like a Champion” on cold calling. Although I don’t always use randomization, I’ve found I get better class participation when I do.
I don’t use popsicle sticks (too much trouble to set up). Instead I use a numbered class list and roll dice to get a uniform distribution. I re-roll if the number is not on the class list or if the student is absent. The time it takes to roll the dice is built-in think-time for the students.
What dice I use depends on the class size. For example, if I have 32 students, I would do D8*4+D4-8. For 40 students, I would do D4*10+D10-10. The biggest problem is making sure that I have remembered to bring an up-to-date class list and dice to class, along with all the other stuff I have to lug around.
I don’t do cold-calling in lab—I rarely give more than 3 minutes of lecture in lab and spend most of the time answering student questions, not asking them questions (other than things like “where’s your schematic?” “have you turned on the power?” “what are you trying to do?”)
I use cards, but in order to make sure kids don’t immediately tune out after their card has been called, everyone in a class has three name cards in the stack. I shuffle at the beginning of class (and later if I get to the end of the stack during class). That way everybody has multiple chances to be called, but no one can be called endlessly.
Also, I can see the next name in the stack, and I can tailor the question to the student if necessary. Also, I sometimes phrase the questions as asking for opinions, which takes away some of the stigma of being wrong where most students are likely to be unsure, and I often ask students to critique each others’ answers this way.
Sometimes I call on kids whose names didn’t come up, maybe because I can see from their expression that they have something to add, maybe because I want to get their attention back on the subject at hand, maybe because they’re shaking their head in disagreement with the last speaker.
Personally, I have found that I’m not very good at making sure everyone gets to participate — some kids are great at hiding in plain sight, and the cards do make it pretty obvious to the kids that I’m not playing favorites.
I have tongue depressors of destiny! (I’m going to steal the nomenclature ;-) I really like your ideas; some of them even make me wish I was teaching math (I’m an English and social studies teacher).
Im making a poster that has a list of alternatives to ‘I don’t know’
● I don’t understand
● Can you help me?
● I can try!
● This is a little hard for me.
● I’m guessing…
● Can I think for a minute?
● Before I can respond, I need…
● I’m not sure, but I CAN tell you that…
● I’m confused exactly here…
● It’s just a hunch but…
Awesome ideas all around. I’ve taken the “popsicle sticks” idea and added a new wrinkle- I put the sticks in my back pocket, and after I draw a student, I transfer the stick to the other pocket. Everyone knows that they will be picked, (so they can be ready) but this helps me subvert my unconscious bias in only picking the students who consistently give good answers. Add an extra bonus, the sticks make it really easy to select pools of students for quick groups-just start drawing sticks!
Sam, I thought your points were great! I especially liked your idea about having students circle their feelings about their work on a problem before it was graded. I’m curious to hear about how that changes the conversations that you have with students, or even how that changes how you teach the material in the future. I also could tell from your post that you value the process of “being wrong” and are working towards stressing that to your students as well. I also enjoyed hearing about how your rule of having everyone in the group raise your hand has changed your classroom dynamic for the better!
And… I didn’t follow through on the test confidence level thingie this year. But I have done it for a number of years in the past in non-AP calculus. The conversations with kids — when I met one on one with them — was often driven by their confidence level versus their performance… And how we can weed out false confidence (if they rated high confidence but showed misconceptions&errors) and if they had low confidence on a question, we talked about how they prepared and how they were understanding (or not understanding) the material in class and at home.