I started this post a long time ago (maybe two or three months ago), but scrapped it. But I’ve decided to finish it up and make a little plea for advice at the end.
What do you do when you ask a question and get a totally wrong answer? Okay, this question screams newbie, but it happens to me enough and I often get caught in an awkward situation. Let me explain.
A completely made-up but not unrealisitic example:
Me: So we now we have this:
. Where do you think we go from here? What are we trying to do again? StudentX?
[Context: We’ve learned how to graph quadratics, use the quadratic formula, complete the square, factor, and seen equations like this all year. It should be second nature to them. And for many it is, but for some it isn’t. The problem is this: we’re way beyond this. We’re working on some other concept, and these gaps force me to veer away from the current lesson and take a bunch of steps back to reteach these things to the few that don’t get it…]
StudentX: Um… well, we could add 2x to both sides…
Me: [awkward silence while I think of what to say, because I don’t want to do that…]
Me: At every step, we want to ask ourselves: (1) why do we do that? and (2) what are we trying to find out? So why would we add 2x to both sides? What are we trying to do?[Context: Even when they are on the right track, I will ask this question. I want them to think about every move they make.]
StudentX: I don’t know.
At this point, I’ll ask what type of equation we have, and what we know about it. StudentX will finally get it (“quadratic!”), and we’ll move on.
Sometimes I don’t make it a drawn out process. If I’m in a rush, I will ask if someone else has a different idea and call on someone who I know will have the right answer, and then move from there. And then I’ll return briefly to the original idea and explain why it won’t get us to where we want to be.
But this interaction takes 3-5 minutes, I know 80% of the students in the class are bored, some are trying to whisper the answer to the student, and we get held up.[1]
Of course, I’m all about meeting students where they’re at. And I’m happy to review. But these moments happen all too often, and using every one of them as a teachable moment takes too much time and would be bad practice. I have a curriculum to cover. Taking three steps back constantly is tough.
That tension, between moving forward in the curriculum and making sure students are up to speed on the older stuff, is palpable.
I often feel like I sacrifice the majority of the class when I do too many of these types of things. I don’t want to praise a wrong answer (“That’s a great idea, but I’m not sure it’ll help”), I don’t want to scare a student from speaking in class (“No”), I don’t want to spend a lot of time on a basic skill that the rest of the class knows, I don’t want to make the student feel dumb or ignored (“Anyone else have a different idea?”).
I’m afraid I’ve done all three.
To make this into a truly teachable moment would require me to add 2x to both sides, and then stick with the student and ask them what next. And just stick with them until they see that they’re stuck. But I tend to only go down really wrong paths in math when we’re learning something new and we have the time to have these dead end explorations.
Basically, when it comes down to it, I recognize that I still don’t know how to organize and manage a differentiated classroom well, how to scaffold lessons, how to keep everyone engaged and learning, while still moving forward in a fast-paced curriculum. It’s not that I don’t try. About 30% of my students have some learning difference or another, and I do think about that when I’m designing my lessons. I do. But what I’m doing isn’t working. At least not as well as I’d like.
I think that in addition to classroom management, this is one of those big topics that doesn’t often get explicitly addressed in teacher blogs. Maybe that’s because a good many teachers do it without thinking about it – it’s natural. But even though I do a lot of things naturally well, planning a scaffolded lesson for a pretty differentiated class isn’t one of my fortes. Yet.
So anyway, if you know of any blog posts or websites, or have any advice, holla out in the comments.[2]
Yeah, I know, I know. Everything about this screams “Newbie.”
[1] One of my fears is that I’m going too slow for a bunch of my kids, and I’m not sure where my focus should go. The middle of the road? Those that don’t get it? Those that do? For me, I think a complicating factor is that I was always one of those kids who did get it, and really quickly. I identify with them. I don’t want those kids to be bored. And I feel guilty because I am pretty sure they are bored.
[2] Five or so years ago, I read about differentiated classrooms in one of my teaching classes, but the readings were all academic mumbo jumbo with no connection to reality. I’m looking for something useful.
Continuous Everywhere but Differentiable Nowhere 
One quick suggestion – when you first teach the concept, record your instruction or find a math cast that demonstrates what you are doing.(Here’s a great site for HS math http://schellenbergmath.wikispaces.com/Math+10) Then refer the student to that site for their review. Give them one or two problems that reflect the skill that they haven’t mastered and ask them to complete that for homework. (if they still don’t get it, you don’t want them to have to complete 10 of the same type of problem. one or two should give you an idea if they get it).
Hi!
Leture time is over. Put kids in groups of three; have them solve problem in group; have one group member describe what they did. Keep doing similar problems until objective is attained.
KarenJan sent me over, and I need to think a bit on this, but the two suggestions above are the beginning. The problem with “whole class instruction” – the reason it really ‘never’ works, is because what you are describing is inevitable. If you are lucky (and your room is a perfect Bell Curve of something), you’ll be boring 1/3 of the class, at the right moment for 1/3, and leaving the last 1/3 completely lost.
So you need to use contemporary tools to go back to the techniques which existed before graded classrooms. You need teams, as Jim Hollis, suggests – but teams backed with tech supports, websites and other learning tools which explain things in different ways or offer supportive solutions. You may need to program certain supports into the calculators of certain students so they can focus on concepts rather than the mechanics. You may need to assign differing homework to keep everyone interested – not extra-credit or catch up work, but fully different assignments based on need. And you may need to depend on the combination of technology (web sites, software) and peer teaching (that ‘fastest’ third working for that ‘slowest’ third) in order to multiply yourself.
You are finding yourself in the impossible system our leaders create for you. Breaking through isn’t easy, but technology and groups and differentiated assignments make it almost possible.
One (low tech) way that I handle this type of situation is that when I get to the point in the example where we have reached a previous concept I have them finish it on there own in their notes. I will circle the room to make sure students are doing the right thing. When I find someone who has it correct, I usually send them to the board to write the rest out. This allows the ones who are confused the chance to make that false start (add 2x to both sides) and give them the learning moment they need. It allows enough time for my average students to complete the problem on their own. And it gives at least one of my advanced students something to do. In addition to this, whenever a student writes out a solution on the board, there is almost always something I can say about the work that needs to be a bit more clear, further indicating the importance of clear communication of the steps.
Thanks everyone for some great suggestions.
@Karen: interestingly, I actually had my students make those instructional videos using SmartBoard. This year (my first) it was a moderate success, I’d say, but it could be more successful next year with all that I’ve learned. I’m going to spend some quality time next year teaching students how to teach (how to say and write clear explanations).
@Ira: I love the idea of offering differing homework assignments. A lot.
@Andy: Using the time a student who “gets” it to get it set up on the board to allow others more time to work is awesome. I also think that having students teach is great. I’ve been doing that more and more as the year has gone on.
Right now I have students sitting in desks of 2 and I’ll often put up a problem for students to work on together, or discuss a question with their partner, to check their understanding. I try to be conscientious of who I’m placing with whom.
But I do find that I tend to be a very teacher-centered teacher. I feel like I lecture more than maybe I should — with pauses for “check yourself” bits.
Maybe next year I’ll have groups of 4 and more groupwork activity built into the lessons… I’ll definitely be doing some differentiated homework, and be collecting some mathcast videos on the web to post somewhere for students to refer to.
Thanks for helping a newbie out.
I do use group work – a lot.
One thing I sometimes do that seems to work, when a student puts up a solution that is incorrect (or gives an answer that is… flawed), I have another student explain how/where the first student’s thinking went wrong. The students often use less “mathy” language than I would. This gets through better to the student having difficulty. Then we clean up the explanation.