Saturday, March 19, 2011

What do you make of this?

On the subway, just now, I overheard two high school students talking about their math teachers:

- ...the old one? did you have him? He was f-ing horrible.  
- I heard so. 
- yeah cuz he gave us these difficult problems and no one got them and one time I was working on a different problem and he asked if I could do the one on the board and I said no and then he said, like in front of the whole class, "oh that means you have a lot to revise!".  
- jerk 
- yeah... 
- but you know then we had a different teacher and she was awesome! if someone didn't get something she was like "OK let's do this again!" and she explained it and was really patient. It was great.  
- yeah there are so few teachers like that, who can get contact with their students, no wonder at the end of high school everyone is so tired of studying.

Overhearing this exchange was really awesome for me, because it gets right to what I've been most concerned with all year: the differences in what students want, and what I want.

Because what these students are saying, what I think most of my weaker math-students would say if I asked them, is that teachers that give a lot of help, teachers who guide students through problems, teachers who make mathematics simple, are the good teachers. Teachers who give challenges, and then expect students to stick with the problem until they solve it, are the bad teachers.
Meanwhile, what I want is to engage students in thinking, to show them that they can do math more or less on their own, form their own conjectures and prove them, too. I hope that this way math comes alive and students develop interest and confidence as well as understanding and skill.

This is nothing new, and part of the invisible contract which Ben Blum-Smith wrote about beautifully in this post a year ago. But I do wonder about the effects of this discrepancy in teacher and student attitudes.
Could it be that these students are right? That, for them at least, and at this late stage in their relationship with mathematics, it is better to provide a crazy amount of scaffolding and to sacrifice ideals of creativity, fun and even deeper understanding for the benefit of getting the students to feel confident and safe in math class.
This has been my main question this year and I still don't know how to answer it.


  1. I think good teachers will struggle with this for as long as students come to math class involuntarily.

  2. To me the dilemma becomes how to help them feel safe, and still get them to struggle with hard questions.

  3. Sue, maybe a gradual weaning is in order? Get them to "struggle" with easy stuff, then up the complexity?

    Thing is - last year, many of my lower level seniors graduated with wonderful results. Several students told me this was all due to what a great teacher I am, that I explained things sooo well and made math seem soooo easy. And that I repeatedly told them I expected high results from them.
    This year, I don't think anyone will tell me I'm a great math teacher. I don't explain things, and I don't tell them I expect high results (I tell them that I expect full understanding and mastery, but that doesn't seem to translate into motivation for most students). But personally, I think I'm a better teacher now than before.

    You say this is the dilemma. How do you actually, concretely, handle it?

  4. I read the above exchange and found myself agreeing with the students: the first teacher seemed to take great joy in belittling the student, "oh that means you have a lot to revise!"

    I think the thing I find myself disagreeing about your approach, Julia, is that I feel you are treating your students as if they all are at the same ability level: last year, you explained to everyone; this year, you explained to no one. I'm not always successful in knowing my students as well as I want to, but when I am, I know who is going to need me to help them as soon as they get lost and who I can smile at and say, "No, keep working at it until you figure it out." I wish I didn't have to provide so much support to some students who struggle, but sometimes it's the difference between them finally getting it and them still completely clueless come the test. I'm not saying I always get it right--sometimes I may be guilty of helping a student who's ready to be weaned--but I just couldn't conceive of not providing greater differentiation, even for a supposedly homogeneous honors course.

  5. Paul - hmmm... I just took a longish think about what you are saying and well, I don't fully agree.
    I do differentiate, but I do it by having students work on investigations in groups. In groups, students natrally take different positions, including the position of asking other students to explain.
    Also, I differentiate in terms of difficulty of challenge. I don't give my lower level math class the same kind of challenges as I give my higher level math class (I recently asked to prove Goldbach's conjecture). And when a student asks me for help, I do give different responses depending on what I know about this student.

    However, you are right that I don't use radically different approaches within the same group of students and the reason is that I simply lack the skill to organize my lessons in such a way as to make such differentiation possible, while still striving for both depth and speed. For example, in one of my groups I have a standard and a higher level course,with a more advanced syllabus, combined. Ideally I would somehow teach the basics to the standard level group and then also the more advanced stuff to the higher level group. This never, ever, happens and instead I squeeze all the advanced stuff into the one hour per week that I meet with my higher level students alone. I wish I knew how to do things differently but right now the activities I have planned for every class are just too time-demanding and require almost constant interaction between me and the students, to make such differentiation possible. (This is also due to the time pressure imposed on this class - the IB recommends 150h but the school currently only allows 135 or something).

    How do YOU differentiate and yet manage to aim for depth of understanding when teaching, say, logarithms?

  6. First let me say that I don't envy you having to try to differentiate over a wide range in a large class. I bet there's no really good answer to that one. What bothers me sometimes is when (e.g., in several Teachers TV videos I watched recently) `"differentiation" means that there are hard, middle and easy things to do - but still no principled reason to think that, and no thought about how to check that, the difficulty levels are actually appropriate to help the students learn. If your easy thing is still too hard for your weakest students to learn from or your hard thing is still too easy for your strongest to learn from, it isn't effective differentiation, and you literally might as well not bother to differentiate at all: a miss is as good as a mile. I'm (sorry!) suspicious of your differentiation by groupwork for this reason.

    I think that generally people are more willing to have a go and struggle a bit *if* they know that help is available when they decide to ask for it (security!). Really difficult to ensure that it genuinely is in practice, though, if students are working on lots of different problems. Maybe giving problems to which you have printed worked solutions, and allowing students to ask for the solutions when they want them, would sometimes be worth trying? It might be that students saying "No, don't tell me!" is a thing to aim for.

    FWIW, at university the problem we have more often than students wanting help too soon, IME, is students not asking for help when we could easily have helped them if only they'd asked.

  7. Perdita, I take your point. Definitely differentiation by group-work is not ideal, but I just don't have an option right now. But I'm learning!

    I am moving more towards giving them markschemes. They have been asking for them all year, but I've only reluctantly given it. I guess I whole heartedly believe(d) Dan's "be less helpful" credo. But it's a question of balance. I want to show them there is support, but also encourage them to work hard on their own, because I sincerely believe - I know - that even if every kid in my classes can't figure everything out themselves, TOGETHER they can understand and master everything. (But I also understand that this kind of cooperations is time-consuming and sometimes not realistic).
    Like so many things it's a matter of trying different approaches, modifying them, finding what works - then changing it again with the next group. :) That's part of what makes this work so incredibly challenging and fun. :)