I live in a dorm on our campus and we have about 80 boys in our building. Tonight one of them asked me to help him study for a test tomorrow in his Precalc class on conic sections. Earlier in the day at school a boy from Calculus Honors was working through L’Hopital’s Rule and struggling a bit. He was in my room working during one of my free periods and I helped him out a bit as I was running in and out of the class. In each case, I found myself really concentrating on ‘how do I do this?’ questions with these guys. Normally, I think of myself as a teacher who really focuses on process. I ask my students many questions and I try to emphasize ideas, connections, principles at work. But I find that when I am in this sort of tutoring type of environment – especially when I am working with students from other classes, not my students – then I switch to a much more functional, how do you solve this problem approach. Don’t know why I do that and I think I’m unhappy about it. I just noticed this in a very obvious way today and I want to toss that observation out to the world. Do you find yourself being a different teacher in these situations? Is there a good reason for it?

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I think some people change their teaching style when working with students not in their immediate class out of respect for that student’s classroom teacher. The presumption is that the concepts, ideas, etc. are being explained to the student from elsewhere and there isn’t really a reason to inundate the student with another explanation of concepts — some that the student may have already understood or is trying to synthesize.

I think it’s natural to switch into “functional” teaching. There’s also nothing wrong to teach the process, especially with mathematics.

A current “cultural” trend in math education is to emphasize teaching concepts and to view teaching mechanics as this ugly “industrial” approach. I think that’s why some of us start to feel a bit dirty about focusing on process. The truth, though, is that progress in mathematics requires both conceptual and procedural understanding. Concepts without process are just a fantasy. Process without concepts are dangerous.

Context. That’s got to be part of it, anyway.

When I’m working with a student from another class, I don’t know what she did yesterday, what she did two weeks ago, what she struggles with in general, what she’s going to do in class tomorrow or in a week. Without that context , I find I often slip into the same style you described.

Another issue might be time. Developing processes, conceptually understanding, and habits of mind take time. I work 180 days a year with my own students, and they often end the year lacking in one (or all three) of those important categories. When faced with a student from another class in a one-time or short series of tutoring sessions, the time to develop those ideas and habits isn’t always available.

Great question/reflection. Thanks for sharing!

You also don’t want to undermine the conceptual underpinnings that the student’s “regular” teacher may have put in place. Consciously or not, you know that the procedural is a safe route.

Tutoring is different from teaching. In a tutoring scenario, you are not establishing a conceptual system with shared language and experiences. You are not creating the intellectual world the student is living in. When you are tutoring, your job is short term and focused. Help this student do this this thing. It has taken me many years to begin to understand this difference.

I agree with everything else that people have said already. Foremost for me is remembering that tutoring is different from teaching.

I used to find myself being a much more patient teacher with students who are not mine. Sadly, I was more likely to get frustrated with my own, saying things like “we covered this in class” and being generally annoyed when they didn’t get it the first time.

Now, it’s almost the opposite. With my own students, I ask the probing questions, getting them to explain their thinking as well as their reasoning. Since those are things that we have focused on in class, they are used to those types of questions (mostly). With other students, I am more likely to give them the process and let them do the calculation. Students who are not used to the struggle are much more likely to give up.

I don’t have an answer. Only observations.

When tutoring, I sometimes find myself doing the same thing.

Sometimes it is selfish, wishing to demonstrate that I can solve a problem that posed them difficulty. This does not really help a student much, as watching someone else solve a problem does not affect understanding and retention nearly as much as solving it yourself.

Sometimes it is out of desperation, because all the other approaches I have tried did not seem to help the student.

Sometimes it is out of need, because their test starts in 10 minutes.

Sometimes it is because I cannot think of any good questions to ask about the situation that might open up a new line of thought for the student. This happens most often with topics I have not helped students with very often, but can also happen with students who have difficulty talking about their mathematical thinking. If they have not had much practice using the vocabulary that they have listened to in Math class, they can struggle to voice their thoughts.

When I am not in one of the above situations, I will often try to start the dialogue with questions like:

– If this applies to the situation: Have you “doodled” the problem (created your own illustration of all information relevant to the problem)? Sometimes just rewriting the algebraic part of the problem statement will lead to ideas for how to solve the problem.

– What kind of mathematical situation is this?

– Have you seen another situation like this? If so, what and when? Are you feeling as though you are “supposed” to take some particular approach?

– Have you tried to start this problem, even if you are unsure if the approach will work? If so, may I see what you tried?

– What possible first steps come to mind – make a list, then tell me which you lean towards using and why, or why not.

– What part/aspect of this problem bugs you the most? Focus on that and see if there is a way to simplify it or rewrite it so that it seems less daunting.

– If you “step back”, and simplify the problem a bit while keeping the same structure (substitute integers for each term, or just cover up expressions in parentheses with a fingertip), does that result in a situation you know how to approach with confidence?

Whit

To begin with, thank you for such a thoughtful comment. You tickled my brain this morning.

I find myself using more boring questions than you suggested, I often start with asking to see their notebook and other examples they’ve done so I can align myself with what they’ve seen. I love your prompts about doodling and asking what seems reasonable. I also like the question about what bothers them the most. I often talk in class about what part of the problem they dislike the most so that’s a comfortable strategy for me.