A few days ago, some colleagues and I were discussing the year that just ended, and the curriculum in general, and the frequent lament about needing to repeat ourselves came up. Due to some quirks of our calendar, we have a lot of students taking courses out of sequence, and as a result, have to teach the same mathematical techniques in multiple classes.
On top of that, though, the students tend to say that any given technique is entirely new to them, even when they’ve already seen it. When that part came up, one of my colleagues said “Well, of course they do that– I did that when I was an undergrad, too. Everybody does.”
I realized, though, that I didn’t. If a faculty member asked me “Have you seen this before?” I’d say “I think so– it looks sort of familiar,” whether I had or not, because I didn’t want to admit ignorance. Then I’d go home and frantically read about the technique in question in whatever books I had, to get caught up. In fact, I still tend to do this.
It occurs to me that either this is a new way of dividing the world into Two Kinds of People, or I’m just an insecure freak. So, a poll for those readers who are still around:
If somebody is explaining something, and says “You’ve seen this before, right?,” what do you say?
Do you say “No, explain it again,” even if you’ve seen it, or do you say “Sure, keep going,” even though you haven’t?
Answer honestly, now…
(There’s probably some connection between this phenomenon and the idea of “interactional expertise” recently discussed by ZapperZ and Tom, which in turn connects to this article about the advantages of being a non-scientist in a science writing position. That’s a longer and smarter post than I have time or energy for, though.)
Well, I tend to say “I think I’ve seen it before, but could you explain it again?”
I’m generally of the “Yeah, I’ve done that before, though I’m a bit rusty” camp. Of course, if I’m in a class, I’m praying that someone is brave enough to stop the professor and say “I’ve never seen that thing before, what on earth are you doing?” Pretty much I’m a wimp that doesn’t want to look dumb.
Depends on the setting, of course. Generally, if I’m completely clueless I’m fine with admitting it and making them explain. But if I’ve kinda-sorta seen something like it before, I’ll let them go on and take just enough notes that I can catch up on the details if needed later.
Disclaimer: I’m a computer science grad student, so usually when this situation comes up my colleague has some sort of source code and/or paper available that I know I can crib from later. So all I really need anyways is the general gist of going on; no amount of talking will help me understand all the details.
Hrm… I think I try to be honest with regard to this question, though I’m a bit reckless. For example, if I’ve never seen something before, I will definitely say I haven’t, but if I have, even if I barely remember it and couldn’t use the technique, I’ll say “Oh, yes, I’m very familiar with it!”
This gets me into trouble. 🙁
When I was younger, I was in the “sure I’ve seen it” camp. I’m now much more likely to say, “No, I have no idea. Please explain.” I might add the “but it seems familiar” part, if it does.
The unfortunate effect is sometimes an in-depth discussion on the point in question, when all I really needed was a quick summary. I’m very comfortable figuring things out on my own later, but I’d like just enough context to avoid getting completely lost in the ensuing discussion.
I try to be honest. If it’s in that fuzzy area, and I’m not sure, I’ll say it’s ringing some bells, but I want to make sure I understand. Then I’ll ask them to explain…until the point where I get the gist of it and pipe up with, “Oh! I remember!” (Sometimes that never happens, though.)
I spent my first year of undergrad nodding and saying I understood, when 90% of the time I didn’t and never was able to figure it out. I really wish I hadn’t done that because it caused me SO much trouble.
When I was a teenager I trained myself to never admit ignorance — I don’t know why, probably just insecurity. I realized the problem with this just a few years later: I learn less if I never ask questions. Since then I’ve been struggling with this, trying to teach myself to ask for explanations instead of hiding the holes in my knowledge.
If I want the person to continue, I would say, “It’s not important whether I have. Please go on.” If I want the person to skip it, I would say, “I’m familiar with this. Feel free to jump to the next step.”
It’s funny – when I’m talking with someone I know well, and they ask me that, I’ll admit that I don’t know. I’m much less likely to do that with other people.
“Do you say “No, explain it again,” even if you’ve seen it, or do you say “Sure, keep going,” even though you haven’t?”
When I was an undergraduate, I fell into the latter camp, and always feigned understanding even when I was clueless, much to the chagrin of the postdoc supervising me.
He did me a great service, though, in ‘beating’ that habit out of me. Now I will almost certainly ask someone to clarify a point or explain it to me if I’m unfamiliar with it. As a scientist, this is an extremely healthy attitude to have.
It depends, doesn’t it, on whether it’s something you’re supposed to have seen before. For instance, I skipped taking complex analysis as an undergrad because it wasn’t required and didn’t sound like fun, and I didn’t know that it was going to be important later. So I have a pretty sketchy understanding of Cauchy integrals and residues and all that, picked up piecemeal later on. But I’m loathe to admit how poorly I understand it — it’s embarrassing.
On the other hand, someone was trying to talk to me about cryptography and information theory the other day and, although I’ve read a little about it from general interest, there is absolutely no reason for them to expect me to have that in my background. In that case, I’d rather let them explain even things I thought I sort of understood already.
I guess in gneral, if I think my ignorance is excusable, I’ll go with admitting the igorance or even pretending to be more ignorant than I am, so as to not look stupid by saying something wrong about something I’m supposed to understand.
“Sure, keep going.” Nearly always. I wonder if this is a standard characteristic of bloggers.
I would usually say I’m familiar with it, not wanting to admit ignorance. Sometimes I end up looking stupid later, though, defeating the purpose of pretending I know.
Depends entirely on my mood.
I used to say “I think I have seen that before” but now that I’ve joined the working world I have found that many people don’t know what they are talking about so I now say “No, could you please explain it” to make sure we are talking about the same thing regardless of if I know what it is or not. Using the same words but meaning different things is a major headache-causer.
Maybe you should say “no” anyway, because you might learn more from a new angle on the problem, or your mind might “see” something in it you didn’t see before.
A lot of physics undergrads aren’t as strong as they maybe should be in math. It’s possible that their understanding of a technique is weak enough that they don’t remember being exposed to it. It’s also possible that they are trying not to impress you but to get a good grade, and they think if they claim they have never seen something before, you are less likely to penalize them for not knowing it or more likely to teach it again.
Depends a lot on who I’m talking to; frequently I’ll say “it’s sort of familiar, but I don’t remember the details”, but as Brian said above, I’m more likely to admit total ignorance when talking to someone I know well.
I have a big problem with assuming other people know things — I tend to err on the side of not wanting to insult them by acting as if they don’t know something, only to err in the other direction and talk about something as if they’re completely familiar with it but it turns out they have no idea what I’m saying.
What AliceB said.
Through high school I was a know-it-all, so I’d say I was familiar with it.
Somewhere between high school and my career in IT, I learned just how profoundly stupid this was. I have learned how to say, “I’m sorry, no, I’m not familiar with that yet. It looks intriguing; can you tell me more or point me to a good resource to get up to speed on it?”
It’s amazing how much this has helped me, not just in my learning but in my relationships with clients and managers.
Option C, which you didn’t provide: I answer honestly. I don’t always say I know it or always say I don’t know it. I actually answer the question.
Being willing to admit being wrong, or at best, somewhat incorrect, is key to this. Not wanting to admit to not knowing everything, even in your own sub-specialty, is simply hubris that ends up wasting someone’s time, and I’m woefully short on that these days, so I reigned in my know-it-all streak hardcore during the later part of my undergrad years. I was spending all too much of my life muddled and confused.
I always pretend I know what they’re talking about then use Google.
Just out of curiosity, could you blog that list of math techniques they had not seen?
If it was just math being worked out, I’d say “No, but keep going” because I could usually figure it out on the fly. That’s not quite the same as going directly to an answer without showing the steps. In that case I’d only say I knew how to do it if I actually did. I had profs that would ask you to fill in the blanks if you said you had seen it before.
A more critical question is why your students don’t retain a basic skill they have seen. If you even suspect that they have seen it before, you need to make the point that any math used in an undergrad physics class is as basic as multiplication. Even if they haven’t, you need to tell them that. Most students just don’t get the idea of prerequisites. (If you are interested, there was a nice cross-discipline discussion of it on my blog late last week, on 17 and 20 June.)
But it is not always their fault. I remember when my prof in field theory asked about the Wigner-Eckart theorem and we were all ignorant, to his horror. I looked back at my quantum notes and discovered it was there without any highlights of any kind. That prof derived it like it was just another random example, and never told us it was Important and would be used every day the next year. Not good teaching, even for grad school.
i tend to say that i am familiar with something even when i am not. however, i am learning that when you say you don’t know about something (whether you know or not) there are some positives. if you really don’t know the subject, you might be treated to the knowledge of one who is enlightened and thereby flatter the lecturer with your undivided attention. and if you are familiar with a subject, you get the same lecture, but can make insightful comments and look like a genius for picking up the material, so quickly.
I nearly always say that something seems familiar, but that’s because nearly everything I hear or see really does seem familiar — even when it’s new to me.
If I am an undergrad, and I can use the same knowledge to pass exams in different classes, it economizes my time and makes it easier for me. It is therefore to my advantage to say no even if I have seen the material before.
Also, I would be wary of telling a different teacher I already knew something. Oftentimes, the teachers are not referring to exactly the same thing, and the assume previous teachers have taught you stuff they have not, or they want to apply the old knowledge differently than you have before.
I have taught music to kids, and I am here to testify, the question “do you know your basic scales and chords?” has revealed to me that there is NOT agreement among music teachers what constitutes basic knowledge of scales and chords, and a simple “yes” or “no” answer tells me nothing, zip, zero, nada, about the student’s actual knowledge of what I consider to be the basics. I have to verify what they know regardless of how they answer that question.
I swing your way, as it were. Most of the time it works out. There are cases where a professor uses different terms or notation, but it is normally easier to ask questions as things you don’t understand come up, or to work them out yourself (gaining a more complete understanding for working through it again).
Of course, here in the UK you come to university to take a physics degree, and only a physics degree. Every part of your course is set up by the department, and vital maths tends to be taught the term before the course it is needed for (in dedicated mathematics modules taught by professors who do work in the physics department). There are only a few cases where a prerequisite may not have been covered, assuming it was taught before we got into their system Matrix algebra more or less just appeared with the assumption we could already use it, which was half true I suppose.
The only other real flaws were when two courses being taught at once were supposed to tie together, but one got ahead of the other for some reason, or one got amended to cover a narrower section of material.
When I was a teenager, I never asked for re-explanation, because everything seemed obvious the first time that it was explained. Caltech broke me of that habit. For example, I’d been using Calculus since I was 13, but Tom Apostol in person, teaching from his own excellent textbook, made me understand more deeply and more rigorously what an integral REALLY was. And then Lebesgue integration showed me a yet deeper understanding. I thought I knew statics, dynamics, electromagnetics, and relativity. But then the Physics course from Feynman’s book, and time with Feynman himself, made me appreciate that — to oversimplify — everything I’d been taught before college was a little white lie, and the truth was more gnarly.
Isaac Asimov also explains that everything was obvious on first explanation to him, until the point in his college calculus class where he was getting the right answer in integration by parts, but couldn’t see why it worked. That utterly freaked him out. He dropped the class, never took math again, got his PhD, became a professor, wrote or edited over 500 books — and felt guilty about it forever after. Many of his best esssays start with something that he’d known since childhood, and went into quantitative analysis (pre-calculus at most) and history and biography to reach deeper understanding.
Grad school forced me deeper in Computer Science, Mathematical Biology, and other subjects. Now, I ask experts to explain the simplest things for me, before they even ask me if I’ve seen it before.
The older I get, and the more I teach others, the more I am willing to admit to myself and others that I am wrong, and the less I know that I know, and the more willing to start over. And I’m an arrogant self-centered guy too, so it should be easier for people with more normal ego sizes to make this transition, when they are ready.
My son followed the same trajectory. But I’ve gone on long enough for now.
Excellent question!
I’ve generally had a tendency to wonder, “Is that something I should already know?” It was more true when I was in high school or college. I especially wouldn’t want a respected professor to realize what an idiot I am.
That tendency manifests much less now though. I realize that despite how little I know, I still know more than most.
From a slightly less cynical angle, I also came to see that generally people are not proper super sets of one another. So even if I do know something fairly well, I can still learn from someone else, even someone with less expertise on a given topic.
Plus if college taught me nothing else, I learned that I can become an expert in anything in one long night. 🙂 So don’t worry!
If only mathematical techniques worked like surgical ones. Medical school motto: “See one, do one, teach one.”