>> Well, let me ask you this now. When you yourself are faced with a new concept or you're trying to figure out something brand new and it's difficult, what advice would you have in general for learners to be able to grapple with and assimilate these new ideas or solve a new area that they're first facing? >> Well, just like with the test question that we talked about. I think there are a lot of different ways to approach a difficult task. And in fact, as we were thinking about talking about this issue. Rich and I realize that we approach things differently. I'm a rather big picture person more of a global kind of learner. And so often when I'm looking at some difficult material, I'll take time if I have something chapter or if I have some sort of text, I'll look through it. I'll just skim through. I'll read a little at the end. I'll pick up a piece here and there and then begin to dig in a little bit deeper, but I do better when I sort of have a general sense of what it is I'm supposed to be learning. I might skip to the back and look at what kind of problems am I supposed to be able to solve with this. And so when you're working in discipline is where problem solving is an important part, that can be a way to get into it to begin to make sense of it. And the way that I differ from Rebecca is I'm a strongly sequential learner. And so I take the first step, then the next step, then the next step. But again, I never learned anything passively, anything nontrivial. If it's just a simple fact or definition of the term, I can read it and memorize it. But if it's really conceptually difficult whether it's part of a problem solving procedure or derivation that I'm trying to work through or anything else, the only way I learn anything is by doing it. So read this and then I'll try to explain it to myself. When I've learned things best of anything at all is when I've had to teach and I think practically, every teacher would tell you the same thing. I thought I knew this stuff. I got As in all those courses back in college, but it wasn't until I had to explain to these students that I was teaching that I found out that I really didn't understand it at the level I thought I did. And so I try to find examples. I try to find clear ways of explaining difficult concepts. And in the course of doing that, that's when the real understanding came. And so this is another strong argument, among other things for working in groups. If you're working with other people and together, you're trying to figure something out and you get a certain point and then you try to explain it to the others. You're reinforcing your understanding and they may or may not understand it after you're finished figuring out how to explain it, but boy do you. And so those two pieces of advice. I learn by doing things like trying them. If it's a mathematical method or procedure or something in physics or in engineering, then I try to work out the solution myself without looking back at the book, the text or whatever it is. And when I can do it by myself without referring back, then obviously, I know how to do it. And then to really reinforce that understanding, it's explaining it to someone else. Put those two things together and well, at least how I learn. >> I think using your resources too, whatever those resources may be. You've got text, you've got things online. You have people who really understand that difficult thing that you're trying to learn. And so not being afraid to just go out, ask questions. Work with all the resources you have to try to find what's going to work for you to make it clear, to make you more confident in how you're doing. >> Absolutely. >> Playing off that, one of my biggest problems as a professor is getting students to ask questions. They don't want to do it and it's not that well, sometimes they're so confused that they don't know what to ask. But much more often, it's a matter of fear. If I ask a question in class, it could be seen by my classmates as a dumb question and we as instructors can make all of the pretty speeches we want about how there are no dumb questions. All questions are good, because they teach. Forget that. The students are not buying that and besides, to be perfectly honest, there are dumb questions. >> [LAUGH] >> And we've all heard them. And so the student is reasoning, if I open my mouth to ask a question, I could be perceived as dumb by my colleagues, my classmates, my professor. If I keep my mouth shut, I'm risking nothing. And so they don't ask and I also can't persuade most of them to come to my office. I have office hours every week in which I tell the students, I'm there for you. I promise I will be there. I will be welcoming of any questions that you ask. I'll find out where you're getting stuck and you won't leave my office until you have the answer to that question. Maybe for the same fear, they don't want to come. And so they're not taking advantage of the resources that Rebecca was referring to. And if a student can be persuaded to overcome that fear and just ask, either in class or in the office in five minutes, they can get things cleared up that they could spend three hours at home banging their heads against and not getting clear. Let me go back to a couple points I made before. The best way to get the illusion of competence when you don't really understand something is to listen to a lecture or to read a text like a novel or to read over old homework solutions and imagine that you understand them, because you don't. The best way to get over the illusion of competence is to do it. Solve the problem again without looking back at the old solution. Work out the derivation one step at time without looking back at the textbook or your lecture notes, or whatever it is. And when you can do it by yourself without looking, get any reference, when you can reproduce that solution entirely by yourself, then it's not an illusion of competence. Clearly you can do it, because you did it. But it's not until you do it, actually unaided that you can rest that okay, I'm ready for the test or whatever it may be. >> This can also be a good time for working with your peers. Taking turns, explaining, perhaps a worked out example in the text explaining it step by step to each other. When you start trying to verbalize it, then you begin to see. Well, wait a minute. I I thought I knew how they made that step. But when I try to explain it, I don't. So what's going on? Let's look at it. And so I think that working with other people can really help you in that way too. So one of the things that you can do to make sure you are thinking about all the different aspects of the subject that you're trying to understand and it's to set it up, look at a complex system that might be used in a problem in your text and then just think about. What are the things that a teacher might ask me to do with this system? And in working through that, you begin to think about all of the elements that need to be in place. So that's a great way to study for a test. It's also a great way to sort of get past that illusion of competency. Because as you're looking at it and as you're working through the example and what which you think you might be asked, you'll uncover some things that maybe you don't know as well as you thought you did.