<p>Today was our first day back this semester. One of my upper division math courses is being taught in "discovery mode" where the students teach themselves the material in the classroom, providing all the solutions to the material. This is a proof based class on number theory. 40% of our grade is classroom participation. Yikes!</p>
<p>My question to everyone here is has anyone else had a course taught in this style? If so, what can you tell me about it? How do you prepare for something when new material is sprung upon you every class for you to solve the same class period? I'm a little worried over the unfamiliar style of teaching.</p>
<p>Do you have a textbook and/or a syllabus? A syllabus with a description of what topics are going to be covered, paired with a textbook, will give you a pretty good idea of what to prepare. If you only have a textbook, you’ll probably follow the organization of the book (read the preface to see what alternate routes through the book are suggested). If you only have a syllabus, you can get a text from the library. If you have neither, you can still get a text from the library, because math classes tend to be structured in pretty similar ways.</p>
<p>As far as developing the skills: most math textbooks will guide you through exactly this sort of method, assuming that every time you hit a problem you stop and try to solve it yourself rather than just reading through the explanation. If you want to practice the skill of figuring out how to do various things, pick up one of your old math texts and go through a few chapters that way.</p>
<p>Your professor is probably expecting that at least some of you will be learning how to approach this sort of class as you go. Make sure you go to class every time and try to answer every time you’re called on and be ready to make mistakes. Everyone does. If you can’t handle making mistakes, you can’t be a mathematician. And feel free to go to office hours, even just to say, “I’m not sure what to expect from this course, and I wanted to know how best to prepare for class.”</p>
<p>I wouldn’t recommend watching the movie “The Paper Chase” (about law school) before you settle in and get comfortable, but you might enjoy it once the class gets going. And your professor might get a kick out of it if you showed up for class with a copy of Plato’s “Meno”. :)</p>
<p>There is no textbook. The professor gives a hand out and we work problems from the handout with the brief summary of techniques that is on the handout as well. The syllabus has only the grade break down. No actual topics. It is so vague, which is what worries me. </p>
<p>I’ll check out The Paper Chase. I’ve heard others give it good reviews and I wanna see it.</p>
<p>It should not be too bad, provided you are motivated to participate actively and prepare for class. It will be time-consuming, but it should not be overwhelming. If your class is taught well, your professor will break the tricky proofs down into several manageable lemmas. </p>
<p>The first week or two will be rough as you adjust to the active learning style and get used to the style of number theory arguments. You might have to learn to construct your own examples to illustrate definitions or theorems, and get used to some new machinery if you have not worked with number theory before. You will probably collaborate a lot with your classmates outside of class. </p>
<p>If you put in the effort, you will get a <em>lot</em> more out of the class than you would get out of a typical lecture class. It is the difference between following someone else’s argument and constructing your own!</p>
<p>My closest personal experience was a class that provided the definitions, theorems and a few examples in class, but assigned every single proof as homework. I did learn a lot more this way than in any of my traditional math classes!</p>
<p>You are right. I too believe that I will end up getting more out of this class than I would have a more traditional way. You are probably also right in that the first few weeks will be a learning curve and then get better. I like a lot of structure and this is throwing me for a loop.</p>