Syllabus

This afternoon I put an hour or so into revamping my 280 syllabus for this oh-so-imminent semester.

As I hinted in my last post, I'm going to be asking the students to write their own textbook, in a sense: at the end of every "section" of the class (of which there are seven, listed in the syllabus excerpt below) I'll ask for several students to serve as the primary authors of a "chapter" of the "textbook" that will deal with the ideas we've just finished discussing as a class. That chapter will include examples, explanations, exercises, and proofs.

Here's the relevant snippet from the syllabus:

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I feel that it will be a far more meaningful exercise for you to construct your own textbook for the course, instead of following along in a textbook that's already been written. Therefore, at the end of each "section" (of which there are 7 we'll discuss throughout the course, and they're listed below) I will ask a group of three to five of you to spend roughly a week composing your own definitions, explanatory text, examples, computations, and proofs to create a "chapter" of text. Once you've typeset your chapter using the LaTeX software, you will post it to the course's Moodle [the University's online course management and social networking platform] site, where others will have a chance to offer feedback: do the definitions seem right? Do the examples make sense? Are the proofs correct? Others may ask to permission to edit your chapter (or at least ask you to perform edits). In this sense the textbook you create is a wiki, communally created by you as a class.

Incidentally, although there will be a due date for each initial chapter posting, there will be no due date on revisions once a chapter is posted; therefore once a chapter is up, it's fair game for modification for the rest of the semester.

Here is a list of the "sections" we'll discuss during the semester; you will each be expected to work on two chapters:

1. Introduction to mathematical statements, quantifiers, and basic logic

2. Basic proof techniques (direct, contradiction, contraposition, induction)

3. Set theory (including set operations and cardinality)

4. Combinatorics (basic counting principles, permutations and combinations)

5. Relations (including equivalence relations and order relations)

6. Functions

7. Combinatorics redux

Some of these sections are more involved than others; I will assign more of you to collaborate on the more complicated ones, allowing you to more effectively divide the work. However, the writing of each chapter should be a well-coordinated task yielding a well-composed whole; therefore I strongly advise you to select a "chief editor" for each chapter once you're placed on a given team of authors. I'll give you some more tips as the time nears to write the first chapter.

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I recognize that this addition to the class is going to impose on the students a substantial amount of work, and therefore I'll be looking for ways to streamline the ordinary homework assignments and create meaningful connections between those homeworks and the textbook chapters the students will be asked to write. (For instance, what can I do in writing my own homework problems that will help the students to write their own homework problems for the chapters?) Moreover, I'm thinking of scrapping the end-of-semester presentations in order to help students free up time for "textbook" revisions at the semester's end.

As another time-saver (and means of encouraging student self-authorship), for each worksheet I'll be looking for volunteers to serve as "discussion leaders"; these people will be expected to digest each worksheet as it's handed out and before the class addresses it, and they may be called upon to lead the class in completion of the worksheet's activities in class. This slight change in classroom operations should help in-class activities to run more smoothly.

We'll see how it goes. It should help a lot that this class is by far the smallest of the 280 sections I've taught at UNCA so far: only 14 people are registered right now, and I don't think that's likely to go up.

For the MATH 280 alumni among my readers, what would you think about the above changes? I'd really like to know your thoughts.