User:Arided/MathCourses

Here are outlines of the courses I have in mind:


 * 1) Short Precalculus (including "learning how to learn mathematics")
 * 2) Short Calculus
 * 3) Short Advanced Calculus (i.e. Calc II and/or Calc III in 6 weeks!)
 * 4) Mathematics for computer programmers (probably focusing on "Concrete Mathematics")
 * 5) Mathematics for game designers (a completely new course in early development phase!)
 * 6) Short statistics

The selection of topics is based on a very informal assessment of the initial interests of participants in the "DIY Math" course at P2PU this past autumn. One of the reasons for planning several courses at once is that I'd rather not leave anyone out. (It's also fine to add to the above list.)

I think these more structured courses can be supported by:


 * DIY Math, a drop-in area for any mathematical discussion (including planning work related to these and other ongoing mathematics courses) -- a sort of ongoing "departmental seminar".
 * Math Designers, a course/project related to the design of mathematics courses suited to the peer-based learning context. This can take the six courses I outlined above can be taken as a starting point, but it would be great to develop them further.  I hope that people from PlanetMath may want to participate in this, as it would be an excellent way to improve the quality of the PlanetMath corpus (check completeness, introduce pedagogy, etc.).

It is my view that a "course facilitator" should generally NOT have to act as a "teacher surrogate", but in fact, that courses should be co-facilitated by their participants. To the extent possible, the course material can also be made suitable for self-directed study. At the same time, it is very useful to be able to ask and answer questions (both about the content and also about "meta" how-to-learn-mathematics stuff). The drop-in area should be useful for meta-discussions.

In my experience, open-ended discussions do not replace a structured learning environment -- as for how a given individual will want to structure their learning experiences, that will depend on various factors. Feel free to add more courses to the list :)

How is this supposed to work?
As a general model, if a given subject can be clumped into 6 pieces like the ones in "Short Precalculus", that seems like a decent start. The "depth" of a given course should mirror how much time people want to put in per week. One hour? Ten hours? Mostly, though, I think we'd just look for ways to cluster all known mathematics in bunches of six (without too much overlap at the top level of the overall outline)! Some overlap is OK, e.g. the course for game designers might feature some bits and pieces from some of the other courses. As I've indicated in the Short Advanced Calculus course, non-overlapping topics can also be merged to increase the depth (and time-intensity) of a given course.

What are the real challenges?
So far in my limited experience, it seems like "follow-through" is the main challenge. Hopefully the structured design sketched above should help a lot. I think it would also be good if the system kept track of the kinds of courses people might like to take, and if people were required to ante up a certain level of commitment before a given course would run. Ideally the facilitator shouldn't have to chase people to make them do work. I've said more about these topics in http://metameso.org/~joe/docs/probation-report-final.pdf in case you want details (see the "Pilot Study" section).

All that in six weeks?!
For any given course, I think it is likely to be better to set ambitious goals and get people to commit to them up front. If someone wants to go slowly through a topic, that's OK with me! (See the alternative pacings for Short Advanced Calculus.) My working guess is that people will do better in the courses if they know they are going to have to work hard.