Tricki
a repository of mathematical know-how

Different levels in the same topic

Different levels in the same topic

I was reading over the article on "How to solve quadratic equations", which is fine as written if it's a teacher who needs to explain the topic and needs a refresher on all the different approaches, or a college undergraduate who hasn't taken that level of algebra for a while. But I would hesitate to send an actual neophyte to solving quadratic equations to the same page; it's written at too high a level. Might it be worth it to make "elementary" versions of some pages (with some appropriate logistics for naming attached), or are we presuming our audience won't be of that level?

My view is that having different levels of explanation is an excellent idea. One could even imagine having essentially the same article written in two different styles. To some extent we can obviate the need for this by using the hidden-text facilities, but that may not always be the best solution. For instance, Henry Wilton has written a very nice article on groups acting on topological spaces. He assumes you know what it means for a group to act properly discontinuously. Now one could just add some hidden text that explains that definition for people who don't know it (and in fact I'll probably do this), but one could also imagine an alternative version of the same article that started with an explanation of some of the concepts (freely discontinuous actions is not the only moderately advanced definition he assumes) and then proceeded with the article much as it is. Experts might not want to wade through an introduction of this kind, so it could be good to have two versions of the same article.

But I think we should be cautious about this: one can imagine other possibilities (such as an entire hidden section of text) that would probably work in the case of HW's article. For the quadratic-equations one, there is probably more of a case for writing an entirely separate article. Incidentally, my target audience for that article was somebody who had been taught about quadratic equations at school but had been left with an incomplete understanding of how all the various methods fit together, and of the fact that different methods are appropriate for different problems. It wasn't aimed at the genuine beginner. In principle, I have nothing against parts of the Tricki being extremely elementary, however. But if we start writing articles aimed at a school audience, then we may wish to label them clearly as such, and make navigating about in the elementary articles an easy process.

Perhaps one could have some sort of flags set to specify one's desired difficulty level in different topics? For example I might set my "computer science" flag as high, my "combinatorics" flag as moderate, and my "analysis" flag as easy. This would cause certain text to start automatically revealed or hidden.

Also if we do have school audience material, it would be nice to have a separate portal that automatically used the school audience specific flags, so one could just give one's student a direct link without worrying about them having to log in and set things.