Question

Would it be helpful to have some kind of Advanced Algebra subject classification?

We seem to expect a linear progression something like:
Prealgebra -> Algebra -> Pre-Calculus -> Calculus

plus a few extra areas like Geometry, Trigonometry, Statistics.

If a student has an advanced algebra question where does it go? If put under algebra then it may be too advanced. It is not necessarily preparatory for calculus, so does not really belong in Pre-Calculus. If it's algebra then it does not really have anything to do with calculus.

Would an Abstract Algebra subject area be appropriate and popular enough?

Answer 1

It could fit in either Algebra or Pre-calculus. It WILL be seen and responded to in either case.

Explanation:

The distinctions are guides for learners. Not every curriculum uses the same terminology, and even the "sequence" can be quite varied. Your specific example is excellent, as in some places "Pre-Calculus" is the term with a very nondescript definition. Isn't every basic math course preceding "Calculus" a pre-calculus course or topic?

Questions or topics can always be "searched" if a particular one is needed. Some questions end up in slightly "off-topic" areas (in some opinions) in any case because the questioner doesn't really know where it should be anyway.

In each category many contributors look at a variety of topics although they may primarily respond to one or two specific types of questions. Thus, a "too advanced" question may be ignored by more contributors in a beginner topic, BUT it will still likely be seen by those capable of answering it.

Answer 2

Some thoughts below, leading to a suggestion of an "Advanced Math Topics" category with subcategorizations into Abstract Algebra and the like.

Explanation:

I've been thinking about this question a bit and wanted to chime in.

I think there are two questions that are being asked (or perhaps merely inferred): What will the Questioner experience be like, and What will the Contributor experience be like.

For a Questioner, how does one look for a pre-existing answer? I can think of two ways:

• enter the site and enter search terms into the search box, and
• browse the applicable topic

I don't interact on Socratic as a Questioner very often, but when I do I always simply drop search terms into the search box (when I want to find new and unique ways to use the graphing function, I search for "graph" or some such). And with that ease, I would imagine that most Questioners will do the same. And so, in some ways, categorization might not be helpful to a Questioner.

When posing a question, the Questioner asks Where Should My Question Go? And in a way, this then is an issue that is about Having the Right Contributor See My Question. If there are overlapping areas where a question could go (for instance, a combinations question can go into Statistics or it can go into Algebra - both have subtopics for combinations) a novice Questioner will pick one category more or less blindly but a more advanced Questioner may look at the activity on each page and put their question where there is a higher activity count or where their favourite Contributor has most recently been active.

For a Contributor, categorization is essential. There are days when, if a Combinametrics category existed, I'd only be there. There are other days when I browse through a lot of categories, looking for questions that appeal. And other days still where I'm in a couple of categories solely.

If there were a Linear Algebra category for example, would Contributors go there? Probably. I wouldn't - I have no confidence in my Linear Algebra skills, but others who do would. And if there were also an Abstract Algebra category, would Contributors go there? Probably, but I probably wouldn't. And if there were a Discreet Algebra category, would Contributors go there? Probably. But at some point, Contributors would, I think, not go to all those pages - I think we have to keep in mind that we're talking about a small set of people who are at home in all these topics. At some point, having too many categories will create a barrier for at least some members of that set of people to work with these different types of questions.

And so in any discussion of what categories should exist vs subtopics within a category, I think it should be kept in mind that:

• Categories, at least as far as I can tell, are something that is more useful to a Contributor than to a Questioner, and
• that a balance be kept between the numbers/types of Categories and subtopics.

As a suggestion then, might it be appropriate to have a category of "Advanced Math Topics" and then subcategorize into Abstract Algebra and the like? I can see myself wandering into this category and perhaps finding a question that I can answer (although far more likely to simply watch the answer feed and have my head spin as our resident math geniuses work their magic).