There are three categories of sites on Stack exchange (essentially).
Where should Math Educators lie in this spectrum?
The reality of the site so far seems to be #2 -- answers are drawn from personal experience. I would love to see some answers that cite educational research, but we don't seem to have many, possibly because we don't currently have many participants who are familiar with the educational literature.
I would prefer for the site to be more like #3, with some answers drawn from personal experience but other answers citing educational research when appropriate. As with some other issues that have been raised for the site, the only solution is to try to attract a wider and more diverse audience, and to upvote questions and answers that involve educational research.
We shoud go with option 3. The majority of experienced math teachers learn primarily through eperience, occasionally supplemented by research. The standards of the site should reflect this. When research is available, it should be used, but if it is not available, answers from pertinent personal experience should be allowed.
I believe firmly that matheducators.SE will not reach its potential - in particular, it won't be in a position to look like #3 - until it has attracted a significant number of participants from two constituencies currently very underrepresented:
(1) Math education researchers - university professors and graduate students who study math education as their object of study; usually found in schools of education as opposed to math departments.
(2) Primary and secondary level teachers. (I.e. K-12 teachers.)
Math education researchers are the only people whose profession requires them to be conversant with research literature on teaching and learning math. Primary and secondary level teachers usually have some acquaintance with this literature as well, as a result of it being required of them for their teaching credential (unlike university-level math teachers); also it is common for this literature to play some role in ongoing required professional development, at least in public schools in the US. Then their personal professional experience puts them in a position to view this research in relation to the actual practice of math education; so primary and secondary teachers can offer a unique perspective linking the two.
If matheducators.SE hopes to become a site in which the answers are based on an integration of research and personal experience, we must make a concerted effort to recruit many participants from these two constituencies.
We should definitely be in group 3.
To completely ignore personal experience is to ignore what teaching is. It is hard to be research in education. How, for example, does one objectively evaluate how different methods work? So, if we are interested in taking about how concretely to improve teaching, then we have to rely on personal experience.
To completely rely on personal experience would be bad because we then turn into a discussion. Experiences will vary. Many teachers have limited experience in that they have taught only certain types of classes. Some teach high school and others direct graduate students in college. But both groups have to deal with some of the same issues (e.g. how do you motivate students?). I think a good answer is honest about the level of experience of the person providing the answer.
I think the best middle ground is to require some level of "objective information" in the answer. There are many education/psychology journals out there and I think that whenever possible we should encourage people to support their personal experience with research or other objective information. This might even take the form of pointing out that your experience matches that of this other person who wrote about it somewhere.
Part of the reason for requiring a bit of objective information is that it makes the person stop and evaluate their own beliefs. Are my experiences supported by any facts? Just as with an argumentative essay, the argument becomes much more forceful if you can cite a few references.
Again, this is difficult and if you look at the few answers that I have given, I have filed at this. I still would hold to the above point because I think it will elevate the quality of the site and increase the likelihood of its survival.
I would prefer to see the site more like #1 as it establishes itself and (hopefully) moves out of beta.
Ultimately I would like to see the site appear like #3, but I think an important consideration is what the word expert refers to when you write: "Those where experts frequently draw on both [#1 and #2]."
More precisely, I think it is a mistake to believe that anyone who teaches mathematics is an expert in issues about mathematics education. Having read through answers to the questions asked thus far, I see mostly users giving off-hand opinions; I have found unfortunately little by way of research-oriented responses. (Here is an example of a math-ed answer I provided on MO that I think fits more closely with the style I'd like to find here.)
Perhaps the current state of affairs is due to a combination of the newness of the site's public version and the quality of the questions being asked. Nevertheless, my vote would go to Category #1 for the time being, and I would like to see those answering in the spirit of #2 provide at least some sort of evidence that their personal experience is reliable.
I am currently agnostic about the usefulness of educational research. However, I hope that this site will attract people who are familiar with the literature, and I will be very interested to see what kind of insights they can offer
I believe reasoned opinions are also a worthwhile category of answer here.
Many questions in education involve moral or political judgments, and those questions are not settled by either research or by experience. However, we can have reasoned discussions about them, and I would like us to encourage those discussions here.
This is especially clear for the many questions with the word "should", e.g.:
We can answer these questions by articulating a goal and explaining how to get there. E.g.:
Neither research nor experience will dictate what one should do. The same issues are often present even without the word "should".
Articulating appropriate goals for mathematics education is a matter of ethics or politics, so I see a role for reasoned opinion here.
Let me be unpopular and give arguments for #2 (primarily personal experience):
from T. W. Körner's The Naked Lecturer:
Like most mathematicians, I remain unconvinced that [educationalists] have, as yet, much to offer. They are welcome to put this down to arrogance and intellectual laziness but they would do better to reflect on the reasons we give for our views.
(1) Much of what is quoted as educational research is mere expression of opinion. Much of the rest hardly rises above what Feynman calls cargo cult science (see Surely You’re Joking Mr Feynman! again).
(2) The only outcomes of education that we can measure (student satisfaction, recall of material after two months and so on) are unsatisfactory proxies for whatever outcome it is that we actually wish for.
(3) Education is not a generic process. The education required to produce a literary critic, a chemist, a violinist or a mathematician is very different. It is now customary in British Universities to provide courses on lecturing to new lecturers. Often such courses include the advice that you should only put three sentences on a blackboard at at a time. So far as mathematicians are concerned, one might as well advise mountaineers to avoid steep slopes or surgeons only to operate on the exceptionally healthy.
(4) Many good mathematicians are also good lecturers. (It is only youthful innocence that causes our students to believe that those who lecture badly do so because they are great thinkers.) After all, good research usually demands insight and clarity and these virtues provide a very good foundation for good lecturing. However, if it is necessary to make a choice, most mathematicians would prefer someone with something to say but who says it badly to some one with nothing to say who says it brilliantly. The better mathematician trumps the better lecturer.
