There are three categories of sites on Stack exchange (essentially).

  1. Those where answers are primarily drawn from research or other official sources (e.g. mathoverflow, physics, skeptics, etc.)
  2. Those where answers are primarily drawn from personal experience (e.g. cooking, workplace, academia)
  3. Those where experts frequently draw on both (e.g. Stackoverflow)

Where should Math Educators lie in this spectrum?

  • 2
    $\begingroup$ I believe I am one of those who sometimes refer to research in math education. However, for the most questions, this is hardly possible. I outlined this in a post on the use of extrinsic motivation in math classes. There is a gap between research and teaching and many questions here address best practice in teaching, but not in educational research. Roughly speaking, they are somehow too specific to a teaching situation and too unspecific to psychological theories and models. It would be great if we can bridge this gap, but I don't know how. $\endgroup$ – Anschewski Mar 24 '14 at 10:57
  • $\begingroup$ We should not forget that on this site as well as on some others (in particular Math.SE) there also is a relevant amount of answers that speak for themselves. $\endgroup$ – Wrzlprmft Mar 25 '14 at 15:12

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.

  • 1
    $\begingroup$ I think you would need the site to be more like #1, at least for the time being, in order to attract "participants who are familiar with the educational literature." $\endgroup$ – Benjamin Dickman Mar 25 '14 at 13:32
  • 2
    $\begingroup$ Probably the current state reflects the existing demographics. After all, you advertised the site vigorously (thank you) at Meta.Math.SE, so the population you drew in consists mostly of college/university level teachers. We are largely untrained in educational research, but have spent a significant fraction of our adult lives teaching. Ergo, type #2 answers/questions proliferate. $\endgroup$ – Jyrki Lahtonen Mar 26 '14 at 5:55

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.

  • $\begingroup$ I agree whole-heartedly! $\endgroup$ – Namaste Apr 7 at 0:49

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.

  • 1
    $\begingroup$ I like the 'some level of objective information' part. That would come from research or actual observations in your career. $\endgroup$ – Brian Rushton Mar 24 '14 at 2:16
  • $\begingroup$ One does not necessarily strive for objectivity. And why should research in math education strive for objectivity? The experience of learning mathematics is subjective. Therefore, research methods are needed that recognize this. $\endgroup$ – JPBurke Apr 22 '14 at 20:32
  • $\begingroup$ I guess I should explain that not all those who do not conduct research have a grasp of social science research methods, what purpose they serve, what validity and trustworthiness mean for interpretive social sciences, and other issues that are important to the conduct of education science and the interpretation of it. That's to be expected; that's why people specialize. Researchers can and should should help bridge between research and practice. I see this site as a place where that can happen without, necessarily, turning everyone into math ed researchers. $\endgroup$ – JPBurke Apr 22 '14 at 20:37

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.

  • 2
    $\begingroup$ I think one might need to distinguish between professionals in mathematics education (research) and professionals in teaching (of course this is not disjoint). If one seeks analogy with Stack Overflow the typical "expert" should rather be the latter not the former. That being said, I do not think the analogy with Stack Overflow is very good to begin with, one might look rather for analogy with Programmers.SE. $\endgroup$ – quid Mar 25 '14 at 15:02
  • $\begingroup$ @quid I wish only to point out that professionals in teaching (which I read as: people who are teachers by occupation) may not necessarily be experts in teaching. Thus, if a member of the latter group is to answer as an expert, I would wish to see evidence as to why I should believe their answer beyond noting their profession. $\endgroup$ – Benjamin Dickman Mar 25 '14 at 15:03
  • $\begingroup$ I would say this depends on ones notion of expert. But I think I undestand what you mean. Yet, this site never claimed to be a site of experts in teaching or even mathematics education, it claims to be "a question and answer site for those involved in the field of teaching mathematics." I certainly hope there will be more scholarly content later than we have now (mainly so that I can learn something from it, I certainly have essentially know theoretical knowledge in education). However, I think it would be a mistake to push too hard for it right away. $\endgroup$ – quid Mar 25 '14 at 16:17
  • $\begingroup$ re the too hard: one might wish to recall that MO started out a lot softer then it is now, and some other sites that tried to start out at or above the then already more advanced level of MO had serious difficulty. $\endgroup$ – quid Mar 25 '14 at 16:19
  • $\begingroup$ I agree whole-heartedly. I'd like to recruit more math ed researchers and specialists to participate on this site. Any suggestions? $\endgroup$ – Namaste Apr 7 at 0:54

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

  • $\begingroup$ I think this sums up my position too. I'm hoping that this site will be a meeting point for those who are experts in mathematical education and those who are practitioners. $\endgroup$ – Loop Space Apr 23 '14 at 8:12

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.:

  • Should I design my exams to have time-pressure?
  • How should one tutor a student in analysis?
  • Should students use more than one notation for the derivative?

We can answer these questions by articulating a goal and explaining how to get there. E.g.:

  • "In order to prepare your students for time-pressures in work situations...." or "In order to best test your students' knowledge...."
  • "In order to help your student pass the class...." or "In order to help your student learn these concepts...."
  • "In order to prepare your students for what they will encounter outside of class...." or "In order to help your students master a differentiation algorithm...."

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.

  • 1
    $\begingroup$ I believe that such answers should have at least a valid convincing argument. There have been many answers on this site (especially from new visitors) that just asserts their opinion with no convincing argument whatsoever. When they their opinion in three lines without any justification, it lowers the quality of the site, in my opinion. $\endgroup$ – Brian Rushton Mar 26 '14 at 16:01

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.

  • 1
    $\begingroup$ Right in this answer you see the mathematician is wrapping himself in self-undermining assumptions. If he didn't dismiss "educationalists" perhaps he might have the opportunity to realize why "many mathematicians are good lecturers" is not the best basis for an argument about the reliable authority of mathematicians in education. Many math teachers I know have learned this even without research. Side note: I am kind of shocked to learn this was written in 2013. Based on the dismissal of science, I expected it to be from the 50's. $\endgroup$ – JPBurke Apr 22 '14 at 20:46

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