7
$\begingroup$

The easiest question to ask a professional educator is:

  • I have noticed problem X in my classroom. What have you tried to address this problem?

I worry that this creates poor questions for a StackExchange site, because every question becomes a soft question, with no answer more "correct" than any other. This makes voting somewhat confusing; we would like to +1 the correct answers, but every answer is equally correct.

Maybe I am incorrect, or maybe this is not a problem at all, but I think it is worth discussing.

| |
$\endgroup$
  • 6
    $\begingroup$ Please see Good Subjective, Bad Subjective (if you haven't already). $\endgroup$ – Jon Ericson Mar 13 '14 at 21:32
  • 3
    $\begingroup$ If problem X is occurring, then it needs solving. If you need help, where are you going to ask? If you are able to clearly articulate it here, and others have suggestions to help solve it, then this was an appropriate place to ask it. I think there are too many concerns being expressed on ME.SE at the moment that are splitting hairs over how things should be worded. If you see a question that's unclear, and you have some idea what they mean, leave a comment to help the OP reword it. Very few teachers are naive enough to believe in "simple" solutions. $\endgroup$ – Geoff Pointer Mar 16 '14 at 22:59
6
$\begingroup$

It often helps to be specific. Consider this question: What are some good simple examples that getting the right result is not enough?

Let's go back to the beginning: what are we trying to accomplish here? I think the problem is that students often look at math as a subject where getting the answer right is all that matters. With my own son, I know that I struggle to help him think through the process required to arrive at the answer when all he wants to do is guess. The purpose of gathering examples of wrong processes that result in correct answers is (if I understand) to help students grasp the importance of using the proper process.

Asking for such examples might help you or some future reader solve the original problem, but not directly. I have a friend who loved to prove that $$1 + 1 = 4$$ or somesuch. The proof depended on an illicit division by zero and was a fun puzzle to sort out. I could easily imagine a scenario where the proof could be used in a teaching situation to teach the importance of using correct methods. But that's not what he used it for; it was just a bit of fun. And we hate fun.

You see the primary purpose of this site is to help mathematics educators solve problems that arise from their vocation. When I'm trying to help my son work out homework problems after he guesses the correct answer, my problem isn't that I don't have a portfolio of counter-examples demonstrating the dangers of being lazy. Showing him one or two examples might be part of my strategy, but they aren't useful teaching techniques on their own.

In order to be a useful Q&A site, the vast majority of questions should focus on specific teaching situations and few (if any) should be general tips and tricks. You are expert educators and this is your site. Don't settle for questions that just anyone can answer. Whenever possible ask questions with specific students, topics, methods, and situations in mind. If you are preparing to teach why division by zero is not defined and anticipate a student asking why we don't just define $${x\over 0} = 0$$ ask that question and I'll dig up the proof that shows why that's a bad idea.


It seems I need to clarify a few things. Closing questions is better than the alternative. This has always been a struggle; I myself once wrote Closing Questions Considered Harmful. But I've come to embrace early closing, which serves at least two useful purposes:

  1. It avoids wasting time on answers that do not maximize the expertise of the community. There are tons of sites where math educators swap teaching examples. But this proposal was initiated on Area 51 because many saw a need for a site where teachers can ask questions that arise from their day-to-day work.

  2. More importantly, it helps maintain the "expert" nature of the site. One of the best arguments comes from one of our co-founder's talk about the Cultural Anthropology of Stack Exchange. As a network, we value answers of permanent value and so we politely decline to field certain types of questions. When an expert visits one of our sites, we expect them to see questions that they are uniquely qualified to answer and to evaluate the answers. Bike shed questions are expecially hazardous to the first impression of a site. A few "fun" questions are fine, but they have to be the absolute cream of the crop.

It's better to have ten questions prompted by specific experiences than one general (and giant) question. Compiling a list of tips and tricks isn't that much a waste of time, but maintaining it can be. How many people have really read all 38 answers to the Math.SE version of the question? What about all the comments? Did all those people vote (up or down) on the answers? Stack Exchange questions get unwieldy much beyond 5 answers.

Meanwhile, if the question had been about teaching fifth grade using the Common Core Standards when a student asks why it's not good enough to get the right answer, the responses stand to be extremely useful to all teachers who find themselves in that position. We'd rather cover lots of questions extremely well than a few questions. Again, the strength of the network lies in getting help with deep issues that experts actually face.

| |
$\endgroup$
  • 1
    $\begingroup$ You say "it was just a bit of fun" as though that's a problem. I have a Physics lecturer who shows a short YouTube video in the middle of his lecture, unrelated to the topic of the lecture and claims it's based on some theory about student concentration and the need for periodic breaks. Many teachers use a bit of humour to carry a presentation through and to keep people alert. I'm not yet saying what my opinion is on those points, but these techniques could be validly discussed on an Educators forum. You talk about teaching your son, but are you an experienced and qualified Educator? $\endgroup$ – Geoff Pointer Mar 15 '14 at 0:35
  • 1
    $\begingroup$ @Geoff Pointer: I think asking about the technique of mixing in humor could be a great question. But asking for a list of short YouTube videos to use sells the potential of this community way short. $\endgroup$ – Jon Ericson Mar 15 '14 at 0:45
  • $\begingroup$ I can't imagine anyone wanting the latter question here - you are stating the obvious. If I had the power to close vote I would flag such a question the instant I saw it. Only a very narrow view of what I was saying would come to the conclusion that I might suggest that such a question would be welcome. My point is about the utility of humour not about examples of it. You say "But asking for a list of short YouTube videos to use sells the potential of this community way short." No one has asked it have they? Don't you mean: "[If someone asked] for a short list ..."? $\endgroup$ – Geoff Pointer Mar 15 '14 at 1:00
  • $\begingroup$ On the topic of lists, a list of unrelated humorous videos is a completely different beast to a list of actual mathematics problems where wrong logic coincidentally leads to the right answer. The OP in the question you link to could also improve their question by giving the context of the level of maths involved. In more advanced, more pure mathematics, there is no solution - the solution is the theorem in the question. The proof is the solution and you would have probability very close to zero of getting the proof correct by accident. $\endgroup$ – Geoff Pointer Mar 15 '14 at 1:09
  • $\begingroup$ I'm accepting this answer as a very well-thought-out discussion with a very good, topical link. Thanks for the comments discussion as well, which I also think was productive. $\endgroup$ – Chris Cunningham Mar 15 '14 at 18:08
  • $\begingroup$ @JonEricson -1 I wasn't having a go at you about your son. Teaching a child in isolation is nowhere near the same as teaching a class with 35 mixed ability students. No one is saying that lists of useful resources are the be all and end all of teaching. Elsewhere you are encouraging focussed questions, but you're criticising the idea of a list of counterexamples because it's not enough on it's own. Obviously. No question here should attempt to be a one size fits all education manual should it? Well focussed lists of resources are very useful to teachers and represent only one type of resource. $\endgroup$ – Geoff Pointer Mar 16 '14 at 22:41
  • 1
    $\begingroup$ @JonEricson I have been asking my question here BECAUSE I do not want answers "Look what funny mistake my student made on the exam, ha ha ha." but "This example is useful for a lecture.". I am actually quite sure that most of the posters and voters here know the difference. $\endgroup$ – user11235 Mar 16 '14 at 23:03
  • 2
    $\begingroup$ @JonEricson If you closed my question because of issues with the particular wording, etc, that is fine. But since you closed my question because this kind of question is not welcome here, you are saying that I am not welcome here, because these are the actual problems that turn up in my teaching. Finding examples for particular abstract issues. And there is NOT a big list of good examples. The list in the "duplicate" thread on Math.SE does contain coffee talk about stupid students, and very little useful examples. $\endgroup$ – user11235 Mar 16 '14 at 23:09
  • $\begingroup$ Impressed and humbled by the quality of the discussion you provide! $\endgroup$ – user89 Mar 18 '14 at 21:13
8
$\begingroup$

I suppose with a question phrased as "what have you tried to address this problem?" it's technically true that every (honest) answer is equally "correct", but if the question were phrased as "what is a good (or the best) way to address this problem?" then some answers could be more correct than others. It does seem potentialy problematic that there is no unique correct answer; but actually I have a hard time thinking of any questions to ask on this site that would have a unique correct answer.

| |
$\endgroup$
  • $\begingroup$ This is more of a comment than an answer and would be more appropriate in a discussion about the element of subjectivity. It isn't really addressing the actual OP which is predominantly about lists. Also, if a question has many answers equally subjective but each recommending a different approach, then you may find at least one that strikes a chord that you haven't tried before or find one that you have, but is looked at in a different way and inspires a rethink. So, even questions that don't start out as lists, may end up with many answers - and I don't see that as a bad thing. $\endgroup$ – Geoff Pointer Mar 16 '14 at 22:50
  • $\begingroup$ I was answering the text of the question rather than its title. $\endgroup$ – Mike Shulman Mar 17 '14 at 15:01
  • $\begingroup$ None the less you haven't answered definitively whether or not you think we should have list type questions and why you think so either way. $\endgroup$ – Geoff Pointer Mar 17 '14 at 23:09
  • 1
    $\begingroup$ Sorry. My experience at mathoverflow was that generally when someone asks a different question in the title and in the text, it's the one in the text that they are actually asking, the one in the title being a shortened version that inadvertently changed the meaning. $\endgroup$ – Mike Shulman Mar 18 '14 at 4:35
3
$\begingroup$

The OP needs some clarification of exactly what is meant by "simply" lists.

One thing many teachers love, at high school level any way, is ready availability of resources that minimise their preparation time so that they can focus on what's important. A lot of resource sharing goes on in high schools. This type of issue would lead to list type answers. If someone ends using them inappropriately, I don't see that the idea of the list itself is encouraging that. And fun, why shouldn't there be a little fun in the classroom?

The idea of answering a question and getting voted as the best is more of a concrete content based thing (than it is a "many ways to skin a cat" teaching thing) where encouragement of good solutions is logical when solutions, due to cold hard mathematical logic can be readily compared. But, even on Maths.SE, for example, questions don't always have to be closed by a ticked answer and many ticked answers are followed later in time by answers that turn out to be somewhat better (in my opinion) but only end up with acknowledgement based on up votes.

A list of examples can continue to be voted on as interested parties come to find examples they haven't seen before and might be handy to use and vote up the ones they like (and possibly even down vote ones they think are inappropriate - who knows?). There are some very good lists at TeX.SE that serve as good examples of this.

I think it's clear though that any list should be focussed and where possible some explanation of the particular utility of provided examples based on experience would be good. Which particular method works is often a function of the individual teacher's personality. What doesn't work well for one may work very well for another. And often by explaining how you tried one thing that failed you may get another perspective that gives a variation that will make it work next time.

And I really don't see how allowing list type questions in general is going to lead to questions that anyone can answer if they're framed well enough.

| |
$\endgroup$
3
$\begingroup$

I do not think that lists of tips and tricks are a problem, but the questions should have a reasonable scope.

The wording "What have you tried?" is questionable, but I really do think that "Please give only useful answers." goes without stating it explicitly. I am quite opposed to the proposed restriction that only people should answer who have already been in that situation. This is unreasonable because they could about a solution, from colleagues, from a study, etc and thus give a good answer.

| |
$\endgroup$
  • $\begingroup$ @GeoffPointer Post has been edited, my comments have been deleted. $\endgroup$ – user11235 Mar 17 '14 at 10:04
1
$\begingroup$

One way to avoid questions which generate a wide zoo of random tips & tricks is to rephrase the question. Instead of "I have noticed problem X in my classroom. What have you tried to address this problem?", one could ask

  • I have noticed problem X in my classroom. How did you successfully address this problem? How and why did it work?

I think that this can help to make answers thorough and be able to explain. I don't think that first-hand experience is strictly required; anecdotes from colleagues or conferences, quotes from text books as well studies can also provide this kind of answers, provided there is some kind of discussion of the method and not just mentioning it.

| |
$\endgroup$
  • 2
    $\begingroup$ -1 Your version of the question does not narrow it's scope. All the examples that might accrue from the OP's question would just constitute one type of resource that be used to address the implicit problem which should be stated which is one of considering the relative importance of answers vs the processes involved in finding them. $\endgroup$ – Geoff Pointer Mar 15 '14 at 0:44
  • $\begingroup$ @GeoffPointer Could you break down your critique into two or three smaller sentences? Do you see it as a problem that my version of the question does not narrow the scope? Do you favor a broad range of possible answers, some of which have been tried in the field, some of which are just ideas what one could try? $\endgroup$ – Roland Mar 15 '14 at 8:14
  • $\begingroup$ I personally think it's obvious that we're all after suggestions that work, but this can vary from teacher to teacher - we're not all cast in the same mould. By using the caveat successful you will still end up with a list: a list of successful methods. And often discussing what doesn't work also leads to better solutions. The OP is predominantly about the idea of lists. I think that type of question is inevitable and how it's worded will depend on the context, I don't think you'll come up with a template for such questions but perhaps rather a list [:-)] of guidelines. $\endgroup$ – Geoff Pointer Mar 15 '14 at 8:55

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .