There is no such thing as "just a quick question"
We often get students in the MLC saying that they have "just a quick question": "Finally you're up to me - it seems like a long time to wait when it's just a quick question..."; "I know it's 4:05 and the Centre closed five minutes ago, but it's just a quick question..."; "I'm sorry to interrupt you when you're talking to another student, but it's just a quick question...". I do understand these students' need to have their question answered, but the problem is that at the MLC there is no such thing as a quick question. Here's why...
The first and most banal reason is that many so-called "quick" questions do not have quick answers. For example, the question of "How do I find where these two lines meet?" is not at all easy to explain quickly, and the question of "Where have I made the error in this working?" can take a good ten to twenty minutes of focussed attention even for the most experienced mathematician (longer if the working is longer).
However, the real reason is to do with the aims of the MLC. Our aim is to help students learn how to learn and solve problems for themselves, and to fill in missing background knowledge. Even when it is actually possible to answer the question quickly, we wouldn't be fulfilling our aims if we did!
Let me give some examples.
Consider the question, "Have I chosen the right hypothesis test for this assignment question?" Using my experience in this area I could look at the question and say yes or no in a few seconds, but that wouldn't help the student to know how to make this decision for themselves. Instead, I need to talk through the sorts of information you need to be looking for to decide if it's the right hypothesis test, and show them how to find that information in their assignment question, and then also discuss how changes in the information might change the hypothesis test. Not to mention the possibility of whether they actually know how to do that hypothesis test. So it's not a quick question after all!
Consider the request, "We've solved this differential equation. We don't want you to check if the answer is right, we just want to know if we've applied the method in the right way." I only know a small amount about differential equations, so I couldn't just tell them if they've used the method correctly even if I wanted to! But even if I did know the answer, that wouldn't help them to know if they'd done it right for themselves. In order to help them learn that, we'd need to go into their textbook and lecture notes to find explanations of the mechanics of this method, and also pick apart some examples to make sure they know how it works. I'd help them make a list of the steps that need to be taken, and then we'd look at their working and check off the list. So it's not a quick question after all!
Consider the question, "I've done this derivative and set it equal to zero to find the maximum, but it's not coming out to the answer I expect. What's going wrong?" As already mentioned, it can take a while to find errors, but even then, me finding the errors for them won't help the student know how to find errors for themselves. So at the very least I need to talk through the strategies I have for finding errors and fixing them. And it may happen that as we look at the working, I discover that they don't know how to use the product rule for derivatives, so I would need to explain how that works with various other examples. Or it may happen that looking at their attempt to solve the equation I discover some serious misconceptions about how algebra works which also need attention. So what might have taken 10 minutes even if I just told them the answer, becomes a good half an hour to an hour of serious background knowledge learning. So it's not a quick question after all!
Finally, consider the question, "Why do I have to use the right-hand rule to decide the direction of a cross product?" The simple answer would be that it's just because it's the definition of the cross product, but that would not be encouraging the student to make connections in order to understand. So at the very least we would need to talk about how the cross product produces a vector perpendicular to both the inputs, and how there are actually two possible directions to choose and we need a consistent way to make that choice, which the right-hand rule supplies. I would probably ask if they knew how to calculate the cross product and under which situations they might use it, in order to strengthen connections to the rest of the topic. I might also talk about how it all boils down to knowing what happens to the standard basis vectors of i, j and k and it seems reasonable for i×j = k. And in order to help them understand how ideas come about in maths I might possibly also discuss Hamilton and how the quest for vector multiplication was actually inspired by the complex numbers. So it's not a quick question after all.
So if we are doing our job properly we will always find some way to help students learn more of what they really need, which takes time. (And incidentally I think it's worth waiting for.) So that's why in the MLC there is in fact no such thing as a quick question.
These comments were left on the original blog post:
apm 12 October 2018:
Brilliant! You take an approach that is similar to an enrichment exploration activity. “What else do we need to know?” is comparable to “What else can we learn about this?” Funny, but the thought of having a gifted math club going on simultaneously at your center came to mind. I’ve always enjoyed teaching to the extremes but I hadn’t reflected on the exploratory similarities in meeting the needs of struggling learners and gifted math students. Perhaps not the takeaway you intended but well-crafted writing often provides unexpected insights to readers.
David Butler 18 October 2018:
Thank you so much for the reply and the insights you brought. I’ve never reflected on it before you said it “aloud”, but yes there are a lot of similarities between helping the struggling and the flying learners. I often say to my strugglers that they are struggling because they are thinking of worry questions that no-one else is bothered about.