I just read an interesting post, addressing a student's question "Why does this matter?" and it's got me thinking.
As a teacher, being prepared to answer the question of how whatever we're teaching is relevant is important. In fact, I hope that it drives our planning, that we are riveted, fascinated, engaged in the usefulness and application of what we teach. If we are clear about the context, meaning, beauty and application of a given lesson, being transparent about the topic preempts the question.
In my experience, whenever this question does get asked it's not because they actually want to know why a lesson or topic is important. It's because they're not learning. If they have time to ask this question, either they are not experiencing enough challenge or they are not experiencing enough success and one or the other is arresting their learning.
"What's the point" is code for "I'm bored and I don't want to do this because it doesn't matter" or "I'm lost, and I've been lost, and I don't want to do this because it sucks to feel lost." In either case, an explanation of the value of the topic doesn't actually address the real concern: if actually doing the math is not interesting or engaging or challenging enough to capture their interest, no amount of verbal explanation is likely to help; if they are too confused to do the math in the first place, no amount of verbal explanation is going to get them to "get it."
I think it's our job to figure out what to do to get the kids learning again. Even with an awesome explanation for the worth of algebra, if they're asking why it matters then something more basic is missing for them. When they are learning, both feeling successful and being challenged, the question doesn't come up.
I think that's a great way to address that issue. It's something I hear and don't really know what to do with. But, we all do things that may have no significance because it's fun or interesting or we just like it. I want to try to look at things from the perspective of, "Would I enjoy doing this if I didn't have to do it?"
ReplyDeleteI agree.
ReplyDeleteA lot of times I do have examples of how these ideas are applied to real life problems. However, I can see the people thinking that it would not come up for them in their life so it still isn't worth the effort for them.
For example, to explain combinatorics I often give an example of a programmer that needs to create a unique order key for each order given in a day given that x amount of orders are expected. But, almost no one I am answering this "what is it for" question thinks they will be faced with this problem, so it doesn't motivate.
I am always shocked when i'm asked this question, because for me, the material is so obviously facinating. I agree completely, that if we are doing our job, which is infecting the passion and joy of mathematics in other people, that this question will be answered. No small task. I wonder how we got this and when? I can't remember not loving math.
Wow, I never thought of it that way, though the sentiment hits me as being totally true in my experience - when I was a student in a classroom.
ReplyDeleteThat being said, the question itself ("Why does it matter?") is one worth thinking about as a teacher.
Sam
when am i going to use this in real life?
ReplyDeleteoh yeah, in two weeks... :)
Jesse I think you're onto something really important. I second you and Sam that it's worth thinking as much as possible and so having something to say about what it's all for, but you're right - the question doesn't usually mean what it means on the surface, so it can't be answered by "well, it's useful this way and this way..."
ReplyDeletePart of it is that the practice of mathematics (at least pure mathematics) isn't driven by this question, but by curiosity. So if we're teaching math, feeling too beholden to the question "what's it for?" is a really big constraint. For a lot of really exciting mathematics, I'm not aware of any answer to that question that any of my students could relate to, and even if I am aware of such an answer, that answer is not what excites me about teaching it to them.
So, for me anyway, a big goal of teaching math is to try to get people curious enough so that they stop needing a "usefulness" reason to stay motivated. (Jesse I think you probably said it better but this is what I took you to be saying too?) Obviously this is hard and maybe it will never work with everyone, but it just makes sense to me that as a teacher I need the inspiration in my room to be driven by something that inspires _me_. For me, the inspiration comes from curiosity and delight with finding surprising structure, with a sense of power that comes from generalizing and proving and solving hard problems, stuff like that. So that has to be the #1 reason to do math in my room. I'm just not that excited about applications (most of the time) so I can't expect applications to get other people excited.
Alex, clearly you're opening up a huge question but I have a little bit of a thought about it:
I think almost everyone loves the essential activity that we engage in when we do math, but that most people don't associate that activity with math. To be more straightforward: just about everyone loves figuring things out. But a lot of people see math as an area where instead of just figuring it out you have to already know something, or remember something, or correctly guess something.
A metaphor for this is how Sudoku puzzles in the paper say "THIS PUZZLE DOESN'T INVOLVE ANY MATH!" To a mathematician, that's ridiculous - of course it does. Any time you figure something out deductively, that's math. But most people don't think that's math, and don't like math, so they need to be told Sudoku is not math before they can do it. But actually they love doing it. It's a total fad. People are next to me on the train doing it every day. That tells me that actually there are tons of people who love math's essential activity but think they hate math. I think we can get to those people by giving them chances to figure stuff out in a more overtly mathy context.