I really like Ben’s definition, because it leaves room for the curiosity, beauty, and fantasy aspects of math that attract me. It reminds me of Lockhart’s video for Measurement:

“That’s amazing! That’s completely unexpected. I would have expected: You make some crazy blob and connect the middles, it’s gonna be another crazy blob. But it isn’t – it’s always a slanted box, beautifully parallel. WHY is it that?!”

That’s the sort of wonderment that entices students to think about math.

Re: Design Question 2 – Student motivation and classroom culture.

This reminds me of another distinction you made about “two very different schools of thought.” On the one hand seeing “content and management (as) functionally the same,” and on the other hand developing them seperatley. (https://blog.mrmeyer.com/?cat=49)

I just got back from a visit to the Ron Clark Academy*, so maybe this is more vivid for me right now, but I think we could place tremendous emphasis on motivation and culture without thinking twice about content. I mean, the ‘Standard Model’ of teaching is incredibly robust in this aspect with recomendations like “Have a clear system of classroom procedures (for everything!)” and “Kids will do amazing things for candy.”

So having a bunch of songs, dances, buttons, and trampolines can be a great way to bring some enegry into your room, but there’s a stark contrast here when Mr. Lanier decides to Ditch the Stickers because although ” It still seems good to me to recognize one’s success and progress—and stickers aren’t an awful way to do this, but I think there are better ways. The best, of course, is when what one has done or gained or accomplished is the reward.” (http://lanier180.wordpress.com/2012/09/05/ditching-stickers/)

Likewise, there’s a difference between having a long list of clear expectations, values, rules, and procedures (or whatever) and Mrs. Nguyen saying “Maybe I’ll go over our classroom rules and procedures on Day 2. It should take all of 10 minutes to go over them anyway. (If you need more than 10 minutes, then I think you have too many!).” Because Day 1 has been all booked up for a “few years” now with “doing math.” (http://fawnnguyen.com/2012/07/29/20120728.aspx)

*The Ron Clark Academy is a tremendous school. Although their trademark methods were definitly in-your-face energetic magic tricks (non-content), they were also very clear about the necesity of rigorous content standards. From interacting with their students, I’d say they are succesfully cultivating a genuine interest in academics… as well as dancing, singing, and general purpose social skills.

Conrad Wolfram:

…for “relevant to” I mean (hope I said!) “actually used today in”.

Even if you believe that the main purpose of mathematics education is to prepare students with skills that are relevant to a job or the “real-world,” isn’s it unwise to prepare them for what is “relevant” today instead of helping them to be able to adapt to what may be “relevant” in the future?

Real world and relevance may be taking away from understanding Wolfram’s point. And in this one tweet exchange the thrust of the idea has been undersold. Computing has changed what mathematics is. The importance of the “real world” comment here is only to underscore how the essence of the subject is shifting. Other disciplines are not changing fundamentally in the same way because of technology. The problems we choose, whether they are “real world” in the sense of what you will need in a high paying job today, or “relevant,” as in what do students want to solve or what will engage them, need to include the concepts that have been created since computing technology became ubiquitous. The role of teachers building classroom culture and engaging students was at the heart of the conference.

Over the past few years, I’ve been coming to understand that there are huge differences between and among the many different forms of the fundamental student question about the “relevance” of mathematics. Right now, I understand these questions to fall into two main categories.

The first is the kind of question that asks, How is this new/strange/perplexing idea/concept/skill connected to other things/ideas/skills/concepts in our world? These forms of the question express a kind of openness to perplexity and to student agency and to the possibilities that math can help us to unlock.

However there are also forms of this question that are not genuine questions at all but rather blind, mute, and highly emotional defense mechanisms – rhetorical forms of a question that seeks not to actually *ask* a question about mathematical relevance but rather to express a stance of resistance against engagement in the classroom community. In this regard, they are a kind of “acting out” against the didactic contract – an attempt to use willfulness as their own last, best defense against attempts to guide them to owning their own agency. For whatever reason, rightly or wrongly, any such effort seems to feel to these students like a threat to their very subjectivity.

I’m not trying to defend or attack this second form of questions and questioners – I’m extremely interested in coming to understand what is going on with these students because it seems to me that their relationship with the learning process has become so poisoned they feel compelled to defend themselves against it.

So I’m curious to hear what others may have to say about this phenomenon.

For whatever reason, there still seem to be a lot of students (meaning > 0) who feel the need to resist what others of us experience as math’s “call to adventure.” I think that cultivating perplexity and a healthy classroom culture of inquiry and a spirit of delight in discovery can help to erode this resistance among a great number of students. But there remain some students who continue to see this as a form of entrapment, and I have no clue how to help move them through this self-defeating defense system.

Thanks for another great post+conversation about all this.

– Elizabeth (@cheesemonkeysf)

I had to give a speech on this recently at my school in front of a lot of parents – and I got in a bit of trouble for my answer.

In Sweden, the idea of trying to make math more “real world” is actually written into the school law and high schools have been criticized for not doing enough in this regard. In junior high (which I currently teach) there is less pressure since we are required to give them a more general background, but in Sweden already in high school students have to pick a “program”, which is more or less a major and the classes they take are tailed to that program, though there are some general ed classes (like math).

For example, in high school students might opt into the “vehicle” major, where there learn all about cars with the idea that most of them will end up being truck drivers or mechanics or something along those lines, and not go to university. They still have to take math the first year, but it should have a lot of car problems in it according to the law.

Anyway, at my junior high parent meeting, the issue about “when will we use this” was on the table.

I first asked how many of the parents had heard of Mozart. Nearly all raise their hand. I asked how many of them worked with classical music in their jobs and none raised their hands (with kids I have asked the same except with them I ask how many of them listen to classical music in their free time).

Same for Picasso and painting.

Then I asked how many had heard of Gauss, and only 6 out of 200 raised their hands (more than I expected actually). I explained who he was and asked why they thought this was okay from a cultural point of view, especially considering he probably has had a lot more direct impact on their daily lives and our society than the other two.

I made comparisons to art and history and literature – things society agrees that in some way enrich our lives and are part of this bigger concept called “generally educated” (not a great translation of the Swedish word I use here, but close), even if we don’t work with them in our jobs, even if we don’t “use them in the real world”.

I pointed out that studies have recently shown that literature gives doctors a better bedside manner and increases empathy in most people. The point being that sometimes the benefits are not obvious. I talked about how I thought math could enrich a persons life and view of the world even if they didn’t use it in their job.

A lot of them liked my speech, but some didn’t like the idea that I wasn’t pushing the practical “calculate your taxes” reason for learning math. My administration wasn’t thrilled with me either.

One parent said they got chills (the positive kind) from my speech, another parent came up and grilled me about the use of percent in “real life” and how dare I not talk to the students about that.

It is a very sensitive topic here.

Another of my most respected bloggers — a co-op preschool teacher in Seattle — just made a post that touches on defining “relevant”:

http://teachertomsblog.blogspot.com/2013/11/making-school-relevant.html

Teacher Tom has amazing insight into how children learn _before_ they are introduced to “formal” education; the ideas could be useful in renewing older students’ sense of curiosity.