on teaching math

From Ben Blum-Smith commenting on Dan Meyer's blog (my emphasis):

The real test of whether a math problem is "relevant" is not "do you use this in 'real life'," whatever that means, but "do you want to solve it?" It's not that you want to solve it because it's relevant; wanting to solve it is what it means to be relevant. The solution to the problem of relevance cannot be aimed at any location in the process of education other than what the students want. We can access various natural processes in causing students to want to solve problems: they are naturally curious, hungry for understanding, they want to resolve cognitive dissonance when it comes up, they want to feel accomplished and mentally powerful, they're drawn in by story, attracted to the perception of a grand scheme, to knowledge surrounding things they're passionate about, etc. Curious is the big one. All these forces are amplified by a sense of comfort and orientedness in the face of a problem, and inhibited by any sense of helplessness or disorientation.

The whole (very long, multi-page) comment is worth reading. I don't quite grasp the full scope of the word pseudocontext, but it represents the pointlessly-contrived nature of textbook math problems, compared to things like this.