Is there any way for curriculum designers to notch a win with you, if the “designed” aspect of their work seems to disagree with you?

Julian:

Yet I think there is a really interesting story to tell nonetheless about the history of their discovery and the fear they were held in — it is far more engaging than this pseudocontext, and may help to explain the terminology “irrational” (which in English has quite negative connotations).

Agree. I’d like to know more about the genesis of “irrationality.” Somewhere in the inception of the idea is a conflict which we can adapt for the classroom.

@Julian: “Pythagoras allegedly killed someone over the square root of two” does seem to get kids’ attention. ;)

These are really good points and questions. My sense is that creating ludicrously fictitious contexts is pointless, as it gives the message that mathematics is disconnected from the real world problems that people care about. On the other hand, I am struggling to think of a good example of a genuine real-world application of rational versus irrational numbers. Yet I think there is a really interesting story to tell nonetheless about the history of their discovery and the fear they were held in – it is far more engaging than this pseudocontext, and may help to explain the terminology “irrational” (which in English has quite negative connotations). There is also the potentially interesting discussion of how to represent these numbers – how can computers handle them, for example? (I’m not sure whether this counts as “application”, though.) But some of this gets quite sophisticated quite quickly.

There is also the point to make that much mathematics is interesting for its own sake: it is a subject of intrinsic beauty, and humans as a species like problem-solving. (Think of the prevalence of crossword puzzles, the sudoku craze and so on, which probably have no significant practical applications.) And math is about problem-solving, just because. Sometimes, the problems are practical, sometimes not. But it is the problem-solving aspect which is common to these, not the practical applications.

Paul Hartzer, I like your questions.

I get the point, but on the other hand, if we go too far the other direction with this, we run the risk of communicating that all higher math is pointless because people will just estimate everything they can’t do with plain arithmetic. During one of my education classes, I remember trying to develop a “real world” geometry application of calculating how much carpet is needed for a room. I was told by several people (including the professor) that they’d just take basic measurements and estimate, because there’s going to be waste anyway.

So how *do* we create mathematics problems that are real and that don’t rely on overly fake scenarios? Or do we stop trying to create real world mathematics problems entirely?