Hans Freudenthal changed the conversation from “real world” to “realistic world“:
The fantasy world of fairy tales and even the formal world of mathematics can provide suitable contexts for a problem, as long as they are real in the studentâ€™s mind.
This complicates our task. It’s easy to create real world tasks that aren’t real in the student’s mind. It’s harder to create realistic tasks.
Here’s one way to test if the context is “real in the student’s mind”:
Can they construct an argument about it?
From Jennifer Branch’s presentation handout at CMC-South [pdf], I’ve pulled a series of questions she calls “Eliminate It!”
None of these are “real” in the sense that most of us mean the word. But each of these groups is “real” to different students. Triangles are real. Pentagons are real. Diameters are real. We know they’re real because those students can construct an argument about which one doesn’t belong. That ability to argue proves their realness.
(Of course, the value of the task is that different arguments can be made for each member of the group.)
On the other hand, consider:
These elements are definitely “real.” They’re metals. But are they realistic? Are they real in your mind? Can you construct an argument about their substance?
If not, how is it in our best interests to promote a definition of “real” that admits “magnesium” but denies “pentagons”?
2013 Nov 26. Similarly, it’s “real” if they can sort it meaningfully.