Q: What's the purpose of context in math class?
A: To provoke modeling.
Q: What's the problem with the hot air balloon problem?
A: It offers a context without provoking modeling.
"There were 58 geese and 37 ducks in the marsh. How many birds were in the marsh?"
Q: So is the above bird problem pseudocontext?
A: No, because it's provoking modeling.
In my book, a context doesn't need to be realistic if it serves a purpose, and the purpose of context is to give kids a chance to think about something interesting. If a context provokes modeling? Great! What else can you ask of a context?
(You could ask that it be "real world," but that's a desire that I don't share. And neither should you.)
I was checking out Dan's latest thing, and I came across this comment:
I dunno, this one made me wish the follow-up showed him just throwing the paint away and starting over. There’s just not enough investment in materials & time to make me think past. Plus if 6 tablespoons was enough paint to do the job then 30 is just a waste of paint far in excess of throwing away 6.
Which if the class brings it up organically would be a big win; then you can talk about why to choose one path or the other and it’s some good critical thinking. Otherwise it smells like pseudocontext to me.Pseudocontext, eh? I say, nah, it doesn't really matter if it's realistic. What matters is whether he can do something with his scenario for kids. Context only becomes problematic when it's purposeless.
Update: This is what I mean by "purposeless context."