Dan, perhaps I need to go back and reread your definitions from earlier, which I have lost at this point in the chaos that is the end of the semester…

But to me, I think this question is definitely a start. The larger question, which I have raised over and over here is who’s “world” is the one providing the context? I get the professional’s world and love the idea, but how does that then relate to the world of the student? There’s a translational piece there that’s really interesting to me, and is something that I’m still missing in your definition.

How do students take ownership over the context?

Whenever you throw out the WCYDWT, I find myself wondering who exactly the “you” is. I so wish you’d reframe it as WCYSDWT. What can your students do with this? That would be so much more interesting.

Am I misinterpreting here?

Dan,

When I was a kid, I remember my dad using the formula for the area of a circle and then dividing it by the cost to determine whether or not an Extra Large was a better deal than a large. Before the days of the iPhone, he would carry around a tiny pad of paper just for situations like that.

This problem was a joke, because anyone who eats pizza knows that regardless of the size of the slice, you’ll still usually eat 2-3 slices.

Now, the problem was definitely real-world and my dad was a man with a finance degree, so that probably explains the insanity of it. I don’t think it fits the definition of pseudo-context, but it is still a ridiculous math problem.

Most real world problems like these could be tweaked to make investigations with assessments for students. I’ll be trying a modified version of the oil tank problem with my geometry students and another version with my advanced algebra students.

The pizza problem isn’t completely ridiculous and could be salvaged. I’d like to see what I can do with it for my geometry class.

Seems like a good axiom for whether something’s pseudocontext, but I’m still not convinced that pseudocontext is necessarily, or even usually, a bad thing. Lack of student engagement with a problem is a bad thing, but is this even correlated with the use of pseudocontext? And if so, is it only because the teacher is irritated by the pseudocontext (as Dan obviously is), or does the correlation still exist once you control for the teacher’s feelings about the problem? I’d like to see experimental results on this before devoting effort to eliminating pseudocontext from textbooks etc. Anecdotally, my son adores Descartes’ Cove, which I’d say proudly embraces pseudocontext (typical q: A horse is tied to an exterior corner of an octagon-shaped castle with a rope that is 15ft long. If the length of each side of the castle is 20ft, what is the grazing area, to the nearest square ft, of the horse?).

John, you called that problem ridiculous in a roomful of mathematicians. ;^) Like many of the commenters above, I like that problem. It makes you think about the difference between the way sizes are stated (by diameter) and what really matters, which is the area. I bet it was embarrassing, though, to have your dad pull out his little pad of paper when you were at a pizza stand!

I like what Michael said above. The danger of pseudo-context is that it will convince kids not to use their common sense. Perdita’s comment points to one answer to that problem – use a fantasy world when you have to make up silly problems. As soon as I see the word ‘castle’, I know I’m in a fantasy land, where things are likely to work in strange ways, and I have to trust that things work the way they’re stated in the problem. I have to set aside some of my common sense because the rules may be different in this world. (Although I like the problem of finding the grazing area, even when it’s given a more pedestrian setting.)

Here’s a cool post on using fantasy when you feel a need to give students problems with silly storylines. (I may have mentioned it before…)

@Sue: evidently you don’t live in Scotland, plenty of castles here :-) Seriously, though, I think your point is good, and I like that blog post – thanks for linking.

Oh all right :-) Flatly untrue. Who’d build a castle (not a tower, mind) that was octagonal without taking advantage of the opportunity to have towers at the vertices? It’s also ridiculously small for a castle – area of the whole castle (unless I’ve made a mistake, it’s late here!) is 800/tan 22.5 degrees i.e. < 2000 sq ft. Now, if they'd based the q on the Castel del Monte in Apulia
http://en.wikipedia.org/wiki/Castel_del_Monte,_Apulia
it'd've been interesting in every way ;-)

But if you want to defend that one, I could pick any number of other examples from Descartes' Cove.

Perhaps necessity is the mother of invention and therefore pseudocontext need not apply. That is how we came up with much of our math anyway. We needed to know something and we needed to discover (invent) how to find the answer to our need.

I think pseudocontex occurs when this “need” is artificially (sometimes painfully) forced upon the audience. If I don’t care to know something, there is I have no need, necessarily.

Therefore, can pseudocontext be relative to the observer? One observer can have a need, while another may not, thus creating pseudocontext for the second observer?

Yes, that’s interesting speculation. Here’s my counter-speculation: students not already enamoured of maths will tend to be engaged by problems that have personal relevance to them (and to a lesser extent those that have personal relevance to people who have relevance to them); however, there won’t be any difference between how engaged they are by problems that have relevance to someone they don’t especially care about, and how engaged they are by problems that have relevance to nobody. E.g. unless the student has a truckdriver in the family, the petrol gauge problem will be no better than a pseudocontext presentation of the same material.

As I read through the posts, there were several that addressed the use of the word “world” in my original post. People have observed (correctly) that the context of any problem may not be engaging to all students.

I am not hopeful that we will be able to generate problems that are universally engaging to all students, and that, for any problem, there will be a subset of our students that don’t find the context engaging. I’m afraid that if we try to work that into a definition of pseudocontext that every problem will be pseudocontext.

But it’s OK if some students don’t find the problem engaging, because some will, and part of what I see as my job is to provide students with snapshots of how mathematics gets to play in everybody’s backyard, and that regardless of what my students “grow up to be,” there will be mathematics that is relevant to their professional “world.” If they’re lucky, it might be engaging (read “fun”) mathematics.

It can be the case that Alex was enthusiastic about the problem and his enthusiasm was infectious, though – might not transfer to a different teacher or an everyday practice. The plural of anecdote is not data, as they say.