- The number of party guests increases according to the function g(t) = 2t + 4, where t is the number of hours after the party started and g is the number of guests.
- The number of iPads sold increases according to the function s(t) = 2t + 4, where t is the number of weeks after the iPad went on sale and s is the number of iPads sold in millions.
- The number of points the team scores increases according to the function p(t) = 2t + 4, where t is the number of minutes after halftime and p is the number of points scored.
Party guests. iPads. Points.
They're all the same to the student who doesn't understand abstraction, the process by which we turn those contexts into words and symbols. The idea that any one of those contexts will engage that student any more than another is a fiction.
BTW. Clarifying: the issue at hand isn't that these three problems are simplistic or false abstractions of a context. It's that they start at a high-level of abstraction. (This isn't a revisitation of pseudocontext, in other words.)
2012 Sep 27. Nathan Kraft points us to some research that says, "This kind of superficial personalization, indeed, increases engagement and achievement." So I may have overstated my case considerably. The point of this ladder of abstraction series, though, is that investments in making abstraction more explicit are way more worth our while, not that other investments aren't important also.