> Dear Richard, your problem is very interesting, but when > describing it, you completely omitted mathematics.
Maybe this is because, when the problem is presented to the students, there isn't any mathematics inherent in the problem. (This is true of *any* math problem.) To be more precise, there's mathematics all over the place *for those of us who already know it's there.* But *for the students,* the problem is initially just an interesting story about Richard and his landlady. The object of Richard's series of lessons, as I understand it, is (a) to help the students realize that there *is* math in the problem; (b) to help the students figure out what math is needed to solve the problem; and (c) to help the students solve the problem.
For each of these three parts, the role of the student is very important. Hence we can't limit our thinking to our own understandings of the problem; nor should we compile a list of "items to address before we can set about solving this problem." This is a real-world problem precisely *because* such a list does not exist; in other words, figuring out *how* to solve the problem is an essential part of *solving* the problem. And rather than telling students steps A, B, C, and D to the solution, we should help students figure out for themselves what these steps are.
Kreg A. Sherbine | To doubt everything or to believe Apollo Middle School | everything are two equally convenient Nashville, Tennessee | solutions; both dispense with the email@example.com | necessity of reflection. -H. Poincare