Thanks for responding to my comment…I agree with you that there is certainly room for improvement in the modeling component of math education and that honesty is a vital aspect to classroom management.

I recently read a study by Susan Gerofsky of University of British Columbia in which she interviewed 50 math students and math teachers and not one of them saw any point to contrived math problems. This viewpoint sometimes works to drive these problems out of the curriculum – but to be replaced by what?

Any time I have been involved in “real-life” applications, I recognize the situation as some combination of various aspects of the contrived problems I studied in class. The work I did on the contrived problems then provide me with the tools I need to solve the “real” problem. Keep up the good work!

Also, when ever we are trying to do some problem that is nuts like one of those age problems, I make sure to make fun of the writer of the problem, then the students don’t mind so much and will do it for the sake of the math.

In short, I think application problems need to really be real application problems. You can have word problems that don’t apply, just don’t label them as such. Students need to be prepared for their future classrooms and future lives. I think we can prepare for both.

Rich: So — complaining that textbook problems are not the same as “real-life” applications is equivalent to complaining that you can’t see your mother waving to you on a map of the United States. True, but that’s sort of the whole point of a map!

There is a lot of truth here, Rich. But more often than not, publishers lump all of these problems under the same heading “Applications,” essentially telling students there isn’t a difference between the terrain and a map of the terrain. I’d be a little quieter if there were a little more disclosure of the difference.

Real world problems which involve mathematical problem-solving are typically very particular, and the skills one uses in solving one of them do not necessarily transfer to other problems.

Contrived, textbook problems are typically designed to embed a collection of problem-solving skills which would be broadly applicable in solving any one of 100 “real-life” problems.

So – complaining that textbook problems are not the same as “real-life” applications is equivalent to complaining that you can’t see your mother waving to you on a map of the United States. True, but that’s sort of the whole point of a map!

No, “real world” is not truly opposed to “fake world,” unless we want to believe fatuously that “real numbers” are actually real, and that “imaginary numbers” are somehow disconnected from reality. The day someone can show me “one” (not “one of something,” not “the numeral or word ‘one,'” but the essential “one” in itself), I’ll show you the actual 3 + 2i in itself. ;)