I completely disagree. The structure of these problem steps does not “sterilize” the process for students. It provides students with multiple entry points for approaching this problem. The idea that students would have forgotten about what the problem is after engaging in it using visual and geometric strategies speaks to our society’s algebra-centric approach to learning math.

My one tweak to this process would be to remove the ordering. There is no compelling reason that students would need to do these steps in this specific order, though some may find drawing and labeling the diagram a useful first step.

Watch the video “1500 ft Hole” (http://www.youtube.com/watch?v=1JRq80whGDk). Is the claim that the hole is 1500 ft deep accurate? Use your own calculations and the principles of physics to support your answer. A hint to get you started: the speed of sound is about 1125 feet/sec.

Here is what I dislike about the first problem. It puts a nice, tidy box around the problem solving process in such a way that any potential messiness is removed.

Beyond the potential for solving the problem without going through these steps (which I think has been alluded to in other comments), I think the punch line is in Question 17 – “Solve the equation and answer the question.”

The student will need to be reminded to do this, because after the sterilizing effects of questions 13-16, the student will have forgotten all about the original problem.

By drawing a picture first, then using labels on the picture, we are teaching a generalized skill that will help the student get through many similar problems. Is it a perfect problem? no. Is it better than most of the ones that my textbook provides me? In my opinion…absolutely. Instead of 5 illogical steps that students wouldn’t get on their own, this is actually the process that I would like them to learn.

Both problems concede that the student is just too helpless to solve either on their own. Even the first problem says, “C’mon, you guys. Since you will never figure out what I want you to REALLY do, just follow these five simple steps so we can all get out of here.” Furthermore, I am not at all convinced that these five steps can be applied universally to other problems the students might encounter.

Written problems are great, but I love problems that you don’t need the written context to solve. Fantastic!

In general, the textbooks are too helpful but most of the time students don’t even get that far because the reading is dense. My students head for the hills when they see word problems.

Maybe the book could just add another question or two that are more likely to require a variable or an equation. For example, if there were three pictures in the row, the second being 50% wider than the first and third, this may be getting to be a little much for some to juggle in their head without at least labeling the diagram with a variable. Or don’t give the width of the paper and ask them to graph paper width as a function of picture width on the calculator.

And, how about this exchange –

S: I don’t know where to start.
T: Okay, it’s a geometry problem. What do you always do when you don’t know where to start a geometry problem?

Not everything needs (or wants) to be done on a computer, and I find it a totally applicable problem to give in my math classroom. In fact, I think I may have given that EXACT same problem in my geometry or algebra class in the past couple years.

The second problem does make me cringe, however…