The last comment to my post about "My Favorite Problem" was interesting to me because I feel her pain. I enjoy problems like the one in my last post the same as I enjoy doing Sudoku or Crossword puzzles, but I don't think that they are diagnostic of intelligence or academic ability. They're just fun. The same way multiple choice questions are frought with pitfalls if they are not well constructed. I don't want to measure my students distractability, I want to know what they know. I give compare and contrast and essay questions on my exams, but then I only have about 50 students a semester, so it's not too onerous.
I use the "Book Worm" problem in the introduction to my classes to introduce the need to apply whole brain thinking to science problems and to avoid getting tricked into using just one pattern of problem solving, but I also hope to dispel any ideas that there are simple answers and purely "right or wrong" answers.
I've talked about this in previous posts, such as Science Tricks and Is Black a Color. Levels of explanation are important, as are identification of assumptions and qualification of the parameters of an explanation.
If you liked the "Book Worm" problem, you'll love this one. It's taken from the problem set for "Conceptual Physical Science" by Hewitt, Suchocki and Hewitt (Addison Wesley).
A motorist wishes to travel 40 kilometers at an average speed of 40 km/hr. During the first 20 km, an average speed of 40 km/hr is maintained. During the next 10 km, however, the motorist goofs off and averages only 20 km/hr. To drive the last 10 km and average 40 km/hr, the motorist must drive:
a) 60 km/hr
b) 80 km/hr
c) 90 km/hr
d) faster than the speed of light
I use this one in my introduction too, sometimes, to show how using math as a model to solve a problem isn't always a bad thing, and shouldn't be scary. Since I'm teaching future elementary teachers, we promise not to use too much math, even though it is a physical science content course. Try teaching physics without math and you'll see just what "The Teacher with a Bad Attitude" was talking about when visualization is the only tool applied to solving non-intuitive problems. Math can be very illuminating. All tools that can be applied to solving a problem should be applied.
And this brings up another pet peeve of mine. I don't like giving students limitations on exams. Information that must be memorized is a tool for problem solving. Skills are tools for problem solving. The best "test" of a student's knowledge and skills is their application to a problem. Scientists don't limit themselves to a text book or what resources are available in their local library. We don't rely solely on Google or Yahoo or Microsoft. I tell my students that they will need to know the vocabulary they learn to understand my questions and provide quality answers, but the question will pose a problem that requires the application of knowledge and skills to answer.
It's a challenge as a teacher to get beyond the building blocks into the construction phase, but it should be our goal. If kids can be taught to solve problems then they will learn how to find the resources they need, and challenging them to solve problems can accelerate their aquisition of knowledge and skills.