February 7, 2008:
I bought my car new on January 15, 2006. Today, February 7, 2008, it has 37,846 miles on it. On what date will I need my 120,000-mile tune up?
February 20, 2009:
On what date will my car need its 120,000-mile tune up?
In 2008, my students proceeded admirably through a challenging problem, successfully navigating proportional reasoning, but let's not pretend I did anything for their ability to see the world through a mathematical framework.
In 2009, my students had to ask themselves, "what do I need to know in order to answer this question?" a line of inquiry thoroughly absent in 2008, a line of inquiry thoroughly absent in my textbook, which supplies only relevant information and, in some cases, "helpfully" suggests a route to the solution.
As my (patient) readership has no doubt realized, the impotency of our textbooks to do anything but teach procedure has recently whacked me over the head. Part of this, I realize, is fundamental to the print medium, which doesn't permit a layered application of mathematical structures, but part of this is the inexcusable lack of imagination of publishing houses, whose bundled supplements are both costly and unhelpful, who don't understand that they need to help students less:
Dan bought his car new on January 15, 2006. It's a four-door sedan with 16-inch wheels. Today, February 7, 2008, the car has 37,846 miles on it. He lives 24 miles from his job and drives, on average, 48 miles per hour. The weather in his hometown ranged from 23° to 107°. On what date will he need his 120,000-mile tune up?