Rudbeckia Hirta (a clever pseudonym for a math professor who carefully keeps her true identity hidden) observes:
Due to reasons beyond my understanding, high school math and college math are completely unaligned. The K-12 system sends us students whose knowledge is a mile wide and an inch deep: we get students who are shaky at algebra, frightened of fractions, and unsure of how to find the areas of basic plane figures (and completely unable to accept the idea that it is a reasonable request to ask them to solve non-standard problems where the method of solution is not immediately obvious), but they have been exposed to matrix arithmetic, computations from polynomial calculus and other supposedly “advanced” procedures. You would think that the “college prep” track would prepare students for college, but it doesn’t.
Among the comments to this post is the following:
The problems are many, I think. They range from schools wanting to look good by having X students in Calculus or X students in Algebra in 7th grade or 8th grade. Also, much of the focus in most high school classes is on the use of formulas. If you can plug and chug, you are good to go. There are so few non-standard questions posed to the students that they can’t even hope to understand that they need to be able to solve them. (This is not 100% true, but is true a lot!) It’s kind of a broken system in which everyone thinks they’re doing the right thing, but in the long run, they may not be.