Well, there’s certainly no reason why it can’t be taught. However, let’s think about how the school curriculum is set up.
In the US educational system, most things are taught as subjects – English, US History, Algebra, etc. Furthermore, each of these “subject areas” are tested as subjects, in a stove-piped manner. In many cases, this leads to the process of “teaching to the test”, and students, teachers, and schools are rewarded (or punished) based on the results of these tests.
Therefore, the most direct way to teach generic problem solving would be to teach a subject – Generic Problem Solving.
But that doesn’t really answer your question. Answering why it’s not taught is a little trickier.
Approximately one hundred years ago, attention was being given to the philosophy of education in the US, and how it should be structured. There are sources who suggest that individuals (read – powerful people) and institutions (such as the Rockefeller Foundation) turned to the Prussian school system as a model for the US system, and that this resulted in the “factory” system of education being adopted. Under this system, children are grouped by age in classrooms, and sit obediently while the teacher transmits the knowledge to the passive, obedient students. Students are not expected to ask questions or challenge the (expert) teacher. In this manner, compliant factory workers would be produced efficiently. (Disclaimer – not every source endorses this view).
We want one class of persons to have a liberal education, and we want another class of persons, a very much larger class, of necessity, in every society, to forego the privileges of a liberal education and fit themselves to perform specific difficult manual tasks.
- “The Meaning of a Liberal Education”, Address to the New York City High School Teachers Association (9 January 1909)
So there you have it. The US educational education system was basically set up to produce workers for the economy. Bureaucratic inertia has caused it to linger in the same form as we see it today. The addition of batteries of standardized tests only serve to perpetuate the existing system and prevent change.