In this country many teachers have been taught that it's important for kids to be able to use a range of approaches to solve a problem.

They then force them to use each of the prescribed set of methods even when they are totally inappropriate for the task. Any deviation from the method they are told to use for that question is wrong. No creation of your own adapted methods is acceptable.

In other words, the teachers were taught that kids should use different methods, but seemingly weren't taught why.