A number of people have written about the "Tyranny of the Right Answer" (for example see SmartBlogs or The Huffington Post or Corwin Connect or Russ on Reading ). Many of them pick out Mathematics as the one subject where this tyranny is at its mightiest. This post is to argue the contrary.
The fundamental claim of those who are against the "Tyranny" is that there is, in general, no "one right answer" and that reality is more nuanced. I don't think anyone will argue with that. At the same time, we can argue that training a to-be-car-mechanic to fix a car by putting the student in a garage full of tools and waiting for the discovery process to succeed is not going to work either!
All of education is a careful balance between passing on the knowledge and skills that the teachers have, and helping the student find her/his own solutions to the problems. Again, I don't think that this statement will leads to screams of disagreement. The problem, of course, is that the balancing point will differ from teacher to teacher and student to student.
So the real question is to identify indicators that will guide each one of us to our own centre.
As argued elsewhere, Mathematics is a centuries old art, probably older than most tools, and certainly older than agriculture and masonry. Thus, it would indeed be a foolish teacher who left a student for too long trying to discover numbers and arithmetic instead of helping her/him acquire the skill of dealing with them. After all, some people discover things later than others --- "usko ab samajh mein aaya!"
The primary discovery in Mathematics (which too few students make!) is that every answer in Mathematics can be "reasoned out". So a student should first find a solution that she/he is satisfied with ("khud ko satisfy nahin karega to kiska satisfy karega"). Upon critical examination by the teacher, the errors will pointed out and the student can self-correct. Of course, such errors will lead to lower grades, after all getting critical feedback is one of the keys to learning!
The fallback to "blind" application of standard technique is an alternative if one "fails to understand". Indeed, Mathematics is one of the few cases where it is possible to be competent without being creative; imagine trying to write an essay in History by application of "standard" skills.
How far one is on the scale between screw turner and a Zen master of motorcyle maintenance is ultimately irrelevant if one can at least fix the bike enough to get on the road!