Purposeful Ramblings Through My Mind

You're also basing your understanding on a system that did not support those students in earlier years enough for them to develop an abstract understanding of the math they were doing. If procedural understanding was accepted as evidence, it was quite possible the kids didn't really understand even when they passed. That didn't have to be that way, and what you were seeing was the end result of years of educational neglect, much of it premised on the very idea you're clinging to: that these kids simply couldn't do it. We don't know if they could have done it, because they weren't given the chance and the support necessary to take advantage of that chance, at any stage of their education.