It takes an a extraordinary educator to understand that learning and achieving are not the same thing, and this understanding can go a long ways in arguing for the abolition of grades.
When my students conduct science experiments in class, they do so with the understanding that the number one priority is that they learn. Whether they actually produce a successful, working experiment is entirely secondary.
Here's an example:
My students were planning and conducting buoyancy experiments. One group wanted to make a brick float inside a large plastic tub. They figured they could add oil to the water to make it thicker and therefore more dense - and this would help them make the brick float.
This line of thinking is flawed in a couple ways. Firstly, density and viscosity are two different concepts - a fluid with a high viscosity does not guarantee that it will have a high density. A real life example: oil is more viscous than water but water is more dense; therefore, adding oil to water will actually reduce the average density of the fluid, making it harder to float the brick.
After about 15 minutes of experimenting, the students figured out that something was wrong with their idea. I had been observing all the experiments, including this one, without interfering - however, class was almost over and I wanted to help this group learn from their mistakes.
After a 5 minute discussion, and some guidance from me, my students understood viscosity, density and buoyancy quite well, but that didn't change the fact that their experiment looked like an utter failure. They had a hell of a mess to clean up.
In a traditional classroom, the teacher may have judged their final product as a failure. The irony is that this group, despite their lack of achievement, may have learned more about buoyancy than the groups who did get their brick to float.
I use this experience all the time to show how students can achieve or produce very little while still learning a lot. Needless to say, when it came to assess these students, I had to report that they had a very strong understanding for the science concepts we were focusing on - even though they had nothing but their learning to show for it.