What does it mean to understand something? Well, I think it means you can tell a convincing story about it.
Sometimes we talk about 'knowledge, skills and understanding' as the three aspects of learning. Knowledge and skills seem OK to me. Understanding is more problematic, yet in some ways seems the most important, the most fundamental. Knowledge: I know that flash memory is based on a MOSFET (metal-oxide-semiconductor field effect transistor) technology. Skills: I can do calculations on the capacity and speeds of flash memories. But, do I understand flash memory?
The first thing to say is that it is of course a continuum. I understand flash memory to some extent (like I know some things about flash memory and I can do some things relevant to flash memory). What makes me say I understand flash memory to some extent? Well, I can tell a story about what it is and how it works, and that story makes sense to me. That is, I can tell a convincing story about flash memory. Convincing to whom? I'm the one saying I understand it, so it is convincing to me. It may not be convincing to you, so you may say I don't understand it.
I'm writing about flash memory for T325 ("Technologies for digital media" - a new OU course for 2009), so I'm telling a story about it in the course text. We want students to understand it, and we'll be asking questions to check whether they do. They'll need to tell a story back to us to convince us that they understand.
That's the story I tell about understanding anyway.