This is a great idea, Niranjan. I homeschool, so we don't do formal tests at all. Either they know the material, or they don't. And if they don't, we keep at it. The way we do it is a luxury that classroom teachers often can't afford, but it should be built into the lesson plan whenever possible. Thanks for pointing me to your idea, we're on the same page.
I haven't had a chance to try this class yet, it's just been living in my head for a while, percolating. I would imagine the follow up questions would be along the lines of: "What did you discover about solving the problem? Do you think anything you've done could be applied in another setting (solve another problem)?" etc. In my mind, the class would be separated into groups of up to 7 and given instruction, tools, and materials for brainstorming and prototyping their ideas. I'd imagine this could carry over 3 or 4 class periods, depending on the problem, at least 1 more class period for the Presentation of Failures, and then a final class discussing what they've learned by failing. This could be a terribly fun class to be in. I'd love to hear how you would envision it, and if you try it, please let me know!