[Rescued from my old blog.]
Rudbeckia Hirta over at Learning Curves submits a great idea for a new TV blockbuster:
I’ve read that Charlotte Mason used oral exams like this with her students, though of course without the pressure and sarcastic comments. I’d love to hear how this works in “real life.”
Grading is one of the things that puzzles me about Charlotte Mason style oral exams. I don’t give grades to young students, but grades are important in high school. I need to read more, but my current understanding was that Mason’s tests were summary reviews with some problems to work (such as a student might have been set to work on a blackboard) and mostly rather general questions (such as, “Tell me what you know about fractions” or slope or conic sections or whatever). It seems to me the general questions would be very hard to grade. I guess the teacher would have in mind certain points he or she expects the student to mention about the topic. Still, I can see math being easier to grade in this way than a similar history exam: “Tell me what you remember about World History.” My ninth-grade teacher actually used that for a final exam—just that one question, with an hour to write the answer. Aaaargh!
Has anyone tried oral exams, especially in high school math? Please share!
Denise Gaskins' Let's Play Math 
Personally, I think a test with vague, general questions like “What do you know about trigonometry?”, whether written or oral, would be a very poor and unfair test. How is the student expected to know what the teacher has in mind? If the teacher’s grading system is, “I’ll give 10 points for an explanation of sines and cosines, 10 points for defining different types of triangles, …” etc how does the student know what’s worth points and what isn’t? Someone might give a complete and accurate discussion of alternative co-ordinate systems, not bother to mention the difference between acute and obtuse angles because he thinks that’s too simple and obvious to be worth mentioning … and then get a poor grade because the first was not on the teacher’s list but the latter was. This kind of test sounds more like “I’m thinking of a number. Guess what it is.”