While in college, my geology teacher used pyramid testing for our assessments. Basically, he gave us a very difficult exam, expecting us not to be able to do all of the problems. After we turned in our individual attempts, we worked in groups of two or three to redo the test together and talk about questions. He used a weighted average to get our grade. Although a little more time consuming than a regular test (both in the classroom and for grading), the test then became a tool for learning and not just assessment.
I enjoyed this (although I was always upset that I had problems with the questions the first time around) but I hadn't incorporated it into my teaching. I graded midterms this past weekend and was dreading the two days of standing in front of the classroom, going over the exam, question by question. (A good teacher should get out of the way and not be the one talking all period.) My exams are hard and no one had a perfect score on the multiple choice questions the first time through. I decided to modify the pyramid test and on the first day of the next quarter, I gave the students the question packets back (I kept the answer sheets with the right and wrong corrections) and had the students work in groups of two or three to redo the problems for an extra point on their 2nd quarter average.
What I saw was amazing. My students that seem so shy to speak up in class, often so distracted while working on problems in class, were arguing with each other about discontinuities. Hands were waving in the air, drawing imaginary graphs to explain ideas. Pencils were scratching at paper, calculators were being passed around, and even the students with the least confidence in their ability were describing their reasoning to others. Having the motivation of a test in front them totally changed how they attacked the problems.
Then I got their new set of answers back. The number of correct answers more than doubled. The problems I needed to share because there was class-wide misunderstandings were few.
I think I might need to do this for every test, maybe even every quiz.
I just did some googling and found this more in depth explanation of pyramid testing, a few variations of how to do it, and why it works so well in reformed calculus classroom.