I offer daily quizzes in all my classes. I know that might seem scary to a few (developing, grading, student anxiety) but it is one of the few times I get to see students 'work'. These quizzes are based on three levels of participation (5 points = a quality attempt, 2 points = a minimal attempt, 0 points = no attempt) and have a variety of purposes which I have talked about before. I do review them right after the student's attempt for additional feedback, to model a solution method, and to start the day's lesson.

In Calculus I we are reviewing the limit definition of the integral. Suffice it to say that this is a difficult area because it relies on both conceptual understanding, but also computational understanding of things we have not seen together (limits, summation, etc.) There are three major tasks for each question; setting up a generalized area formula, taking a summation of these areas, and then taking the limit of these areas. The specifics aren't important for this discussion, but if you know them great.

So we have a fairly detailed process to learn and students find difficulty in what to do next. Solution: multiple daily quizzes that are similarly structured, break the question down into constituent parts, and provide a model for how students should approach questions in the homework. This quiz was the last of the four quizzes structured in this way that I gave last week. The only difference between them is the function and the interval we are looking at. (Today's quiz integrated x^2 on [0, x], foreshadowing The FTC.) I had received positive feedback from students that they like how these quizzes broke down the process, and it had helped them in homework.

By Friday I felt that students were getting a little bored of reviewing the same type of quiz, so I wanted to shake students up a bit. Humans love novelty and if I can make my class novel and even silly in pursuit of understanding the material, why not? So at the end of the quiz I made a list in my head of those students who had completed the quiz. At that time I called those students my 'exemplars', took their quizzes and tapped them to different walls. They were to then stand by their quiz and explain to others how they found each part of the process. At the end I collected the quizzes and graded them as normal. In hind sight I should have probably identified their quizzes as 'exemplars' and not the students themselves...

I think this helped all students develop a better understanding of the process, some by talking to these students who provided exemplar solutions, others by having to explain their method. It was also a nice way to break out in a different way, one where the focus was not on me or my methods, but on other students' methods.

Today I asked how last class went, and the response was pretty lukewarm. One student said "I think we got out of it as much as if you went through the quiz." In terms of mathematics, maybe, but in terms of developing connections between students and developing mathematical fluency I think it was better than if I reviewed the quiz.

Have you tried something to break students out of their 'shell'? Would you do something like the above for a participation-based quiz? What about for a graded-quiz? What about for a test? Feel free to comment below.