Until It's Easy. 
Takes Longer.  
10/28/00
Something truly exciting just happened to me. A former student took a quiz. My office hour had ended a bit earlier and my office door was still open. Tony, a smiling, energetic, 22yearold, fairly able precalc student from a year ago, stopped by to visit. He’s not taking math but is taking physics, Spanish II, English 132, working 30 hour per week, and has revised the target date for the earning for his first million from age 25 to age 30. It was not unusual for former students to stop by or to juggle college with work. But, no former student had ever asked to take a quiz. 
So, What's a Quiz? What's a quiz? Testing at its best! It is a student, challenged by material, with unpenalized multiple chances for documentation of complete mastery of material, with a teacher acting as a coach and evaluator, with no outside party having an interest in the testing process. Quizzes are questions on topics (and more topics) from order of operations, to graphing, to functions, to solving exponential & log equations, to trig. What makes them unusual is that to earn credit, a student must take a quiz until a perfect paper is achieved. A student keeps the first version of the quiz and the prof keeps all other versions in the files. They are part of the questionbook – a collection of all graded nontest work. Quizzes are usually first administered in class just before a test on that topic. They are sort of a graded review prior to the test. After that, a repeat quiz must be taken during an office hour or by appointment. Few students score perfect papers the first time they take a quiz in remedial algebra or arithmetic. Of those students who retake quizzes, a perfect paper is often achieved on the second or third attempt. Both the numbers and the exact content change with each version. Many students don’t realize at first that even on the same topic the content might change. Even after the test on the topic is taken, graded, and returned, a quiz on that content may be taken – at most once a day on each topic until the questionbook due date late in the semester. It is not unusual for a student to take 2 quizzes on the same day. Here is an order of operations quiz and answer key. Note the two places for names so that the student receives a receipt for taking the quiz and the prof can keep a named copy in the files. 
Questions & Answers
Should you as a professor decide to try perfectorretake on quizzes, here are some implementation questions and answers.

Back To Tony
Though Tony had precalc with me, I picked the above order of operations quiz used in arithmetic, algebra I, and a liberal arts math course. It has "easy" mathematical content, but holds the record for the greatest number of versions taken to achieve a perfect paper. No other quiz comes close to this record. The order of operations quiz, is the hardest quiz because of the required attention to detail, the non multiple choice nature of the question, and inexperience with writing mathematics. A quiz is really about whether or not a student can do the work. The attention to detail may be all a student needs master. The experience with written rather than multipleguess format may be all that is needed. For other quizzes, the mathematics may be the problem, but, for this quiz, the best advise is "Recopy whatever you don't simplify" and reminders that "The impossible takes longer" and "It is hard until it is easy." Many of my students have never had to redo anything smaller than a course. The quiz provides a small enough opportunity for students to take charge of THEIR learning process and experiment with ways in which they learn and problems they must and can attack and correct themselves. A quiz can teach students to teach themselves. Yes, a quiz can teach students to teach themselves. The order of operations quiz is the hardest because students must pay attention to details, stay focused and write mathematics. Once this is mastered, only the content is the problem. Additional quizzes provide additional practice in doing just that  taking charge of their learning, correcting their own errors, paying attention to details, and staying focused. Students learn they, not the material, are the master. A byproduct of required perfect papers is increased office hour use and studenttostudent interaction. If a student has passed a quiz but another has not passed the same version, the successful can assist the unsuccessful and gain experience and reinforcement while at the task.
Tony didn't get a perfect paper. But, for him, getting a perfect paper was not as important as reliving the memory of the positive quiz experience. 

© 2000, 2002, 2006, Agnes Azzolino www.mathnstuff.com/papers/quiz.htm 