It's Hard
Until
It's Easy.

The Impossible
Takes Longer.

      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, 22-year-old, 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.

      What's a quiz? Testing at its best!

      It is a student, challenged by material, with un-penalized 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 non-test 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.

      Should you as a professor decide to try perfect-or-retake on quizzes, here are some implementation questions and answers.

1.   What do you do with students who are absent when the quiz is given the first time in class? Do they miss their chance or do they take make-ups like those who were present but didn't make a perfect score?

Give them a copy of the original quiz (and answer key, if you have one) and permit them to retake other versions as other students would.

 

2.   How long does a student have to take the make-ups? One week? Two weeks? Until the major in-class exam on that material?

Students have till the end of the semester when the rest of the questionbook assignments are due. One powerful use of the quiz is that they CAN take it after the major in-class test. If finals are cumulative, a topic may be revisited repeatedly until mastery is achieved -- hopefully before the final. Isn't a grade supposed to represent a semester's work?

 

3.   Any other helpful hints or warnings?

If you think you've written a quiz that's too hard-- decrease the difficulty or give credit for major mastery even though a detail or something might be wrong. The teacher is the evaluator. Give full credit when a student has mastered a topic.

 

      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 multiple-guess 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 student-to-student 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.

Students learn:
• to partner,
• to DISCUSS THIS WITH YOUR PARTNER and
• to speak and learning mathematics in
  the mother tongue,
  other tongues,
  in formal mathematics speech and
  in informal math speech.

      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.

      A quiz is testing at its best, its most valuable.

• The quiz is graded and results are known immediately.
        Immediacy is important. A student may remember his/her thoughts while writing the error and be able to determine then if the error is careless or minor or if it is a problem which needs to be addressed.
   
• It is graded by a teacher who is able to point out error patterns.
        The teacher need not worry about how severe a penalty to assess but to communicate where an error occurred so the problem may be address before it becomes more of a habit .
        Taking a quiz is like having a coach watch a practice.
   
• A poor grade is not permanent.
        A perfect paper the first time means the student doesn't have to worry about taking the quiz again. An imperfect grade may be replaced without point cost.
   
• The student "voluntarily" walks into the office to take the challenge.
        The student must take the responsibility for retaking a quiz. It is NOT HANDED to him or her in a scheduled class. He or she determines readiness, not the professor.
   
• It feels great to pass a quiz in class and
  a.) Know you know the material.
  b.) Know you don't need to go over the material again or RETAKE THE QUIZ AGAIN.
   
• If you need to retake a quiz, you already know the model AND YOUR WEAKNESSES.
   
• It is a positive vehicle for addressing errors made on a test so those errors might not reappear on the final exam.
   
• It permits a student the opportunity to master something which had defeated them and often provides the inspiration to continue like work.
   
• It is a vehicle for teaching students to take tests -- the challenge is present but the penalty is not.
   
• Versions of the quiz may be reused.
        Since the prof keeps all but the first quiz paper, the answer key doesn't "get around" and may be used for more than one semester.
   
• Quizzes, and other questionbook work, provide a means for the prof to assess the work of an entire class on continued performance in meeting course objectives and mastery of curricular topics so topics may be briefly revisited in class.
   
• Quizzes serve as a vehicle for the "lost" student to assess performance at an instant in time and also a vehicle for a prof to begin work on a student's weakness.
   

References

Questionbooks: Using Writing to Learn Mathematics,"

The AMATYC Review Vol. 9, No 1, Fall/Winter '87;

Algebra & Precalc Questionbook Questions

"Letter to my Students" includes a intro about quizzes:

www.mathnstuff.com/math/letrs02.htm