The course has run its course. The final is finished.  The red ink has dried.  The assessments are formed and recorded. Did everything go as expected?  No.

  • I thought I edited the test to fit its demands to two hours, comfortably, for any prepared student; I was wrong. Approximately 1/3 of the students needed extra time, and many were my well-prepared students.
  • I thought all my students understood the cardinal points of cardinality of sets; I was wrong.  Many students completely missed the finite/infinite distinctions.
  • I thought my students understood the subtleties of counting team formations; I was mostly wrong.  Many clearly had never read the examples in the text.
  • I thought my students understood a notation I introduced early in the quarter and used almost weekly; I was mostly right, but some students had no idea what I was asking.
  • I thought I had proof-read and edited the test to the point of clarity of all questions; I was wrong on at least three of 15 questions.

What about the architecture of the test?  Did it meet my needs?  Here I can be positive.  The test was divided into three sections.  The first section tested basic understanding of definitions and methods.  The second section integrated concepts but sought definite answers.  The third section was open-ended and devoted to proof.  Having the sections so divided did give me a profile of understanding for each student.  If the test had been a little shorter the students may have had time to polish their proofs at the end; but shorter tests magnify errors.  Overall I was pleased with the form and function, even with some very rough edges.  I’ll use the same blueprint again.  But now it is time, finally, to rest.


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