Additional Thoughts on Exams
Borrowed from YouTube (with permission). What a math test could look like.

In a previous post, I detailed my process for actually grading mathematics exams.  Here are some additional thoughts that I’ve learned to build into my courses (before any exam), some commentary for after the exam, and then a few other thoughts.  While these apply to a mathematics exam, they would apply anywhere.

Additional Thoughts on Exams

Here are some other things I’ve learned along the way about the exam experience.  I’m going to divide them up in terms of the chronology of the exam in a course.

Before the Exam

Talk about study skills with your students.  This should happen before the first test (group study vs. single, note cards, etc.).  Then, talk about how to actually take the test (time management, etc.).  If they do better, grading is easier for you and you’ve probably taught them one of the most important skills of his/her life–how to prepare.  There are vast amounts of resources online, too.  You don’t have to reinvent the wheel.  In the future, I’ll probably build these in as a part of the course page in the LMS.  Rather than offer the opportunity one time, in class, I’ll keep the content available all of the time.

Also, make your testing philosophy clear to your students.  My philosophy for a mathematics exam is for the purposes of demonstration.  At the undergraduate level, an expansion of ideas rarely seems appropriate for an exam, to me.  Consequently, I let my students show how they have mastered the content delivered to them.  This also makes the writing/grading of the exam easier for me.

While Grading

This is the part of the exam process I dread most.  What I realized, at some point, was that my behavior as a grader was what I struggled with.  Here are some patterns of behavior to which I adhere.

  1. If I’m struggling to decide between giving one point (or not) on a problem, I give it to the student.  It means way more to them and it simply isn’t worth my time.  An alternative is to give a half or quarter point.  I am, after all, a mathematician and there are infinitely many numbers between any two integers.  However, integers are easier to add.
  2. It’s easier to grade a little more strictly (not much!) and then curve on the final.  A comprehensive mathematics exam isn’t easy for any course so a lower score isn’t unreasonable and the mastery of early content should be anticipated.  However, the curve also concedes that perhaps you graded strictly and wanted to make up for it should the conversation come up again.  Ultimately, this process, too, is a time saver (ultimately) that I learned from a colleague about a decade ago.
  3. Write a comment on the exam offering encouragement.  Find something the student has done particularly well and praise them for it.  They deserve it and it shows them that you’re not a mindless drone who genuinely cares for them.  This great because you’re not (probably) a mindless drone and you do (hopefully) care for your students!  I learned this from the first prof who convinced me that I could do mathematics well.  We never discussed it; she embodied it.
  4. I keep hot tea and chocolates near me when grading.  It’s hard to feel bad with warm, caffeinated beverage and chocolate nearby.  This helps my mood and their grade.

After You Have Returned the Exam

Once the exam is completed, there are a variety of scenarios to address. Here are some of the things that experiences (and not wisdom) have taught.

  • If you’ve got a sufficiently small class, let the students present the solutions to the problems on the board.  Pick students who did well on the problems (if possible) and let them talk it out.  This clearly saves time in the classroom.
  • Don’t pull the punch.  When a student doesn’t do well, it’s rarely a surprise to them.  When talking (actually) one-on-one with them, tell them but then help them to do better.   Trying to avoid the touchiness leads to negotiation which teaches an unwanted lesson and creates additional labor.  There will be some awkward silences; these can be used well for dramatic effect.


What I have realized is that many people can teach the mathematics, many people can give exams and grade them, and many people can assign grades at the end of the term.  However, very few of those people build something bigger than a mathematics class.  Some people–hopefully me, included–also get to influence those students.  While the exam may only assess, the culture of the classroom–which includes exams–should leave some impact on their lives, forever.



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Additional Thoughts on Exams
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