A short while ago Janice Kennedy of the Ottawa Citizen wrote a piece about teachers ignoring what she called "educational kookiness". Reading that piece, I realized that she was looking at the process of determining marks for students as if it had not changed since she was a teacher. In particular, she is assuming the teachers determine a student's final grade by averaging all the marks that student has earned. This prompted me to come up with an example of why current best practices recommend against using averages to determine student grades.
Imagine that two students have written the same series of tests in a course. Each test reflects the cumulative knowledge of the student for the whole course at that point. Student A scores 80% on the first test, 70% on the second test, then 60%, 50%, 40%. Student B scores 40% on the first test, then 50%, 60%, 70%, 80%. If we determine final grades based on averages, then both students get the same grade, 60%. But clearly student B is improving his/her learning while it looks like student A is understanding less and less. There are more statistically sophisticated methods than simple averages that can be used to try and capture the trend being shown, but they are tricky and have potential flaws. The reality is that any given statistical method for calculating final grade will have weaknesses, so Ken O'Connor, a recognized expert in student evaluation, offers this as Guideline #6 in his book How to Grade for Learning K - 12: "Crunch numbers carefully, if at all."
So instead of crunching student results into an average, best practices call for teachers to use their judgement based on the most consistent student results, with the emphasis on the most recent. In the example above, the lack of consistency would mean that a teacher should focus on the most recent results which are 50% and 40% for student A and 70% and 80% for student B. These most recent results suggest that student A may not have learned enough to pass the course while student B's learning can fairly be evaluated as being in the low 70s. That is a big difference from giving both 60%.