Not quite a straight up math error but my high-school english class had a weekly 10 question spelling/definition quiz. Each question was worth "10%" if you got both the spelling and definition correct and "0%" if you got either wrong. I typically got all the definitions correct but very few of the spellings (a major weakness of mine) scored typically 20-30 "%". At the end of the semester these tests were weighted equally with the 2-3 essays and a aggregate reading comprehension score which I did very well on (typical grades of 98%). The result was me scoring "40%" in a class where I was one of the top participants. No amount of explanation from the principal, my family or me could change the teachers mind on the fairness of this.
Actually, this story makes me want to defend the teacher here.
Seems to me that this grading regime was explained beforehand and was a fair way of assessing your spelling and comprehension. Your complaint seems to be that you think the spelling should be a smaller proportion of the grade. While I agree with that, this appears to be a case of the teacher valuing skills differently not (as with so many other anecdotes being posted here) a case of the teacher not evaluating students fairly.
If comprehension and spelling were decoupled but still equally weighted then the aggregate score would've been significantly higher. Let's split the difference and say that 20-30% on the set of [all answers simultaneously spelled correctly AND comprehended] becomes a 25% on the "spells things correctly" axis. If we weight that equally against the "comprehension" axis then you get
let R = 25 # reading
let C = ? # comprehension
let M = 40 # reported mean
(R + C) / 2 == M
(25 + C) / 2 == 40
(25 + C) == 80
C == 55 # implied comprehension grade from a 40% average
If comprehension was any higher than 55% - which this anecdote certainly suggests - then the 40% aggregate score awarded is an ineffective assessment of the holistic learning picture.
This is the grade school equivalent of tossing out resumes over a single copy editing mistake.
