More on Grading: Living with What We Have

In yesterday's posting, I explained why I am unhappy with our system of numerical grading. But I do have to live with this system. So I thought I would pose a few questions about how to use it as responsibly as possible.

1. I have noticed that different faculty convert between a 100-point (or percentage) grading scale to our 4.0 scale in different ways. Is this a problem? Students get upset: to receive a 93% in one class may earn them a 3.25; in another class a 3.5; in another class a 3.75; in another class perhaps even a 4.0. The defense I heard from a math professor is that it does not matter that different professors align their scales differently, because some professors make their exams so hard that a 93% does indicate a remarkable achievement warranting the top grade of our grading scale (4.0), while others align their expectations a bit differently.

2. My own solution is to avoid all conversions altogether. I grade everything on the 4.0 scale, and then just average these grades (using weighted averages as appropriate). Here's how to round to .25 intervals: you take the raw averaged grade, multiply by 4, round this number to the nearest whole number, and divide by 4. It's easy to make a spreadsheet that does all of this for you.

3. My system of grading yields this question: Which is more appropriate for grading within the course, before the final averaging and rounding: (a) use only the .25-interval grades, (b) use even finer gradations (e.g., .125-interval grades), or (c) use coarser intervals (.5-interval grades, or even just the whole number grades, since these are the only ones whose meanings are defined: excellent, good, satisfactory, low-pass, and fail)? Or does it not matter? (Mathematically, do the averages mean something different on these three different scenarios?)

I hope someone can answer question 3 with a convincing and mathematically well-grounded rationale.