### Delicate topics: grades and their distribution have meaning

I have always argued that "qualified faculty implementing outlines based on student learning outcomes produce trustworthy grades." I know grades are not a form of direct learning assessment.

The statistics final, http://www.comfsm.fm/~dleeling/statistics/s53/farawayrainbow.html, is comprehensive with each major area of the course and its outcomes tested. This is a difficult final in a difficult course in a subject area that is arguably the most problematic for the students, mathematics.  I would argue that there is meaning in the distribution of scores for this final.

The final actual had a theoretically possible maximum of 48 points, but no one scored higher than 47. The lowest score was 14. The distribution above is not a "grade" distribution, just a distribution by raw scores. I would argue that the distribution means that the final, as difficult as it was, was achievable and attainable for the students.

The distribution of "grades" on the final, using the traditional 90%, 80%, etc., is as shown below:

This is a flatter or more uniform distribution than the overall raw score distribution, but again I would argue that the students are attaining and achieving. They are performing rather strongly on a difficult final in a difficult course.

I share this because I, like many others, often speak of the weaknesses and inabilities of our students. Yet 55 of them have tackled this final achieving a coursewide average of 73%.  No, this is not a student learning outcome, although I could, with a two thousand, six hundred and forty item analysis effort tell you exactly what each one can and cannot do against the outcomes on the outline.  If the average had not existed, statisticians would have invented it.  There is instant meaning in 73% with a 24% coefficient of variation that a 48 by 60 grid of "achieved/not achieved" will never convey.

Now that I wandered out onto the thin and unpopular ice of defending grades, I thought I might jump up and down until I fall into the icy water.  And again, I am not denigrating the need to assess learning outcomes.  I just do not want to throw out the baby with the bath water.  Having argued that grades are an inferential measure of learning, I intend to skate on the thinnest of all possible ice, and then maybe not come to work for a few years until the anger abates: grades as a very crude and dangerous inferential measure of my performance.

Before I am led to the slaughter of the evil people, remember that I fully believe that former chair Steve Blair was correct that as soon as grades are used to measure anything, slippery slopes develop that lead to artificial and unsupported grade inflation.  Want to improve the "promotion" rate?  Give away A's, B's, and C's.  Please, look at the material in statistics and the final before leveling this charge at me: this is a tough course with low rates of "promotion." The statistics final is no giveaway, nor is the course.