Professional Judgement over Math

Well, after a week off of blogging to go present at InstructureCarn in beautiful Keystone, Colorado, I’m back at it.  I did get a pretty wonderful flat tire on the way home from the conference that tested my tire changing in 100+ degree heat skills.  I passed the test, and we made it home.

Over the last several days on Twitter and during my standards based grading presentation at InstructureCarn, I have been asked many times about how I aggregate standards scores into a current or final score.  For instance, if I have a student who has seven scores for standard 1–say: 1, 1, 2, 3, 3, 3, 4–how do I combine those into a single score for final grading or progress reports?

First, let me say that most student achievement scores aren’t nice and linear like the example above, so that complicates the matter a lot.  Second, there are lots of thoughts on how best to do this, so I want to break a few of them down first.

Common Thoughts on Aggregating Scores

  • Average: While this has been the standard in education (and in many other areas) for a long time, it has long outlived its usefulness and should be avoided.  Averages dilute the data and give no meaningful information to us as teachers.  The average of the scores above is 2.4, which would mean the student has not quite met proficiency with this standard, which I think is demonstrably false, considering that the last four scores are proficient or better.  I don’t feel confident as a professional with 2.4 as the final score for this student.
  • Decaying Average: This is the default method of the Canvas Learning Mastery Gradebook that comes preloaded in Canvas.  This method weighs the most recent score at a higher percentage than the older scores.  The default in Canvas is 65/35, although it can be set anyway that the teacher wants.  Using the default, the student above would have a final score of 3.35 or so, which is proficient, and I feel is more representative of where the student actually is as far as achievement.  However, one of the beautiful parts of standards based grading is simplicity. describing achievement levels from 1-4 is much less complicated than 1-100.  Using a decaying average muddies these waters a little bit by introducing decimals.
  • Most Recent: This method is espoused by many standards based grading practitioners and experts.  It posits that the most recent score is the closest representation of where a student actually is.  In our above example, the student would have a final score of 4, which I am also comfortable with for this student; however, as his teacher, I might want to see a couple more assessments where he scored 4 to be completely comfortable with this rating.  While I think that there is value in this method, I also have a little trepidation adopting it because of the variance of single assessments.  As I said above, student scores are rarely linear like our fictitious student we are talking about, and assessments are rarely 100% perfect as measures.  In order to feel completely comfortable with this method, I would have to be very comfortable with every assessment that I give.  I’m close to that level of comfort, but assessment is a difficult business to be sure about.
  • Mode: This is the default method of the 3D Gradebook. It takes the most frequently occurring score and makes it the current proficiency level score.  The theory behind it is that in order for a student to clearly demonstrate mastery, they need to do it consistently.  I tend to agree with this.  In our example above, the student would have a final score of 3.  As a professional, I’m probably okay with that score.  The student has obviously shown proficiency and is on his way to the advanced level.  He is obviously between a 3 and a 4 on the scale, so anywhere on that scale is going to be fairly accurate.  What I would do with this student is offer him the opportunity to retake one or two of the assessments that he earned threes on and see if he has taken the jump.  It would give him the opportunity to show that he has moved up a level by showing evidence of that learning on multiple measures.

Hiding Behind the Math

In his article “It’s Time to Stop Averaging Grades,” Rick Wormeli brings up an interesting point about the need for professional judgement in making final determinations about grades, not just a good math formula.  He tells a story of a student who came to him with a 93.4% score and asked about the possibility of being rounded up to 94%, the difference between an A- and an A.  Wormeli told the student that he couldn’t round up because that’s not how the math worked; if anything, he would have to round down.  He goes on to say,

I was hiding behind one-tenth of a percentage point. I should have interviewed the student intensely about what he had learned that grading period and made an executive decision about his grade based on the evidence of learning he presented in that moment. The math felt so safe, however, and I was weak. It wasn’t one of my prouder moments.

I think in the end, no matter what our “system” is for calculating grades and final proficiency levels, we need to remember Wormeli’s lesson from his anecdote.  It’s not the math that knows our students.  It’s not the math that understands their strengths and weaknesses, their proficiency levels, and their highs and lows.  It’s the teacher.  And, as teachers, it is our professional responsibility to assign grades and levels of mastery that we can justify as professionals as being representative of what our students know and can do.  No formula can do that 100% accurately all the time, so no matter which of the above systems we decide to use, we need to embrace our role as professionals and understand that the math doesn’t determine grades and final proficiency scores, we do.

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