I didn't always think this way. When I was a new teacher, I graded the way I thought I should... which was probably the way that I was graded as a student. Each question was assigned a certain number of points and I subtracted points based on mistakes. Eventually I started to think about grading as adding points for correct work instead of subtracting points for incorrect work, but I was still pretty discontented. Suppose that I had two equations on a test that were worth different points, say 3 points and 5 points. I usually counted an arithmetic mistake as 1 point. Then, the same arithmetic mistake in each problem was worth a different amount for each question... ~33% versus 20%. Was an arithmetic mistake really worth 33% of the first problem?
What really brought my thinking to a head was when I was helping a student that I had taught in 9th and 11th grades with his senior year math class. I knew from my experience that he struggled with entering computations in his calculator correctly, but you could tell that he had a pretty good grasp of concepts even if his arithmetic was bad. On one test there were about five questions that looked something like, "if f(x) = 2x + 1, find f(3)". He set up every problem correctly, then plugged them into his calculator wrong. The teacher had assigned each question two points and took off one point for his arithmetic mistakes. I thought to myself, "This is crazy! Does this kid really only know 50% of each problem?" Obviously not.
After some serious searching, I stumbled upon Standards-Based Grading... probably from Shawn Cornally. I thought this would solve all of my problems! A rubric for each question! Topics scored instead of arbitrary textbook sections/chapters! This would be perfect! I could really get a picture of what kids know. I would be able to communicate qualitatively with parents and students about strong and weak areas, not about good and bad grades. SBG & Rubrics would be my saving grace!
Whenever I explain what SBG is to a teacher/parent/student they mostly think it's a good idea. There are a few exceptions. I've been fairly successful at implementing an SBG system in my AB and BC Calculus courses. The other courses I teach? Not so much.
Coming next time: Why I had to (mostly) abandon SBG...