Consider grading each problem on a test* on a scale from 0 to 4. Not with a point for each step like I normally do, but more as a rubric ranging from
0 "blank or irrelevant"
1 "did something legit, but far from solution"
2 "going in the right direction, but didn't make it to target"
3 "essentially correct"
4 "completely correct"
I like it because it could be a quick way to assess students' work. The rubric would be known to them. They would know how far off from a correct solution they were without me having to necessarily indicate their mistake or misconception.
I don't like it because the overall test grade cannot be the total number of points earned out of total possible points. This is because some problems are of higher difficulty than others. So consider classifying the level of difficulty of each problem. Could I then calculate a weighted average? But would I weight a novel extension sort of problem twice as heavily as a standard knowledge/procedure-based problem? Is that what I want the percentage to represent? The jury is still out, but the ideas have me thinking!
*This post is a reflection on the grading practices of my professor Dr. Bill Martin when he taught at an International Baccalaureate school in India for a semester.