How do you convert from standard-based grades (often on a 1-4 or 1-5 system) into a percent score required by a gradebook or school district, while still maintaining a sense of what the 1/2/3/4(/5) system means?
While the formulas involved may be too complicated for a gradebook, I approached this problem mathematically: can I create a map from the SBG 1-4 system to the grades I believe they should represent? My understanding of the SBG system is as follows, which informed my selected points and function choice:
- 4 = exceeds standard; demonstrates complete mastery and conceptual understanding with no nontrivial errors
- 3 = meets standard; demonstrates mastery of a skill/topic, perhaps with minor errors
- 2 = approaching standard; shows some understanding, with major (or many minor) errors
- 1 = below standard; shows little or no understanding
- 0 = did not attempt
In my conversation with @druinok, she stated (and I concur) that a student with all 3s has met all standards and should receive a B+/A-. All 4s should clearly represent 100%. In my opinion, all 2s should be enough to scrape by with barely passing the class (60% or D); some may argue that since that student has not shown mastery of the standards he or she should receive a failing grade. A student with a 2.5 average (half twos and half threes, e.g.) should receive a C. A student with 1s should not pass. In my district, the lowest grade we can assign on a report card is a 50, so a 1 average yields this.
In playing around with the numbers, they seemed to fit naturally into a symmetric pattern around 2.5 = 75%. This in turn prompted me to find differences and look for a cubic equation with inflection point around (2.5, 75).
- 1 average = 50%
- 2 average = 60%
- 2.5 average = 75%
- 3 average = 90%
- 4 average = 100%
I also tried a third attempt with different points (3=85% & 2=65%) since I was slightly unhappy that the above function from my second attempt was not monotonically increasing on the interval [1,4]. Still, my second attempt is closer to my understanding of the 4-point scale.
For what it’s worth, I also tried fitting a 5-point scale to percentages.
Anyway, that was a bit of fun. But the formulas aren’t perfect, and are certainly a bit complex for gradebooks (the original challenge).
So my main point in writing this post was to ask: those of you who are standards-based grading aficionados, how do you handle the conversion to a percent or letter score?
Certainly any solution, whether it be a formula like this or a more holistic approach like “a student must meet all standards with a 3 or higher to achieve a grade of A, etc”, must involve clear and open communication about the grading policy with students & families.