At Thursday's planning period meeting, we read and discussed Douglas Reeves's article,
The Case Against Zero. This can be a charged topic (as most education-related topics are), and a free discussion in a large group setting isn't conducive to gaining a nuanced understanding of how to best use grading scales.
Below I have summarized the options that we have available at Chalmette High School, along with some potential benefits and drawbacks.
District Grading Scale
The district grading scale is the one that most teachers are familiar with here.
- Input raw scores
- Computer averages scores and converts to percentages
- Percentages are converted to letter grades
- 100-93% A
- 92-85% B
- 84-75% C
- 74-67% D
- 66-0% F
Benefits
Ease of use. The district grading scale requires no conversion when entering grades. If a student scores 82/100 on a test, you can make the test worth 100 points and enter 82 in the gradebook. If a student scores 14/15 on a homework, you can make the homework worth 15 points and enter 14 in the gradebook. If you have a 100 point quiz that you want to make worth only half a test, don't bother dividing all your scores by two, just change the weight to 0.50 when you create the assignment and enter the raw scores.
High fidelity. There is typically a difference between a student who scores a 84 on a test and one who scores an 75. In a 100-point scale, that difference is accounted for. A student who gets an 84 followed by a 92 will have an average of 88, while a student who scores a 75 and then an 85 will have an average of 80. The first student will have a B average, while the second will have a C average - consistent with their performance. Under a 4-point scale these students would have the same score. You also have the opportunity to differentiate between students who have failing grades - a 65% F is very different from a 12% F, and those numbers can be informative.
Low/no grade inflation. This is related in some ways to the high fidelity of the 100-point scale. Having used both 100-point and 4-point scales, I find it is far more likely for me to look at a student under the 4-point scale and wonder, "How is this student getting such a high score?" than it is under the 100-point scale. Under the 100-point scale, typically every student who has a numerical A truly deserves it, and has demonstrated their understanding to an exceptional level (which is what an A is supposed to be, as I understand it).
Drawbacks
Difficult to recover from very low grades. This is especially true because we're on a nine week schedule for grades. There are relatively few grades put in over the course of nine weeks (as compared to, say, a whole semester), which means each grade has a higher weight than what we might have experienced as students under a semester schedule. If the course has, for example, 8 quizzes over the course of the first grading period, a student who misses the last one and doesn't have time to make it up before the grades go in can do no better than a B average (maximum of 87.5%), even if she has aced all seven previous quizzes. A solid 95% average on the first seven quizzes will drop down to an 83% C with one missing quiz. Similarly, a student who struggles at the beginning of the course and gets a couple of low F's, but works hard and improves to C averages might still keep an overall average below 67%. For example, grades of 35, 45, 55, 65, 75, 80, 85, and 90 on 8 quizzes would still leave the student with an average of 66% and an F.
Conversions from non-percentage grades. If you are, for example, an English teacher who is grading an essay on a rubric, it is likely that the percentage is not going to correspond properly with the grade. In those cases you have to make a decision about what number to enter for an A or a B. Do you choose the highest number (100 for an A, 92 for a B, etc.) or the middle number (96 for an A, 89 for a B, etc.)? Do you discriminate between "high" B's and "low" B's? If so, how do you convert it to a scale that doesn't have equal ranges for each grade?
Inequitable distribution of grades. The ranges for A-F respectively are 7.5%, 8%, 10%, 8%, 66.5% (the half percents are due to rounding). The range for C seems arbitrarily larger than the range for the other grades, except for F, which is wildly larger.
4-Point Scale
The four point scale:
- Input A, B, C, D or F
- Computer converts A to 4, B to 3, etc.
- Computer averages numbers
- Numbers are converted back to letter grades
- 4.0-3.5 A
- 3.4-2.5 B
- 2.4-1.5 C
- 1.5-1.0 D
- 0.9-0.0 F
Benefits
Ease of use. The 4-point scale is also a relatively easy scale to use. Most students want to know their letter grade for assignments anyway, and the calculation isn't difficult. Because there are only 5 possible inputs, putting in grades is quick, and you can easily change the weight of an assignment by changing the point value.
Zeros don't kill you. A zero on the 4-point scale does not significantly damage your chances of getting a good grade in a class. While a zero on the 100-point scale virtually guarantees that you can't get an A (7 100s and 1 zero = 87.5 B), a zero on the 4-point scale is recoverable (7 A's and 1 F = 3.5 A).
Drawbacks
Grade inflation. Under the 4-point scale, a student could potentially be missing half of her assignments and still pass the class if she averages a C on the other half of the assignments. As a math teacher, I cannot imagine that a student who knows only half of the material (and only at a C-level) in my class would be eligible to pass it and move on to the next class, since so much of high school math is sequential.
Lack of fidelity. See the paragraph on "High Fidelity" above.
Inequitable distribution of grades. The ranges for A-F respectively are 0.55, 1.00, 1.00, 0.50, 0.95. This distribution tends to make it more difficult for students to earn A's and D's.
Variations on Above Grading Scales
District Grading Scale
- Use a non-zero value as the minimum grade (50, 58, 59, or 60 are all reasonable choices). This knocks out two of the drawbacks (difficult to recover and inequitable distribution of grades), but can contribute to grade inflation.
- Use the first variation, but continue to mark 0 for missing assignments with the expectation that the student needs to complete the assignment (in other words, if a student gets a 24/100, mark it as a 60, but if she doesn't turn it in, mark it as a 0 until she does).
4-Point Scale
- Input numbers instead of letters. This allows high fidelity on the 4-point scale, but may require some tricky math if your grades are initially computed as percentages. To assist in this endeavor, I created an Excel spreadsheet that allows you to convert raw scores to numbers on the 4-point scale that correspond with the correct grade. If you would like more information about the scores are converted, look at the tab in the Excel file that says "Questions".
- I have seen the suggestion that the minimum score on the 4-point scale be a 1. Unless I'm mistaken, there would be no mathematical possibility of failure under this system. This is territory I would not yet be willing to venture into. I think it may be used in combination with an A, B, C, Incomplete type system that would require a district-wide change.
Other
- I'm unclear if we're allowed to use the old 10-point scale, but it is an option on eSchool. The 10-point scale has a more equitable distribution of grades than the district scale and makes it easier to get an A. 100-90 A, 89-80 B, 79-70 C, 69-60 D, 59-0 F.
- A variation on the 10-point scale would be to make F's only 59-50.
Conclusions
There are many options for grading that have different benefits and drawbacks. Personally, I have used the district grading scale for nearly all of my classes, and I wasn't crazy about the 4-point scale when I used it, but I think the high-fidelity 4-point scale that I mentioned in the variations might be a good option that I will try next semester.
I hope this has been useful to you. If you have any questions or comments please leave them below (you might be asked to create a Google account).
