Mathematically accurate grading

Intent

Remove the inaccuracies inherent in traditional numerical grading, with its 100-point scale and averaging, so that a final grade is more reflective of student learning and achievement.

Problem

Traditional grading schemes use 0-100 scales for assignment grades. Assignment grades are typically averaged to arrive at a final grade, and the numerical average is further mapped onto a 5-letter scale (A-F). Grades of 0 indicate both a failure to hand in an assignment and a lack of success on an assignment.

There are multiple problems with this method of assessing student learning:

1. The 0-100 scale is too fine-grained, which leads to statistical error and high variance. E.g. it is nearly impossible to meaningfully distinguish between work that earns 78 points and work that earns 79 points. This means that the 0-100 scale fails to meaningfully communicate the amount of student learning.

2. The A-F scale weights failure way more heavily than success. The F scale typically ranges from 0-59 points, while the B through A range (“success”) only comprises 80-100 points.

3. Low scores disproportionally drive down averages, which means it is nearly impossible to recover from a low score when scores are averaged together.

4. Averaging all scores a student earned over time hides the trajectory of that student’s progress, penalizing student for taking time to reach proficiency and, in some cases, obscuring the fact that a student reached proficiency by the end of the course.

Solution

To make grades more mathematically accurate, and more reflective of student learning, we can do the following:

1. Use a different indicator for missing work. Reserve scores of 0 for instances where the student completed an assessment but did not answer any items on that assessment correctly. Use a different score – incomplete, for instance – to indicate that an assessment has not been completed. Alternately, you could choose not to enter any score until a student completes an assessment.

2. Use a smaller grading scale. Instead of using the 0-100 scale, use a 0-4 scale, with higher scores indicating higher levels of proficiency. Such coarse scales are cognitively easier for people to grasp. Averaging of scores, should one choose to do so, is more accurately reflective of student learning: low scores don’t “tank” a student’s score as with larger scales. The 0-4 scale weighs success more heavily than failure, which is more motivating to students.

3. Establish a minimum grade. If you can’t use a smaller grading scale, you can still reduce the size of the “failure range” by setting a minimum “failing” grade, e.g. 50. This makes it possible for students to recover from occasional low grades, and does away with the nonsensical idea of different “degrees” of failure.

4. Weight recent experience more heavily. In many cases, it is sufficient for students to achieve proficiency (or higher) by the end of the term, regardless of the particular path a student took to get there. For instance, students with less preparation or fewer resources may need more time and more revisions to achieve proficiency, than those with better preparation and more resources. Weighting final grades more heavily towards the most recent assessments more accurately reflects student learning – if a student performs at the proficient level by the end of the course, their final grade should reflect this. This also promotes a growth mindset in students (and instructors!).

Applicability

This play is very flexible, and can be used in many different contexts. It works with traditional grading schemes, as well as many alternative grading schemes (specifications grading, standards-based grading, etc.).

How to Implement

Instructors who use course management systems may find it challenging to implement some aspects of mathematically-accurate grading. Many course management systems are designed with the assumption that traditional, 0-100, A-F scales will be used, and that scores will be averaged together to calculate final grades. Thus, instructors may need some creativity to realize some aspects of this play.

Many course management systems allow instructors to define their own scales, and/or provide scales other than the 0-100 scale. Some systems convert these to percentages, anyway, which might unsettle students (e.g., a score of “proficient” might appear as 75%, even though it indicates success). In these cases, instructors may need to remind students to ignore the calculated scores.

Some instructors provide students with individual grade sheets, allowing students to self-track their grades. These sheets can be as simple as a paper spreadsheet, or as complex as a fill-in spreadsheet that automatically calculates a student’s grade when new scores are entered. This strategy gets around the limitations of course management systems, and allows students to have a clearer idea of their progress in the course. The downside is that it relies on students to keep track of their grades, something not all students may want to do (or have the executive functioning to be able to consistently do).

See Also

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Source

Source: Feldman, J. (2023). Grading for equity: What it is, why it matters, and how it can transform schools and classrooms. Corwin Press.

Described by: Amy Csizmar Dalal (adalal@carleton.edu)

References

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Community Discussion

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