Grades. Formative assessments. Summative assessments. Whatever we call these things, teachers have the responsibility to report the degree to which students have learned what they were supposed to learn.

While this seems a straight-forward aspect of the work, it is highly contentious, and different educators have very different perspectives on it. I have addressed this is other posts on this blog:

This post focuses on zeros and the question of just how are they to be handled? Typically, one argues that if a student does not hand in work it is recorded as a zero which can and does have significant mathematical effect on the student’s grade. This is an untenable position if we consider the following:

- In the typical classroom, tests and assignments are graded on a scale of 0-100. (This is a recent practice, but that is not important here.) Course grades, on the other hand, are reported as one of five letters: A, B, C, D, F. Ostensibly, teachers are claiming their tests and assignments can sort students into 100 bins and they can measure what students know to that level of detail. When it comes to the end of the course, however, we resort to sorting into five bins. It seems much of the problem of how to handle zeros would go away it educators adopted a consistent grading scheme. Rather than using one scale for assignments and another for course grades, use the same for both.
- Course grades are typically calculated as a mean: Add up all the scores, then divide by the number of scores. Means. Are one of several options for “finding the center” of data sets. We do know, however, that the mean can affected by extreme values. A couple of zeros can make a good grade appear worse and a millionaire can make a poor population appear wealthy. On both cases, the outliers result in the mean being a less accurate representation than other measures.
- If a student has lots of zeros, they probably have at some grades that are not zero. The result would be a multimodal distribution. Creating a histogram of the grades earned on assignments, we see a stack of zeros and a stack of other grades. Multimodal distributions are usually interpreted as “we measured something other than what we claimed.”

To those educators who insist that work not handed in should be counted as a zero on a 100-point scale I pose these questions:

- You are using different scales for assignments and for course grades. Can you explain the rationale?
- How different would your students course grades be if you used a different measure of central tendency? How do you know the one you use is the most accurate?
- For those students whose grades reflet multimodal distribution, what do your assignments measure?

I have had enough conversations about this with teachers to know that the dominant rationale given for averaging zeros is motivation. They reason, “if I don’t give zeros, then students won’t be motivated to hand in work.”

This “bad grades are a punishment” approach is grounded behaviorist psychology which has been found to accurately describe some types human learning, but not the types we seek to developed in schools.

The fact that students who have lots of zeros early in the school year or who get zeros in one class tend to have them later in the year or in other classes (I know this happens based on my observations during a 35-year career in education) suggests they are not the effective motivator advocates for averaging zeros claim. I’m not sure about others, but if I found:

- my grading scheme introduced inaccuracies (by changing scales)
- used the least reliable method of summarizing
- probably measured something other than learning
- was not motivating in the way I claimed

I like to think I would have abandoned it.