Part IV of the Zero Saga
If I had been a better math student, I could much earlier have articulated this argument against the use of zero to represent late or missing school work in the mean (or any other) average.
DansMath.com helped me clarify my thinking so I could progress from using the nearly useless phrase, “apples and oranges,” to “unlike terms.”
Earlier I mentioned a post on the Teacher Magazine blog that includes some comments that I think are demeaning to the intelligence of teaching professionals. In other words, the support of, and even highlighting, the use of zeros by teachers.
If teachers really understand basic math, it confounds me that they can put zeros in place of missing assessments and then run a mean average on the whole collection of numbers.
First, a number that represents the value of a missing assessment, i.e., zero, has no business in a collection of numbers that represents actual assessment evaluations. The zeros and the grades are “unlike terms” (you learn about this in pre-algebra, so I’d expect that teaching professionals, with college degrees, would know this) and cannot be added together! (The zeros represent work not done, and the grades represent evaluations of student output.) If you can’t add them up legitimately, how can you divide the false sum by the total number of assignments both completed and uncompleted and expect to come up with a number that represents what the student knows about the course goals?
Second, introducing zeros to a collection of assessment evaluation numbers (grades) violates the concept of the mean as a measure of central tendency. By introducing “outliers,” even if they were “like terms,” the mean is corrupted and does not represent a measure of central tendency, or in other words, a number that reflects the main body of the student’s assessment scores.
For more details, refer to a post I made sometime ago on statistical integrity.
Rationalizing about the “real world,” “teaching responsibility,” and other overt attempts at student manipulation won’t make the facts go away. Placing zeros that refer to missing work in collections of evaluative data is invalid, illogical, and frankly, unethical.
Shift emphasis from attempted (but largely failed) control of student output to evaluation of student achievement relative to district course goals and the picture becomes clearer. In other words, switch from noting “work completed,” to evaluating and noting the achievement of learning goals.
Does that make too much sense?