Quantification of knowledge has a dubious history. Stephen Jay Gould’s book The Mismeasure of Man described the disturbing history of intelligence testing in the 20th century, the rocky science upon which it is based, and the on-going unjustified application of it in education and public policy. In this post, I consider the quantification of knowledge in classrooms.
I assume all readers are familiar with the 100-point scale that is so widely used in many schools. Even when grades are reported as letter grades, standards-based reports, or other scales, many classroom activities are reported as a percentage, which (of course) is a 100-point scale.
The assignments teachers give to students are the instruments we use to measure students’ learning. A fundamental assumption is that there is a positive association between what each student has learned and the evaluation of that student’s work by the teacher. There is much we could challenge about this assumption, but in this post, I focus on one specific aspect of assignments and the 100-point scale.
All instruments we use to measure have a degree of precision. The rulers we use in the United States are divided into ridiculously difficulty to differentiate fractions of inches compared to the relatively easy to use millimeters on metric rulers. Either way, we can use the marks to measure to the closest millimeter or 1/16th of an inch.
If we were given a collection of things to measure that were less than one inch long and an English ruler, we could put them into one of 16 bins. (Some of us would need a magnifying glass too.) More precise measurements require a different tool—one that is more precise.
All measurement is grounded in the assumption that the instrument is of reliable precision. If we have two objects that differ by less than 1/16” we will put them in one bin: The objects in the 2/16” bin are probably a little longer or a little shorter, but we cannot be sure because our instrument cannot tell the difference.
Consider now, the 100-point scale that is so commonly used in classrooms: By using it, teachers are suggesting their test or assignment would allow them to sort students into 100 bins. While we might be able to calculate the percent of points students earn on an assignment, it is difficult to conclude that we know confidently that a student who scores 90% really knows 1% more of the total than the student who scored 89%.
To make matters worse, many instructors record percentages to tenths. Rather than 90%, they might record 90.5%. In doing this, they are assuming the test can allow them to accurately sort their students into 1000 bins.
So, what is my point? Why do we care?
Grading causes consternation. Teachers exert energy and time defining grading schemes, evaluating assignments, and recording grades. When I started teaching, we also had to calculate them, but we have computer programs to do that work for us now. Students exert energy and time and emotions worrying about grades and in many cases gaming the system. Parents take grades seriously and seek explanation and justification of grades; they assume (inaccurately in many cases) that employers and colleges care about them.
When teachers report grades to a precision that is unjustified, they introduce much more data into the grade reporting, analysis, and interpretation than is needed. Arguing over tenths of percentages is time, energy, emotion, and cognition that is wasted. Teachers cannot really justify those differences as their instruments are not that precise.
We have only so much cognition we can use. That cognition used to process unjustified grading data is wasted. It cannot be used to build new knowledge. The conflict introduced by arguing over grades and the negative feeling introduced when unjustified grades cannot be challenged both interfere with positive relationships necessary for teaching and learning in classrooms.
I am not arguing that we stop grading. I am arguing teachers adopt grading that is justified and defendable and that contributes to students’ learning.