On Continuous Variation

My afternoon walks have been spent listening to some audio books… Richard Dawkins’ The Ancestor’s Tale has been my most recent selection. Listening to Dawkins describe the confusion that can happen when we expect continuous variation to be discontinuous, I heard much that was familiar and much that explains some of our difficulties in education for the last few decades.

Dawkins uses several familiar examples to illustrate continuous variation; the heating of water is perhaps the clearest. On heat, “cold” water becomes “hot,” but we can’t really identify exactly when the change happens. We can use a thermometer to quantify the variation in temperature, and we can define a temperature at which water becomes “hot,” but there may not be agreement among all that the water is indeed hot. (In many cases, out assessment depends on our purpose for heating the water.)

Much that we care about when teaching varies. Students’ abilities to read, write, calculate, etc. changes. While we like to claim students “learned” a specific skill in class, honest educators will admit, they cannot be sure there is any moment when one “learns” anything. Further, if we look at a group of students, the degree to which they have learned anything we have taught varies as well. The variation arises from the fact that students may be able to demonstrate the characteristics of one who has learned on one day or on one problem, buy not another. While there may be a general trend towards being knowledgeable, while on the way to becoming knowledgeable, learners appear to regress as much as they progress.

The trouble starts for educators when they begin defining learning in a discontinuous manner. We get caught up in defining “A” work (and students capable of producing it) from “B” work, and books by grade level and work as either “meeting the standard” or not.

For some purposes, for example deciding when one it an adult, human cultures must define discontinuous quantities, but those are arbitrary. (When I was young, the legal age to drink alcohol was 18 where I lived, it has since increased to 21, with a specific rationale given, but the reality is that each was arbitrary.)

Because education is a public service, it is unlikely that we will ever be free of the need to use discontinuous and arbitrary categories to document what we do. I do hope educators stop agreeing to focus on measuring it so often. The resources we spend deciding which label to apply to learners is wasteful and we are being disingenuous when we claim they are somehow objective.