Stephen Downes’ introductory blog posting for the second week of the Critical Literacies Online Course ( CritLit2010 ) deals mainly with how we describe change, and in fact it would (with some minor edits) be the basis of a good motivational piece for the introduction to a calculus course.
This prompts me to make a suggestion that may well lead to howls of protest. Namely that not only should calculus remain as the mathematical topic through which all mathematics students must pass, but that it should in fact be considered as a Critical Literacy for everyone – without which no person can be considered to be properly, or even minimally, educated.
Certainly there are even mathematicians who would disagree. Many feel that various kinds of discrete mathematics are more appropriate to a digital age, others favour geometry and the study of symmetry as motivation for group theory and abstract algebra, and so on. All of these do have value, and it might well be argued that a survey of all areas of mathematics is also something that everyone should have some exposure to. But actually I believe that none of them is critical, and that while a global appreciation of mathematics is as important to a well-rounded education as an appreciation of literature or art, none of these is in fact a fundamental component of basic functional literacy. Calculus, on the other hand, is crucial.
To what? To having any capacity for understanding the questions, let alone the answers, to any of the key problems facing our survival as a species. All of these key problems have to do with rates of change – whether it is economic, environmental, or political.
Many who have struggled with calculus may think that it was just a bunch of abstract formulas and procedures that couldn’t possibly be useful, and in one part of this they are right. Memorizing the formulas and procedures is not useful. This has nothing to do with the fact that computers can now do that work for us, and in fact it has always been true. Anyone who understands how change works doesn’t actually need the “Product Rule”, and the same applies to almost everything else students think they need to memorize. Calculus is not these things and never has been. What it is is the language we need for describing the various kinds of change that Stephen is talking about – and for understanding the long term consequences of different kinds of change patterns.
Without a commonly understood language of change, political debate about things like energy supply and global warming is pointless. And that language is calculus.