At the beginning of the course, for practice students complete a couple of stand-alone explications of documents provided by me. Then, once they begin work on their papers, similar but different explicated documents that they discover become the core of those papers. In concentrating on explication, I am tapping into our mathematics students’ aptitude and interest in precise, technical work, the nuts-and-bolts of mathematical tasks. As well, I am tapping into their problem-solving inclinations and imagination in the form of detective work to discover what the author wrote. I tell them they have both the advantage and disadvantage of hundreds and in some cases thousands of years of mathematical progress and training in their background beyond that of the author they are reading. The advantage is that they can often “see through” what the arguments are leading to, as they jot notes in the margins using modern symbolism and graphs, and so on. The disadvantage is that by engaging that modern perspective they entirely miss the cultural context of the time, and in fact fail to “see” what the writer has written. Their modern understanding eclipses their attention to the details of what is on the page. We work on stripping back their “overview” to discern what is said and what is not said, what is assumed in that time period and what is anachronistic and ahistorical.
Explications must be “just in time.” It is annoying and loses the reader’s attention to read a long passage which makes little sense to them, only to be followed by a long explication. Such an explication is too late, and often hard to precisely align with the points in the passage where it is meant to apply. It also tempts the reader to ignore the original passage and just read the explication, which denies them the true understanding of the context as well as the substance of the arguments. I will tell students “The author is the focus, not you. With the assistance of your gentle guidance, your light touch, we want to be able to read the author’s work without pause.” I share with my students what the Oxford English Dictionary writes:
Explicate, verb:
To explicate is to cleverly, subtly answer questions before they are asked, so the reader, when he or she raises these questions, realizes the answer has already been handily provided. Thus, apprehension of the material and moments of clarity arrive more quickly because the reader’s intellectual struggle has been diminished by the explicator's apt remarks. An explication is not provided in order to train readers; it is instead to ease their path to understanding what the author wrote. Examples of helpful insertions include:
In the beginning, students are not sensitive to where these additions may be needed. For instance, they often include long explanations of parts well-written by the author (as an unconscious act, I think, to prove to themselves that they understand), and neglect spots of confusion that they “saw through” but which desperately require explanation. My job is to generously red ink their early attempts and point out where there is real need for explanatory assistance. I remind them, “It is harder to be clear than you think!”
Here’s the sheet of advice I give my students for those short practice explications in advance of and separate from writing their papers, although of course the advice is universally useful. As I mentioned above, papers will then center on similar explications, but not consist solely of them. Note that their first task is to accurately type up the original source document, which seems easy, but often reveals a novice inattention to details like unusual or archaic spelling and capitalizations, grammatical oddities, and so on. This too turns out to be good practice for them.
Historical “Proof” Explication
When you read my Explications (and when you review your own)