“forgottenbooks.com” as a Historical Teaching Resource

This week­ we looked at the idea of using games in order to teach mathematical concepts. It began with a round of “headbands”. Normally when this game is played, each player has a noun taped to their forehead and they play ’20 questions’ to try and figure out what it is. In this version, instead of a noun, we had a quadratic function. This was an interesting spin on the game. I don’t know how other people played, but for myself, I first figured out the form of the function (factored, vertex, expanded) and then guessed the parameters. I’m not sure how much could be learned from this game but it is certainly a good way to test your facility in mathematical vocabulary. For example, if I ask “is the function in vertex form”, does the student know that is actually saying “does the function look like f(x) = a(x-b)²+c”? We went from there to discuss different video games and apps that have been developed for the teaching of mathematics. I reserve a slight amount of skepticism with respect to how much can be absorbed passively from playing these games, but as a matter of practicing a concept, I imagine a student will get through many more practice problems if they are disguised as games (chocolate-covered broccoli, as Amy Lin put it). The side of technology that really intrigues me is its use as a virtual manipulative. For example, apps that allow for an intuitive visualization and manipulation of geometric figures would have a useful degree of flexibility that their tangible counterparts would not have.

Since we have a whole forum dedicated in this class to the discussion of different apps, I want to bring up a potentially useful but quite different type of resource.  There is an online PDF library called “Forgotten Books” which contains literally hundreds of thousands of rare historical books on every subject imaginable, from Renaissance literature to essays on witchcraft. Membership can be free or purchased (about $8 a month). The free membership gives unlimited access to all of the books, but every couple of pages the image will be blocked. The paid membership removes the barrier. I bring up this site because it contains many historical works on mathematics as well as math pedagogy. These books present a very interesting perspective and explain concepts in a way that may be unexpected and possibly useful to a teacher. They also make reference to different manipulatives that could be of interest to the modern reader. These are often simple, and could be made by hand without much difficulty. They would also make good projects for someone who would like to try 3D printing. These books can also serve as sources of interesting and instructive word problems as well as ideas for simple yet effective demonstrations of mathematical concepts.

Another use for this library is as a source for historical perspectives on mathematics and pedagogy. These books being so old (+100 years), I find this perspective very refreshing. At the same time, it is very interesting to read a textbook from more than a century ago and see that many of the concepts we credit to modern enlightenment such as “student-centered learning” (and even differentiated instruction, to a degree), were practices treated as merely common sense. In fact, the more I read these books, the more I feel that the derision “traditional” education faces these days is built on a straw man, but I digress. One part of the library I would particularly like to explore are the books on Jesuit education and their pedagogical philosophy. This is not something I know much about, but the historical importance of the Jesuits on the scientific revolution was first impressed upon me when I read Rene Descartes’ biography, Cogito Ergo Sum. In addition to training many of history’s most important mathematicians and physicists (including Descartes), they also educated Marin Mersenne, a French priest who single-handedly organized and maintained correspondence and collaboration between nearly 140 different mathematicians, philosophers, and scientists from all across Europe (a thankless task whose historical importance could not be understated). In conclusion, Forgotten Books is a very fun site to explore. The sheer variety of books available is such that you never know what you will find when you browse, but you will always find something worth reading.