On Tue, Oct 23, 2012 at 9:57 AM, Linda Alvord <lindaalv...@verizon.net> wrote: > What I am trying to do is sort out a sequence for developing concepts in > mathematics education. A starting point is Easy J. Also. I favor explicit > definitions using 13 : as they clearly indicate the placement of arguments.
"Mathematics" covers a huge amount of ground. If I were in your position, I'd pick a vocabulary from J which was tailored to make the subject in question as easy to manipulate as possible. I'd not try to teach "all of J". When making this kind of choice, I would concern myself with the subject matter in related classes, even if I were teaching them. In general, treatments of mathematics feel free to introduce new notation out of the blue wherever it's convenient, so I would try to follow that tradition. But I would want my students focusing on the data and the concepts -- J would just be a convenient toolset for manipulating the data. That said, I would let J's structure influence my presentation. For example, if I needed sine and cosine, I would need to choose between a presentation that talks about even and odd functions (1&o.,: 2&o.) or a presentation that talks about complex exponentials (+.@^@j.) or a presentation which deals with taylor series (which could include either of the above, though I would have to be careful with the exponentials, or could build up the series in some other way). When I was learning APL, I saw it being used to introduce physics concepts (many), chemistry concepts (my rendering of electron orbitals of simple atoms got me co-authorship for some article in some obscure chemical journal back in I think '86 -- but I have long since forgotten all the details about that), biology concepts (mostly statistics), language concepts (mostly drills), and some electronic music (but APL on the computers back then could not implement a variety of interesting techniques, so that was not very satisfying). [All of this APL activity was mostly because of Vin Grannell's influence and support.] But what I observed back then was that each class's application domain usually used a small subset of APL -- typically 6-12 "words" plus the data. So I assume that something similar would hold true with J. So I'd probably work through the class material myself, and try to find ways of illustrating the concepts in J (leaving myself notes that I would come back to, later), and then once I'd gone through the materials I'd have a pretty good idea of where I would want to be in my presentation, so I'd go back to clean things up to place emphasis on the concepts rather than on J. -- Raul ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
