Why don't you take the session you showed a couple of messages back and try to turn it into a lab? Show the student each step, suggest things he might try before going to the next step. Maybe stay away from tacit for a while.
On Sun, Mar 15, 2009 at 2:11 PM, Don Watson <[email protected]> wrote: > Thanks, > > I'll digest > > Don > > ----- Original Message ----- > From: "R.E. Boss" <[email protected]> > To: "'General forum'" <[email protected]> > Sent: Sunday, March 15, 2009 3:58 PM > Subject: Re: [Jgeneral] Teaching > > > > Your > > > > +/(x^i.r+1)*(1,*/(k>:/k+1)+(k<:/k)*n-k=.i.r)%!i. r + 1 > > > > is equal to > > > > x ((^...@{:) +/@:* (!~i.)/@]) n,r > > > > > > 0.5((^...@{:) +/@:*(!~i.)/@])5 6 > > 7.59375 > > 0.5((^...@{:) +/@:*(!~i.)/@])3.3 20 > > 3.8115459 > > 0.9((^...@{:) +/@:*(!~i.)/@])7.21 20 > > 102.28536 > > > > > > R.E. Boss > > > > > > -----Oorspronkelijk bericht----- > > Van: [email protected] [mailto:[email protected] > ] > > Namens Don Watson > > Verzonden: zondag 15 maart 2009 19:06 > > Aan: General forum > > Onderwerp: [Jgeneral] Teaching > > > > BlankThank you all for very helpful responses to my last email. > > > > I will respond first to this comment from Matthew: "I think the idea > > of > > > > introducing graphical characters into J is a bad one and that energy > > towards > > > > getting new users into J would be better spent elsewhere like writing > > Labs." > > > > I repeat that I am not trying to get new users into J - I am trying to > > teach > > > > Mathematics and need an experiential tool that has the ease of > > communication, the independence from operating systems, the free cost to > > education and the well supported, thoroughly professional and reliable > > nature of the J system. It's got almost everything I want, including > tacit > > programming - all I am looking for is how can it become exactly what I > > need > > rather than exactly what the J community needs in a manner that is > > transparent to the J community. > > > > Matthew also says: "I personally like the ascii method, despite it > > deceptively appearing as an ugly mess when first encountered, because > once > > you get used to it it is beautiful. The important questions to me are: > > "How > > long does it take to get used to it and learn the beauty of J?" and: "Are > > average elementary students, secondary students and (say) Post-secondary > > Geography students capable of reaching this level of J understanding in > > the > > limited time that can be delegated to this task within their regular > > curriculum?" > > > > To a comment from Raul: "The first example in your table became " " > > when > > > > I try copying and pasting it into this message. This means you have not > > even > > > > begun to tackle the hard problem of figuring out how this kind of thing > > could even be possible." I copy something I said in a previous email: "In > > my > > > > proposal, keying is done in identical ASCII, storage is done in identical > > ASCII, transmission between systems is done in identical ASCII, mailing > is > > done in identical ASCII and every user of J continues using ASCII in > > exactly > > > > the same way without knowing that anything has happened. The change is > > transparent and causes none of the difficulties that are being > discussed." > > Thus the first example in the table would be stored and translated in > > exactly the same way as it always has. The only change is in output to > the > > screen and the printer, when the two ASCII characters would be translated > > to > > > > a special character. > > > > Fraser says: "If your H1[F(x),G(x)] is mean to represent an > > expression > > > > in J I do not know whether you mean H1(F(x),G(x)) where H1 is a monadic > > fucntion with argument (F,G)x or using H1 dyadically (F H1 G) x" > > Actually I did not mean H1[F(x),G(x)] and [ H2 (F, G) ] (x) to be J > > expressions, but, sort of, Mathematical expressions. All I am saying is > > that > > > > mathematically the % in (+/%#) is not the same kind of function as the % > > in > > 3 % 7. The H2(F,G) has, in J language, verbs as its arguments, rather > than > > nouns. > > > > In response to Bjorn, I am not currently a member of the J-Programming > > forum. I will join and look up what you suggest. > > > > I response to Bill, I promise to read Programming in J. > > > > In response to Don, I know that I can achieve what I want by a > > "program" > > > > with successive lines of code - but I want to be able to show one line > > that > > parallels the mathematical formula. How I do this at present is by copy > > and > > paste - which is something we couldn't do on the old IBM 2741 paper > > printing > > > > terminals!! I am going to give an example of a session to illustrate the > > binomial theorem for (1 + x) ^ n. It is normal to prove theoretically > that > > it works for natural number values of n in pre-calculus, but calculation > > using J can show that it works for any rational n if the series > converges. > > What follows is a demonstration, using copy and paste, to develop the J > > sentence to do it. What I would like to know is, can someone work through > > a > > similar gradual process that is easy for a student to follow and ends up > > with tacit programming instead of a J sentence? If someone can do that, > > you > > might change my opinion. > > > > x=. 0.5 NB. For (1 + x )^n > > n=. 5 > > r=. 6 NB. Take terms up to x^6 > > i.r > > 0 1 2 3 4 5 > > n- k =. i.r > > 5 4 3 2 1 0 > > k<:/k =. i.r > > 1 1 1 1 1 1 > > 0 1 1 1 1 1 > > 0 0 1 1 1 1 > > 0 0 0 1 1 1 > > 0 0 0 0 1 1 > > 0 0 0 0 0 1 > > (k<:/k)*n-k=:i.r > > 5 5 5 5 5 5 > > 0 4 4 4 4 4 > > 0 0 3 3 3 3 > > 0 0 0 2 2 2 > > 0 0 0 0 1 1 > > 0 0 0 0 0 0 > > k>:/k+1 > > 0 0 0 0 0 0 > > 1 0 0 0 0 0 > > 1 1 0 0 0 0 > > 1 1 1 0 0 0 > > 1 1 1 1 0 0 > > 1 1 1 1 1 0 > > (k>:/k+1)+(k<:/k)*n-k=:i.r > > 5 5 5 5 5 5 > > 1 4 4 4 4 4 > > 1 1 3 3 3 3 > > 1 1 1 2 2 2 > > 1 1 1 1 1 1 > > 1 1 1 1 1 0 > > */(k>:/k+1)+(k<:/k)*n-k=:i.r > > 5 20 60 120 120 0 > > 1,*/(k>:/k+1)+(k<:/k)*n-k=:i.r > > 1 5 20 60 120 120 0 > > i. r + 1 > > 0 1 2 3 4 5 6 > > !i.r + 1 > > 1 1 2 6 24 120 720 > > (1,*/(k>:/k+1)+(k<:/k)*n-k=:i.r)%!i.r + 1 > > 1 5 10 10 5 1 0 NB. Same result as Pascal's triangle > > x^i.r+1 > > 1 0.5 0.25 0.125 0.0625 0.03125 0.015625 > > (x^i.r+1)*(1,*/(k>:/k+1)+(k<:/k)*n-k=.i.r)%!i. r + 1 > > 1 2.5 2.5 1.25 0.3125 0.03125 0 > > +/(x^i.r+1)*(1,*/(k>:/k+1)+(k<:/k)*n-k=.i.r)%!i. r + 1 > > 7.59375 > > 1.5^5 NB. Test if it gets the right result > > 7.59375 > > r=. 20 > > n=. 3.3 > > x=. .5 > > +/(x^i.r+1)*(1,*/(k>:/k+1)+(k<:/k)*n-k=.i.r)%!i. r + 1 > > 3.81155 > > 1.5^3.3 > > 3.81155 > > > > x=.0.9 > > n=.7.21 > > +/(x^i.r+1)*(1,*/(k>:/k+1)+(k<:/k)*n-k=.i.r)%!i. r + 1 > > 102.285 > > 1.9^7.21 > > 102.285 > > > > > > > > > > > > > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
