About teaching, a standard university curve is 10 20 40 20 10 percent for grades of A B C D F. When I was teaching math, I addressed mostly the middle 40 per cent, but I made sure to include some material aimed at the top 30 per cent, and some aimed at the top 10 per cent.
--Kip Murray Sent from my iPad > On Feb 21, 2014, at 9:26 AM, Raul Miller <[email protected]> wrote: > > Why can't it be both a table and "just a bunch of lines"? > > I know that when you are teaching a large set of students you need to > address the intersection of their abilities. And I understand that once we > set up ways of thinking for ourselves we tend to like following those > patterns in other contexts. But we also tend to like discovery and learning > new things and if we adhere *too* strictly to our old habits we miss some > of the joys of discovery. > > That said, these questions are not actual programming and I do not know if > you are subscribed to the chat forum, so I am going to Cc you directly. I > also decided to clean up the subject line, since I am not sure I like the > way the mail forum software handles these things. > > Thanks, > > -- > Raul > > > > On Fri, Feb 21, 2014 at 2:35 AM, Linda Alvord <[email protected]>wrote: > >> I wondered if this really was a table or just a bunch of lines, but it >> really is a table. >> >> ]M=:(h"0) 1+i.7 >> 1 0 0 0 0 0 0 >> 1 2 0 0 0 0 0 >> 1 2 1.5 0 0 0 0 >> 1 2 1.5 1.66667 0 0 0 >> 1 2 1.5 1.66667 1.6 0 0 >> 1 2 1.5 1.66667 1.6 1.625 0 >> 1 2 1.5 1.66667 1.6 1.625 1.61538 >> $M >> 7 7 >> >> Linda >> >> -----Original Message----- >> From: [email protected] >> [mailto:[email protected]] On Behalf Of Linda >> Alvord >> Sent: Friday, February 21, 2014 1:55 AM >> To: [email protected] >> Subject: Re: [Jprogramming] What does this do? >> >> The tables show what is happening quite nicely. >> >> >> >> g=: 13 :'(+%)/\ y $ 1x' >> >> (g"0) 1+i.7 >> 1 0 0 0 0 0 0 >> 1 2 0 0 0 0 0 >> 1 2 3r2 0 0 0 0 >> 1 2 3r2 5r3 0 0 0 >> 1 2 3r2 5r3 8r5 0 0 >> 1 2 3r2 5r3 8r5 13r8 0 >> 1 2 3r2 5r3 8r5 13r8 21r13 >> >> h=: 13 :'(+%)/\ y $ 1' >> >> (h"0) 1+i.7 >> 1 0 0 0 0 0 0 >> 1 2 0 0 0 0 0 >> 1 2 1.5 0 0 0 0 >> 1 2 1.5 1.66667 0 0 0 >> 1 2 1.5 1.66667 1.6 0 0 >> 1 2 1.5 1.66667 1.6 1.625 0 >> 1 2 1.5 1.66667 1.6 1.625 1.61538 >> >> Linda >> >> >> -----Original Message----- >> From: [email protected] >> [mailto:[email protected]] On Behalf Of Linda >> Alvord >> Sent: Friday, February 21, 2014 1:01 AM >> To: [email protected] >> Subject: Re: [Jprogramming] What does this do? >> >> WOW! >> >> This is quite impressive! >> >> {|.(+%)/\100$1x >> 573147844013817084101r354224848179261915075 >> >> 0{|.(+%)/\200$1x >> >> 453973694165307953197296969697410619233826r280571172992510140037611932413038 >> 677189525 >> >> >> Linda >> >> -----Original Message----- >> From: [email protected] >> [mailto:[email protected]] On Behalf Of Roger Hui >> Sent: Thursday, February 20, 2014 10:07 PM >> To: Programming forum >> Subject: Re: [Jprogramming] What does this do? >> >> If you want just the n-th term, you can do as follows, (+%)/ instead of >> (+%)/\ >> >> % 1 +. (+%)/ 100$1x >> 354224848179261915075 >> >> >> >> On Thu, Feb 20, 2014 at 6:48 PM, Linda Alvord >> <[email protected]>wrote: >> >>> It allows you to find the 100th term in a Fibonacci series. >>> >>> 0}|.% 1 +. (+%)/\ 100 $ 1x >>> 354224848179261915075 >>> >>> Linda >>> >>> -----Original Message----- >>> From: [email protected] >>> [mailto:[email protected]] On Behalf Of Roger Hui >>> Sent: Thursday, February 20, 2014 5:14 PM >>> To: Programming forum >>> Subject: Re: [Jprogramming] What does this do? >>> >>> See also http://www.jsoftware.com/jwiki/Essays/Fibonacci%20Sequence >>> >>> It is another way to the "Why J?" (or "Why APL?") question. Because it >>> allows, encourages, assists, ... you to think of 10 different ways of >>> generating the Fibonacci numbers and other similar questions. Several >>> factors come into play in such thinking. See section 1 of Ken Iversons' >>> Turing lecture <http://www.jsoftware.com/papers/tot.htm>. Do you get >> the >>> same with another language? >>> >>> More direct answers to the questions you posed: >>> >>> - It's known both in conventional mathematics and in APL that the >>> continued fraction (+%)/n$1 has the golden ratio phi as the limit. >>> - Therefore, (+%)/\n$1 are convergents to phi. >>> - It's known but perhaps less so that (+%)/\n$1x provides rational >>> approximations to phi. >>> - It is known (?) that these rational approximations to phi are of the >>> form x%y where x and y are successive Fibonacci numbers. If you >> didn't >>> know it and you stare at the result of (+%)/\n$1x, the answer comes >>> pretty >>> quickly. >>> - It is known that 1+.r is the reciprocal of the denominator of the >>> rational number (I learned it in my I.P. Sharp days circa 1980). >>> >>> Hope this helps. I am not sure exactly what is "that way" of thinking >> that >>> you refer to. (Array thinking? Mathematical thinking? Sideways >>> thinking?) >>> >>> >>> >>> >>> On Thu, Feb 20, 2014 at 1:27 PM, Peter B. Kessler < >>> [email protected]> wrote: >>> >>>> A more interesting question is: Why did you think of doing it that way? >>>> The really interesting question is: How can I learn to think that way? >>>> >>>> ... peter >>>> >>>> >>>>> On 02/20/14 12:42, Roger Hui wrote: >>>>> >>>>> % 1 +. (+%)/\ 100 $ 1x >>>> ---------------------------------------------------------------------- >>>> 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 >> >> ---------------------------------------------------------------------- >> 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
