I've saw this in my old math and science teacher days. In the British grade system the form 1 and 2's (about grade 7 to 9), were far more curious and engaged than the 5 and 6's. As the science fiction writer Theodore Sturgeon once intoned: don't let your "schooling interfere with your education."
On Fri, Feb 3, 2012 at 1:36 PM, Roger Hui <rogerhui.can...@gmail.com> wrote: > Well, they can make *you* think. In the December talk to a grade 7 class I > told you about< > http://www.jsoftware.com/pipermail/chat/2011-December/004546.html>, > a student asked about order of operations. It surprised me that he asked > that because at that point I had not introduced enough notation for the > order of operations to matter. > > I'd subsequently gave a 40 minute talk to a grade 9 class. It made me > realized that the grade 7 class was special (showed much more interest, > asked more interesting questions, etc.). The grade 9 class mostly sat in > silence until I posed the Monty Hall > problem<http://www.jsoftware.com/jwiki/Essays/The_Monty_Hall_Problem>in > the last 10 minutes. I was flabbergasted when the classproceeded to > argue whether a car or a goat was more desirable ... I'll post the ijx > transcript from the grade 9 presentation in the next few days. > > > > On Fri, Feb 3, 2012 at 11:16 AM, km <k...@math.uh.edu> wrote: > > > Friends, you can lead a freshman to an idea but you can't make him think. > > > > Sent from my iPad > > > > > > On Feb 3, 2012, at 1:03 PM, Raul Miller <rauldmil...@gmail.com> wrote: > > > > > I liked the reference which Roger Hui posted: > > > http://www.jsoftware.com/papers/EvalOrder.htm which points out some of > > > the ambiguities in PEMDAS. > > > > > > -- > > > Raul > > > > > > On Fri, Feb 3, 2012 at 1:55 PM, Devon McCormick <devon...@gmail.com> > > wrote: > > >> You could also highlight the difference in complexity between the > > baroque - > > >> http://en.cppreference.com/w/cpp/language/operator_precedence - and > the > > >> simple - "right to left". > > >> > > >> On Fri, Feb 3, 2012 at 1:19 PM, Roger Hui <rogerhui.can...@gmail.com> > > wrote: > > >> > > >>> You can point out that when there are 100 functions a hierarchy like > > that > > >>> is unwieldy. See also Ken's paper from 1966, *Conventions governing > > order > > >>> of evaluation* <http://www.jsoftware.com/papers/EvalOrder.htm>. > > >>> > > >>> <http://www.jsoftware.com/papers/EvalOrder.htm> > > >>> > > >>> On Fri, Feb 3, 2012 at 9:24 AM, km <k...@math.uh.edu> wrote: > > >>> > > >>>> A big problem for college freshmen is that calculators tell them > > 2*3+4 is > > >>>> 10 and J tells them 14. With apologies to "South Pacific": they > have > > >>> been > > >>>> carefully taught PEMDAS. > > >>>> > > >>>> Sent from my iPad > > >>>> > > >>>> > > >>>> On Feb 3, 2012, at 10:44 AM, Michael Dykman <mdyk...@gmail.com> > > wrote: > > >>>> > > >>>>> This may sound trite, but > > >>>>> > > >>>>> Who is the audience? Everyone who does math, be it for engineering, > > >>>>> finance, or middle-school algebra. Interactive J should be > > >>>>> approachable for a 10 year-old and would be a huge improvement over > > >>>>> the calculators and spreadsheets in current use. > > >>>>> > > >>>>> What do they already know about J? Nothing or less. While I am > > >>>>> occasionally surprised by the extent that J is used among very > senior > > >>>>> financial types, it is a fact that J remains deep in obscurity > within > > >>>>> the IT industry. I can't imagine that the picture is any clearer > > among > > >>>>> educators. > > >>>>> > > >>>>> What the want to know is how to do basic math with the console. > What > > >>>>> they need is enough of a foundation to begin exploring complex > > >>>>> relationships. > > >>>>> > > >>>>> I agree, Khan Academy provides an excellent model. If we (as a > > >>>>> community) were ever fortunate enough to have Khan produce some > > >>>>> introductory materials, usage would explode. > > >>>>> > > >>>>> Having said that, shouldn't this thread be migrated to Chat? > > >>>>> > > >>>>> - michael dykman > > >>>>> > > >>>>> On Fri, Feb 3, 2012 at 11:02 AM, Dan Bron <j...@bron.us> wrote: > > >>>>>> Hmm. I could do a basic intro to J course at one of the NYC JUGs. > > If > > >>>> we > > >>>>>> broadcast & record it, we could then post it on youtube. > > >>>>>> > > >>>>>> The question is: who is the audience? What do they already know > > about > > >>>> J? > > >>>>>> What do they want to know? > > >>>>>> > > >>>>>> -Dan > > >>>>>> > > >>>>>> -----Original Message----- > > >>>>>> From: programming-boun...@jsoftware.com > > >>>>>> [mailto:programming-boun...@jsoftware.com] On Behalf Of William > > >>>> Tanksley, Jr > > >>>>>> Sent: Friday, February 03, 2012 10:43 AM > > >>>>>> To: Programming forum > > >>>>>> Subject: Re: [Jprogramming] Demise of @ and [: debate > > >>>>>> > > >>>>>> I'd love to see a youtube class on J. I'd download every episode > as > > it > > >>>>>> aired to my phone and watch it on the train, using my computer to > do > > >>>>>> experiments and take notes. That's what I do with "njwilberger" > > >>>>>> rational trig and hyperbolic geometry lessons. > > >>>>>> > > >>>>>> -Wm > > >>>>>> > > >>>>>> On Fri, Feb 3, 2012 at 6:57 AM, Skip Cave < > s...@caveconsulting.com> > > >>>> wrote: > > >>>>>>> A methodical approach to teaching J might be to group the > > primitives > > >>>> into > > >>>>>>> groups of similar functionality. Order these groups by complexity > > >>>> (simple > > >>>>>>> to complex), as well as perhaps ranking them by familiarity with > > >>>>>>> already-learned concepts from traditional math classes, most > > familiar > > >>>>>>> first. > > >>>>>>> > > >>>>>>> With a learning sequence defined, spend a class on each group of > > >>>>>>> primitives, starting with the simplest and most familiar > functions > > >>>> (+-*%, > > >>>>>>> or perhaps = =. =:), and progress to the most complex and > > unfamiliar > > >>>>>>> functions.You should probably start with direct execution, and > > >>>> introduce > > >>>>>>> verb creation after a few classes on basic primitives. Some class > > >>> time > > >>>>>>> should be spent on how to read and understand the vocabulary > > >>>> definitions. > > >>>>>>> > > >>>>>>> Homework for each class would focus on usage of that current > > classes' > > >>>>>>> primitives, with previously-covered primitives thrown in for good > > >>>> measure. > > >>>>>>> The homework problems should be constructed to not require > > primitives > > >>>> that > > >>>>>>> haven't been covered yet (though nothing would prevent an > advanced > > >>>> student > > >>>>>>> from looking ahead and trying them). > > >>>>>>> > > >>>>>>> It would be interesting to create an online J class, much like > the > > >>> Khan > > >>>>>>> Academy on youtube. In fact, if you really wanted to introduce J > to > > >>> the > > >>>>>>> masses, create a math tutorial that follows and supports Khan's > > math > > >>>>>>> tutorials, using J as the tool. This would be similar to > Iverson's > > >>>>>>> "Concrete Math Companion" which follows 'Concrete Mathematics' > > >>> (Graham, > > >>>>>>> Knuth, and Patashnik (GKP)). > > >>>>>>> > > >>>>>>> Just a thought.. > > >>>>>>> > > >>>>>>> Skip > > >>>>>>> > > >>>>>>> > > >>>>>>> On Fri, Feb 3, 2012 at 2:27 AM, Linda Alvord > > >>>>>> <lindaalv...@verizon.net>wrote: > > >>>>>>> > > >>>>>>>> I agree, Don. I really was using a post from Roger because I > find > > >>> his > > >>>> the > > >>>>>>>> most difficult to untangle. This thread was a good one to > explain > > my > > >>>> new > > >>>>>>>> thoughts about @ and [: > > >>>>>>>> > > >>>>>>>> My challenges are topics I might use to teach high school > seniors > > >>>>>> studying > > >>>>>>>> precalculus, probability and statistics. They are similar to old > > APL > > >>>>>>>> contests I invented while I was teaching APL - to get better > with > > >>> the > > >>>>>>>> language myself. However, I'm not sure what would work in > classes > > >>>> these > > >>>>>>>> days. > > >>>>>>>> > > >>>>>>>> At least I'm having fun with the readers of the forum. J is even > > >>>> becoming > > >>>>>>>> fun to use! > > >>>>>>>> > > >>>>>>>> Linda > > >>>>>>>> > > >>>>>>>> -----Original Message----- > > >>>>>>>> From: programming-boun...@jsoftware.com > > >>>>>>>> [mailto:programming-boun...@jsoftware.com] On Behalf Of Don > Guinn > > >>>>>>>> Sent: Friday, February 03, 2012 12:04 AM > > >>>>>>>> To: Programming forum > > >>>>>>>> Subject: Re: [Jprogramming] Understanding C. , A. > > >>>>>>>> > > >>>>>>>> Might want to get beginners a little comfortable with J before > > >>> showing > > >>>>>> them > > >>>>>>>> C. and A. > > >>>>>>>> > > >>>>>>>> On Thu, Feb 2, 2012 at 7:56 PM, Linda Alvord < > > >>> lindaalv...@verizon.net > > >>>>>>>>> wrote: > > >>>>>>>> > > >>>>>>>>> I am rethinking my concern with @ and [: and am leaning > > toward > > >>>>>> using > > >>>>>>>>> explicit definitions as a way of teaching J to beginners as a > > >>>> natural > > >>>>>>>>> mathematical language. > > >>>>>>>>> > > >>>>>>>>> Some of the programmers responding to the forum think in idioms > > and > > >>>> use > > >>>>>>>> @ > > >>>>>>>>> happily. > > >>>>>>>>> > > >>>>>>>>> f > > >>>>>>>>> <:@-@[ C.&.|. ] > > >>>>>>>>> i > > >>>>>>>>> -@#@[ |. C. > > >>>>>>>>> k > > >>>>>>>>> <@i.@-@>:@[ C. ] > > >>>>>>>>> > > >>>>>>>>> 0thers favor the tacit approach with lots of [: > > >>>>>>>>> > > >>>>>>>>> g > > >>>>>>>>> ] C.&.|.~ [: <: [: - [ > > >>>>>>>>> h > > >>>>>>>>> [: |. ([: <: [: - [) C. [: |. ] > > >>>>>>>>> j > > >>>>>>>>> C. |.~ [: - [: # [ > > >>>>>>>>> > > >>>>>>>>> > > >>>>>>>>> Both styles are appropriate and I should not suggest one way or > > the > > >>>>>>>> other. > > >>>>>>>>> Many of you have suggested this. > > >>>>>>>>> > > >>>>>>>>> > > >>>>>>>>> We are looking for a simple way to introduce J to beginners. > In > > >>> my > > >>>>>>>>> opinion > > >>>>>>>>> we would introduce J as a mathematical language for solving > > >>> problem. > > >>>>>>>>> > > >>>>>>>>> > > >>>>>>>>> I am suggest starting with expressions that produce desired > > >>> results. > > >>>>>>>>> Developing from right to left may come naturally. > > >>>>>>>>> > > >>>>>>>>> (<:-3 6)C.&.|.'abc*ef*g' > > >>>>>>>>> **abcefg > > >>>>>>>>> > > >>>>>>>>> The next step is making explicit functions indicating if the > > >>> intended > > >>>>>> use > > >>>>>>>>> is > > >>>>>>>>> monadic or dyadic. There is no use of @ or [: allowed at > this > > >>>> point. > > >>>>>>>>> > > >>>>>>>>> g=: 13 :'(<:-x)C.&.|.y' > > >>>>>>>>> h=: 13 :'|.(<:-x)C.|.y' > > >>>>>>>>> j=: 13 :'(-#x)|.x C.y' > > >>>>>>>>> > > >>>>>>>>> Now exploring the tacit definitions would be appropriate in > some > > >>>>>>>>> environments and can be explored an studied in terms of forks > and > > >>>>>> hooks. > > >>>>>>>>> At this special code and common idioms can be explored and > timing > > >>> of > > >>>>>>>>> expressions can be compared. In the end all roads lead to Rome. > > >>>>>>>>> > > >>>>>>>>> 3 6 f 'abc*ef*g' > > >>>>>>>>> **abcefg > > >>>>>>>>> 3 6 g 'abc*ef*g' > > >>>>>>>>> **abcefg > > >>>>>>>>> 3 6 h 'abc*ef*g't > > >>>>>>>>> **abcefg > > >>>>>>>>> 3 6 i 'abc*ef*g' > > >>>>>>>>> **abcefg > > >>>>>>>>> 3 6 j 'abc*ef*g' > > >>>>>>>>> **abcefg > > >>>>>>>>> > > >>>>>>>>> > > >>>>>>>>> -----Original Message----- > > >>>>>>>>> From: programming-boun...@jsoftware.com > > >>>>>>>>> [mailto:programming-boun...@jsoftware.com] On Behalf Of Linda > > >>> Alvord > > >>>>>>>>> Sent: Wednesday, February 01, 2012 6:01 PM > > >>>>>>>>> To: 'Programming forum' > > >>>>>>>>> Subject: Re: [Jprogramming] Understanding C. , A. > > >>>>>>>>> > > >>>>>>>>> Sorry I missed the version by Arie. Nice! > > >>>>>>>>> > > >>>>>>>>> 3 6 (i=:-@#@[ |. C.) 'abc*ef*g' > > >>>>>>>>> **abcefg > > >>>>>>>>> i > > >>>>>>>>> -@#@[ |. C. > > >>>>>>>>> > > >>>>>>>>> j=: 13 :'(-#x)|.x C.y' > > >>>>>>>>> j > > >>>>>>>>> C. |.~ [: - [: # [ > > >>>>>>>>> > > >>>>>>>>> 3 6 j 'abc*ef*g' > > >>>>>>>>> **abcefg > > >>>>>>>>> > > >>>>>>>>> Please let me know if you have concerns or modifications as I > > plan > > >>> to > > >>>>>> use > > >>>>>>>>> different rules beginning with challenge 6. > > >>>>>>>>> > > >>>>>>>>> Henceforth I'll have no opinion concerning the merits of @ > and > > >>> [: > > >>>> I > > >>>>>>>>> hope > > >>>>>>>>> to learn to favor them both gracefully. > > >>>>>>>>> > > >>>>>>>>> Linda > > >>>>>>>>> > > >>>>>>>>> -----Original Message----- > > >>>>>>>>> From: programming-boun...@jsoftware.com > > >>>>>>>>> [mailto:programming-boun...@jsoftware.com] On Behalf Of Linda > > >>> Alvord > > >>>>>>>>> Sent: Wednesday, February 01, 2012 5:20 PM > > >>>>>>>>> To: 'Programming forum' > > >>>>>>>>> Subject: Re: [Jprogramming] Understanding C. , A. > > >>>>>>>>> > > >>>>>>>>> I'm happiest with the explicit version. It shows the arguments > > >>> needed > > >>>>>> for > > >>>>>>>>> the application. > > >>>>>>>>> > > >>>>>>>>> 3 6 (f=:<:@-@[ C.&.|. ]) 'abc*ef*g' > > >>>>>>>>> **abcefg > > >>>>>>>>> 3 6 f a=:'abc*ef*g' > > >>>>>>>>> **abcefg > > >>>>>>>>> > > >>>>>>>>> g=: 13 :'(<:-x)C.&.|.y'! > > >>>>>>>>> 3 6 g a > > >>>>>>>>> **abcefg > > >>>>>>>>> > > >>>>>>>>> f > > >>>>>>>>> <:@-@[ C.&.|. ] > > >>>>>>>>> g > > >>>>>>>>> ] C.&.|.~ [: <: [: - [ > > >>>>>>>>> g=: 13 :'(<:-x)C.&.|.y' > > >>>>>>>>> > > >>>>>>>>> J provides the ~ which shows up in the tacit version above. > > >>>>>>>>> > > >>>>>>>>> Then there is h with no ~ and no &. > > >>>>>>>>> > > >>>>>>>>> h=: 13 :'|.(<:-x)C.|.y' > > >>>>>>>>> h > > >>>>>>>>> [: |. ([: <: [: - [) C. [: |. ] > > >>>>>>>>> 3 6 h a > > >>>>>>>>> **abcefg > > >>>>>>>>> > > >>>>>>>>> Linda > > >>>>>>>>> > > >>>>>>>>> > > >>>>>>>>> -----Original Message----- > > >>>>>>>>> From: programming-boun...@jsoftware.com > > >>>>>>>>> [mailto:programming-boun...@jsoftware.com] On Behalf Of Roger > > Hui > > >>>>>>>>> Sent: Wednesday, February 01, 2012 11:26 AM > > >>>>>>>>> To: Programming forum > > >>>>>>>>> Subject: Re: [Jprogramming] Understanding C. , A. > > >>>>>>>>> > > >>>>>>>>> Personally, I dislike expressions with multiple uses of ~ as > they > > >>>> make > > >>>>>> my > > >>>>>>>>> head spin. > > >>>>>>>>> > > >>>>>>>>> 3 6 (C.&.|.~ <:@-)~ 'abc*ef*g' > > >>>>>>>>> **abcefg > > >>>>>>>>> 3 6 (<:@-@[ C.&.|. ]) 'abc*ef*g' > > >>>>>>>>> **abcefg > > >>>>>>>>> > > >>>>>>>>> I much prefer the second over the first. > > >>>>>>>>> > > >>>>>>>>> > > >>>>>>>>> > > >>>>>>>>> On Wed, Feb 1, 2012 at 8:05 AM, Aai <agroeneveld...@gmail.com> > > >>>> wrote: > > >>>>>>>>> > > >>>>>>>>>> Ah, I see that's a bit like yours David. > > >>>>>>>>>> > > >>>>>>>>>> Modifying it for 1< #x > > >>>>>>>>>> > > >>>>>>>>>> 3 6 (C. |.~ -@#@[) 'abc*ef*g' > > >>>>>>>>>> **abcefg > > >>>>>>>>>> > > >>>>>>>>>> > > >>>>>>>>>> (from Essays) > > >>>>>>>>>> > > >>>>>>>>>> 3 6 (C.&.|.~ <:@-)~ 'abc*ef*g' > > >>>>>>>>>> **abcefg > > >>>>>>>>>> k > > >>>>>>>>>> > > >>>>>>>>>> > > >>>>>>>>>> > > >>>>>>>>>> On 01-02-12 16:47, Aai wrote: > > >>>>>>>>>>> Sorry for the noise. You should forget the previous ones I > > sent: > > >>>>>> they > > >>>>>>>>>>> are wrong. > > >>>>>>>>>>> > > >>>>>>>>>>> It looks like this one is ok: > > >>>>>>>>>>> > > >>>>>>>>>>> mtf=:_1&|.@C. > > >>>>>>>>>>> > > >>>>>>>>>>> ]samples=: '*abcef' |."0 1 ~-i.6 > > >>>>>>>>>>> *abcef > > >>>>>>>>>>> f*abce > > >>>>>>>>>>> ef*abc > > >>>>>>>>>>> cef*ab > > >>>>>>>>>>> bcef*a > > >>>>>>>>>>> abcef* > > >>>>>>>>>>> > > >>>>>>>>>>> > > >>>>>>>>>>> ]res=: '*' ([,-.~) "1 samples > > >>>>>>>>>>> *abcef > > >>>>>>>>>>> *fabce > > >>>>>>>>>>> *efabc > > >>>>>>>>>>> *cefab > > >>>>>>>>>>> *bcefa > > >>>>>>>>>>> *abcef > > >>>>>>>>>>> > > >>>>>>>>>>> res -: mtf&>/"1 (;~I.@:('*'&=))"1 samples > > >>>>>>>>>>> 1 > > >>>> > > >>> > ---------------------------------------------------------------------- > > >>> For information about J forums see > http://www.jsoftware.com/forums.htm > > >>> > > >> > > >> > > >> > > >> -- > > >> Devon McCormick, CFA > > >> ^me^ at acm. > > >> org is my > > >> preferred e-mail > > >> ---------------------------------------------------------------------- > > >> 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 > -- John D. Baker bakerj...@gmail.com ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
