Pardon my cynicism, but there is little hope of introducing your plan by the fifth grade in traditional schools. A creative and experimental teacher might pull it off in one experimental classroom. You'll be lucky to introduce *: in J in the tradition mathematics program by the fifth grade in the next decade.
Linda Ps. Maybe I'll have a brighter outlook in the morning. It's not that the children can't cope. It's the design of the texts, the fear of teachers about change, the testing programs to evaluate teachers and students, the parents who don't understand what the children are learning and on and on.... -----Original Message----- t From: [email protected] [mailto:[email protected]] On Behalf Of km Sent: Tuesday, January 15, 2013 5:05 PM To: [email protected] Subject: Re: [Jprogramming] atop continues to puzzle me Linda, Perhaps we should be in chat, but I do not think you need square root to introduce complex numbers, nor do young students need to calculate with them by hand. We have calculators now. Students are taught early about plotting points in a coordinate plane. I would introduce complex numbers as names for points. Point 2j8 is 2 units to the right and 8 units up from the origin. The point halfway between two complex numbers is halfway between the origin and their sum. Draw rays from the origin to two complex numbers. Multiplying them involves a rotation and stretching of the second ray by amounts indicated by the first ray. "This much" and 'this much." That is why the product of 0j1 and 0j1 is _1j0, called _1 for short. It is also why _1j0 times _1j0 is 1j0. You'll learn more about complex numbers when you get to the sixth grade, and you can already add and multiply them on your calculator. I concede that using 2j8 as a code for "2 and 8" may be a stretch -- but young students are flexible! Kip Murray Sent from my iPad On Jan 15, 2013, at 2:16 PM, Raul Miller <[email protected]> wrote: > Why is the j in i:2j8 more important than the i? > > -- > Raul > > On Tue, Jan 15, 2013 at 3:00 PM, Linda Alvord <[email protected]> wrote: >> I am considering the structure of mathematics education. A domain of >> numbers from _2 to 2 in steps of one half could be understood and >> developed in elementary school even in J. It is not really sensible >> until square root is mastered. After that an imaginary numbers might >> show up. So %:_1 becomes >> 0j1 in J. It will take a while to master numbers like 2j8 and >> other imaginaries. The leap to an idiom which uses 2j8 in a totally >> different way is counterproductive until much later. >> >> How can you explain the connection to imaginary numbers in this expression: >> >> i:2j8 >> _2 _1.5 _1 _0.5 0 0.5 1 1.5 2 >> >> Linda >> >> -----Original Message----- >> Froch: [email protected] >> [mailto:[email protected]] On Behalf Of Raul >> Miller >> Sent: Tuesday, January 15, 2013 11:35 AM Tr o: >> [email protected] >> Subject: Re: [Jprogramming] atop continues to puzzle me >> >> I am uncomfortable with this reasoning, because: >> >> *) i:9j3 is related to complex arithmetic only by notation. >> >> *) class becomes boring when its pace is set for someine else (when >> it does not match the student's needs). >> >> *) simplicity is good, but so are different perspectives. >> >> Waiting to introduce imaginary numbers before introducing this >> notation seems analogous to waiting to introduce polynomials before >> introducing decimal numbers. >> >> Anyways, I this notation can be optional, but if I were stuck >> teaching a class using J (rather than providing guidance, pacing and >> structure to a group of students who had been taught how to learn and >> who were being responsible for their own education) I think I'd >> introduce this as an optional notation about the same time I introduced i: >> >> -- >> Raul >> >> On Tuesday, January 15, 2013, Linda Alvord <[email protected]> wrote: >>> Devon, Since I think of everything going forward from kindergarten >>> (maybe someday we'll do more with prenatal education) I would use Y=: >>> _2 + 0.5 * i.9" until the middle of the second year of algebra. >>> >>> I really like your solution! It would be a great next step when >>> teaching imaginary numbers. >>> >>> Linda >>> >>> -----Original Message----- >>> From: [email protected] >>> [mailto:[email protected]] On Behalf Of Devon >>> McCormick >>> Sent: Monday, January 14, 2013 2:58 PM >>> To: J-programming forum >>> Subject: Re: [Jprogramming] atop continues to puzzle me >>> >>> Linda - >>> >>> a nice short cut for your expression "Y=: _2 + 0.5 * i.9" is "Y=: i:2j8". >>> In general, providing the complex argument PjN to i: gives you N+1 >>> points from -P to P. >>> >>> Regards, >>> >>> Devon >>> >>> >>> On Mon, Jan 14, 2013 at 12:24 PM, Jose Mario Quintana < >>> [email protected]> wrote: >>> >>>> To Henry: >>>> >>>> My apologies, the worst part is that I noticed the misspelling but >>>> I neglected to correct it; I guess watching the playoffs and >>>> writing to the forum do not mix very well. >>>> >>>> To Linda: >>>> >>>> That is a nice feature; thanks for sharing it. One refreshing thing >>>> about J is that one never seems to stop learning it. Moreover, if >>>> one follows the forums and this one in particular one is shown (or >>>> reminded) how capable the J system really is. >>>> >>>> On Mon, Jan 14, 2013 at 3:10 AM, Linda Alvord >>>> <[email protected]> >>>> wrote: >>>>> Jose, Here's a simper version. Using the aspect ratio helps make >>>>> the derivative more obvious. I use Chrome and I don't know how >>>>> this will >>>> look >>>>> elsewhere. >>>>> >>>>> Load 'plot' >>>>> u=: -: >>>>> v=: *: >>>>> Y=:_2 + 0.5 * i.9 >>>>> f=: 13 :'(] ; [:|:u@v d._2 _1 0 1 2 )y' >>>>> f >>>>> plot f Y >>>>> 'aspect 1'plot f Y >>>>> >>>>> Linda >>>>> >>>>> -----Original Message----- >>>>> From: [email protected] >>>>> [mailto:[email protected]] On Behalf Of >>>>> Linda >>>> Alvord >>>>> Sent: Sunday, January 13, 2013 9:21 PM >>>>> To: [email protected] >>>>> Subject: Re: [Jprogramming] atop continues to puzzle me >>>>> >>>>> load'plot' >>>>> >>>>> u=: -: >>>>> v=: *: >>>>> Y=: _2 + 0.01 * i.401 >>>>> f=: 13 :'(] ; [:|:u@v d._2 _1 0 1 2 )y' >>>>> f >>>>> ] ; [: |: u@v d._2 _1 0 1 2 >>>>> plot f Y >>>>> >>>>> If this is in a jijs and then run, it will shw the graph you >>>>> expect bu >>>> t >>>>> it will provide a long J error message in a separate window. I >>>>> don't >>>> know >>>>> how to prevent it. >>>>> >>>>> Also, maybe when u@v can be replaced by ([:u v)"v that will >>>>> work >>>> also. >>>>> >>>>> Linda >>>>> >>>>> >>>>> -----Original Message----- >>>>> From: [email protected] >>>>> [mailto:[email protected]] On Behalf Of >>>>> Jose >>>> Mario >>>>> Quintana >>>>> Sent: Sunday, January 13, 2013 5:17 PM >>>>> To: [email protected] >>>>> Subject: Re: [Jprogramming] atop continues to puzzle me >>>>> >>>>> To Raul: >>>>> >>>>>> I have no idea what "works reasonably well" means. >>>>> >>>>> That is a very subjective statement, apparently one can make use >>>>> of >>>>> (@) and (@:) within the scope of (d.) but, of course, that depends >>>>> on >>>> one's >>>>> point of view. >>>>> >>>>>> But consider also: >>>>>> >>>>>> AT=: 2 :0 >>>>>> u@v"v >>>>>> ) >>>>>> >>>>>> +:AT*: d. 1 >>>>>> 0 4x&p."0 0 0 >>>>>> +:@*: d. 1 >>>>>> 0 4x&p. >>>>> >>>>> Th> >> --- 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 >>> >>> >>> >>> -- >>> 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 > ---------------------------------------------------------------------- > 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
