Robert Hansen (RH) posted Jul 7, 2014 6:29 PM (http://mathforum.org/kb/message.jspa?messageID=9512744): > > On Jul 7, 2014, at 2:37 AM, GS Chandy > <email@example.com> wrote: > > > Robert Hansen (RH) posted Jul 5, 2014 8:36 PM > (http://mathforum.org/kb/message.jspa?messageID=951171 > 6) - GSC's remarks interspersed: > >> > >> (RH): On Jul 5, 2014, at 2:03 AM, GS Chandy > >> <firstname.lastname@example.org> wrote: > >> > >>> (GSC):In real life; in the real world where most > >>> of us > >>> live, the learning and understanding of music or > >>> math > >>> or anything else are all hugely more complex than > >>> RH makes them out to be, and we (humans; science) > >>> know > >>> rather little about any kind of learning that we > >>> humans do. > >> > >> (RH): This might help. Teaching everyone to be a > >> musician or a mathematician isn?t complex, it is > >> impossible. ('A', from Robert Hansen) > >> > > (GSC): It would help even more if you'd refrain from > > falsely suggesting that 'A', above - which has been > > put up by RH - represents any idea that GSC has ever > > put forward. > > (RH): You said that learning and understanding is > complex. > (GSC, now): The learning and understanding of ANY SUBJECT or discipline involve, I maintain, an extremely complex set of mental activities, 'mental models' to be constructed and then used, etc, etc.
Only those who know rather little about what they involve would maintain that 'learning and understanding' are not complex.
(However, I am attaching herewith a brief document in 'pure prose' that very briefly discusses [just a few of] the complexities involved). > > (RH): I am saying that it is only complex when you > define > learning and understanding in the context of teaching > students a subject that they are not inherently > interested in or good at. When you define learning > and understanding in the context of teaching students > a subject they are inherently interested in and good > at, then it isn?t complex. In fact, it is quite easy > once you understand the process. > You are saying wrong, I'm afraid.
You may like to check out the fairly common word "difficult" - as it is used in 'complex systems' vis-a-vis the often used and even more often confused word "complexity".
The case you *may* be seeking to argue is that the complexities involved in 'learning-and-understanding' anything may become inordinately *difficult* for the learner if the subject under consideration is something in which the learner has no interest whatsoever.
This case has NEVER been denied by me (though no doubt you would want at some stage to suggest some such thing). It's not a case that anyone who understands even rather little about 'complex systems' would ever deny. > >(RH): By all means please do clarify what you mean when > you say that learning and understanding is complex, and > give us some details as to who the teacher is and who > the student is the context you are making this > statement. > It's already been clarified above (to the extent such clarification is possible in 'pure prose').
If you require further clarification, we would need to use 'prose + structural graphics' (p+sg; what you prefer to call 'ps&g') in order to do that clarification in a document of readable length.
Learning to read and use 'p+sg' would, I'm afraid, demand some 'learning and understanding' from you. That 'learning and understanding' would also demand some learning alongside some 'unlearning'.
I believe you may be unwilling or unable to put forth the effort needed to learn and adequately understand the differences between 'complexity' and 'difficulty'. In order properly to understand what I'm suggesting here (right through this response) you may need to keep this distinction between 'complexity' and 'difficulty' constantly in mind, at a level somewhat deeper than the conventional dictionaries define.