Pam posted Jun 17, 2013 7:41 PM (GSC's remarks follow): > Posted: Jun 16, 2013 1:01 PM by Joe: > > > R Hansen says: > > >Then prove it. Surely you accept that everyone on <snip> > I think Robert falls into my first category. > > I also think he is confusing thinking with > communicating, and mental imagery with visual aids. > Mental imagery and other forms of thinking are > e fluid, dynamic, abstract processes. Communicating > those processes, whether through mathematical symbols > or visual aids, always falls short, reducing our rich > inner life to something relatively more concrete, > static, and 2-dimensional. > > Pam > Many of Robert Hansen's (RH's) foncusions would probably disappear if he were to read a bit about a) mental models and b) 'systems thinking', e.g.:
There are literally thousands of places on the Internet, and a great many books at any science library providing needed information in these areas.
At the attachments to my message heading the thread "Democracy: how to achieve it" (http://mathforum.org/kb/thread.jspa?threadID=2419536), I have provided information about some simple practical tools that can enable both the understanding of mental models and systems thinking via practical work on developing 'Action Models' for any specified Mission.
However, after a fair amount of interaction with RH (here at Math-teach, over several years), I believe that there are people in this world who prefer to remain with their 'pre-conceived mental models' and 'notions' and that there is practically no kind of 'education' that would make for a change/modification in their erroneous thinking processes that lead to their many foncusions.