On reading your latest thoughts on the "Three Headed Monster: Mean, Median and Mode", I: ++++++ - -- went back to your original contribution here on the topic (dt. Jan 12, 2014 12:46 AM, http://mathforum.org/kb/message.jspa?messageID=9362192, read everthing from there on; (1)
- -- rechecked your ideas on "All of math is just addition and multiplication" (something to that effect); (3)
- -- checked out, in an 'overview kind of fashion', your ideas on Science, Evolution, governance, 'unarchy' etc, etc, -... the study may continue, depending on how much time I find... (4)
- -- checked our, again in an 'overview kind of fashion', your views on the Beatles, music, guitar playing, etc (5). ++++++ Based somewhat loosely on the above, some thoughts:
(1 & 2): I broadly agree with you that there is much in 'elementary math' that does need careful rethinking, or rather I should state:
'the way elementary math is taught' needs HUGE reworking...
[I shall need to qualify my 'agreement' with you to the effect that several Math-teach participants have raised various (in my opinion, quite valid) reservations to several of your ideas].
In any case, the inadequacy of teaching about elementary math has (I claim) huge impact on 'education in general', which is in a terrible state, to judge by the views put forth by many adults!!! (In even the 'nominal democracies' we have achieved in many nations, this is very dangerous indeed. I guess in an autocracy this may be acceptable - if of course we're sure that the autocrats are reasonably wise).
In regard to the way math is taught, I go further: I claim the way math is taught right through school is terrible, seeing as how many students graduate from school with utterly foolish ideas about math..., and indeed, about 'thinking' itself. (Also recall that even President Barack Obama, who is surely a person with a very, VERY high 'IQ' [notwithstanding the idiotic ideas that 'jkisraeliteknight had put forth at his website "The Father's Manifesto"] had confessed that he was extremely poor at math while he was in school!)
Piaget, Maria Montessori (and many others) have put forth some VERY worthwhile ideas - but, alas, our educational systems have *scarcely* learned how to use those excellent ideas, in practice, on the ground.
However, I don't believe you have quite 'got it', so far as I am able to judge from the arguments you've put up here at Math-teach AND at your website.
Though I am in STRONG disagreement with most of Robert Hansen's (RH's) views on practically everything discussed here at Math-teach (INCLUDING mathematics and computer science; of which you will see some instances of disagreement here at Math-teach), I must say his view in this context DOES make rather good sense: he claims that: "it's the raw data that makes much more sense than many of these 'taught concepts' [I don't know if I've quite got his view down correct].
I am here inferring that Robert Hansen may feel there is considerable need for revision and reworking of the way we teach about a great many (I claim, practicall all) concepts)... - and broadly I do agree with that - though I am sure that we would have strong disagreements on just HOW *effective* teaching of math is to be done.
However, I'm afraid RH doesn't 'get it' at all, as may be seen by an examination of his disagreements with me here at Math-teach. This, anyway, is a whole different issue and doubtless the argument will continue till I get my website up (see below).
(3): As to your idea that "all of math is just addition and multiplication", my question to you is simple:
Why not instead claim that
"ALL OF MATH IS JUST 'ADDITION'!" ???
(seeing that multiplication is just 'repeated addition')... I don't believe you've adequately addressed this issue, which I believe I must have brought up earlier here at Math-teach. (If you've responded to this question of mine, I seem to have missed that response, so would be grateful if you'd point me to it).
(4): Your ideas on 'evolution Vs. Intelligent Design': IMHO, they don't make much sense at all. I am not in 100% agreement with the views of the 'supporters of evolution' - though I am rather strongly against the views of the 'Creationists', the 'Intelligent Design'-ers, and so on. In particular, while I do claim that 'evolution' is definitely *considerably more* than a mere theory - we do need in schools to explain the ideas behind 'Intelligent Design', etc. Are these ideas valid? I personally do not believe so, but if we claim to be a democracy, the views of the 'Intelligent Design'-ers do deserve to be made known at least.
(5): I'm not adequately knowledgeable about music (in any practical sense) to comment - though I do enjoy listening to music, and in particular much of what the Beatles created.
Your ideas on science in general: Not much sense there, I'm afraid. (IMHO).
Your ideas on governance, 'unarchy': most interesting: see below.
I have long promoted the idea that our conventional form of discourse, what I call the 'prose mode' of debate and discourse (to which we're limited in conventional forums, including here at Math-teach) - I claim that this 'prose mode' of discourse is severely limiting and does not give sufficient play to the ideas that people always have about their circumstances, about issues, about 'ideas themselves'.
The late John N. Warfield made some seminal contributions to 'systems science', which can enable *effective* discourse on all issues that may come to mind in complex systems. More information about what I call "Warfield's approach to systems science" is available at http://www.jnwarfield.com and from the "John N. Warfield Collection" held at the library of George Mason University (Fairfax, VA-USA), where Warfield was Professor Emeritus - see http://ead.lib.virginia.edu/vivaxtf/view?docId=gmu/vifgm00008.xml.
Some developments from Warfield's 'view of systems', which I call the 'One Page Management System' (OPMS), now enable individuals and groups *effectively* to choose any 'Mission' of interest and to construct, from their own available good ideas about it, and *effective* Action Plan to accomplish it. (Check out the attachments to my poste heading the thread "Democracy: how to achieve it?" - see http://mathforum.org/kb/thread.jspa?threadID=2419536 for some basic information about the OPMS). You personally may like to develop Action Planning to promote your ideas about (say):
- -- 'Mean, median and mode';
- -- 'all of math is just addition and multiplication';
- -- 'Intelligent Design' versus 'evolution';
- -- 'governance'; 'unarchy', etc, etc.
In particular, while I do disagree with many of your ideas on math, science - and in particular about evolution - I do believe your ideas on governance, 'unarchy', etc, are most interesting indeed - but how are you going to get people to listen? How many have been convinced since you put up those pages?
(I am NOT suggesting that I *agree* entirely with you - just that you do have interesting ideas that deserve to be debated *effectively*). How are you going to get that done???