Robert Hansen (RH) posted Jun 13, 2014 3:43 AM (http://mathforum.org/kb/message.jspa?messageID=9485599) - GSC's remarks interspersed: > > I think *coherence* underlies all subjects and some > people become coherent and many of them go on and > recognize the coherence and some of them go further > and study the coherence. > I don't believe ANY subject or discipline under the sun has ever developed "coherently". While a subject or discipline is in its 'formative stages', the discipline itself as well as the methods of imparting knowledge about it are necessarily 'incoherent'.
An instance of this is clearly seen in the ongoing disagreement between the approaches recommended in the 'teaching of elementary math':
-- the 'coherent Chinese view' as advocated by Liping Ma Vs. -- what she describes as 'incoherent US approach.
The entire disagreement arises, I believe, from the fact that the 'discipline of teaching elementary math' (as opposed to the 'discipline of elementary math' itself) is itself in a formative stage. Agreed, 'elementary math' itself as a discipline is quite coherent.
But there are a whole lot of valid grounds to believe that the 'teaching of elementary math' is not a 'scientifically complete system' - it is emphatically NOT a 'coherent discipline'. It may well become so in future, but it is not that now.
At least some of the disagreement arises from the fact that the 'traditionalists of math teaching' do not (IMHO) adequately take into consideration the fact that 'teaching' does not exist 'by-itself' as it were.
Whatever may be the deficiencies of the 'reformist approach' to the teaching of elementary math - and there are many deficiencies indeed!! - they have at least recognised the crucial fact that the teaching of any discipline (including math) does not stand 'by-itself', but is part of a dyad, the dyad of 'learning + teaching'. (I attach herewith a PowerPoint presentation "Thinking Out of the Box", which suggests a very minor extension to our 'conventional language' of prose - that I've called 'prose + structural graphics' [p+sg]: I claim that p+sg could help people communicate effectively about the need for reform in the teaching of elementary math).
To my mind, the single strongest reason supporting the argument that 'math teaching' requires reform is the incontrovertible fact that MOST students graduate from school 'fearing or loathing' math! I believe that the 'foundation' as it were, for most of this 'fear and loathing' is laid during the teaching of elementary math - and that it is extremely difficult - perhaps impossible - to overcome once it is there in the 'mental structure' of a student.
This is, I know, the case in India; I believe it is almost equally the case in the USA. (I do not know the situation relating to 'math education in China': if the Chinese educational system has successfully tackled the 'fear and loathing' problem, then, by all means we should very seriously study how they've accomplished that [starting with the way they teach elementary math]). > > The majority of reformists > though are not in, nor operate in, any of those > groups. Why? Because coherence implies innate > ability. > Entirely incorrect. What exactly do you want to mean by this 'innate ability' term that you throw around? (I DO know that the phrase 'innate ability' means in the English language - and, by the way, I'm entirely sure I've read enough (American) English poetry (as well as [English] English poetry) to cotton onto the 'subtleties' of what you are saying. I am seeking your explanation of the "IMPLICATIONS" of what you wish to mean when you talk of "innate ability" (to be certain that I do not read any unintended or unimplied meanings into it). > > I think we used to teach it for its coherence but now > teach it in spite of it. I think parents like us > bring coherence back for our children, even if we > can't change society. > Once again, entirely incorrect (if I've adequately understood your claims above). Are you claiming that the teaching methods I've elsewhere described as 'Dickensian' were 'coherent'? If that is what you are claiming - or if you're claiming that "Children must be PUSHED (or GOADED) to learn math, then I'm afraid I must substitute the description "rubbish" for the above "entirely incorrect".
GSC Joe n.'s question to which RH was responding: > > On Jun 12, 2014, at 5:04 PM, "Joe Niederberger" > <email@example.com> wrote: > > > > So, is arithemtic a coherent subject or not? Why do > we teach it? Is it really just a delivery system for > logic?