This is the last entry on this subject because I'm at the end of the Barton book. I may have given the impression that I'm reacting as I read the book. But that's not the case. I've given myself some time to reflect upon what I'm reading before I write here because I love the subject of maths and its philosophical underpinnings (ie, where these ideas come from and how they developed over time) and have been reading up on these subjects for many years.
What I've been critical of is, first of all, the shoddy scholarship of Barton who is clearly a non-specialist nor a very interested one at that, and secondly, because I appreciate the highly political nature in which he talks about these issues (aboriginal-government relations, especially aboriginal education). I'm careful to distinguish between "people" and "governments", especially in a "colonialist" context, because people of influence and power are very often just pawns in a larger system who, in a bigger pond, would have been just small fish. There may be no disingenuous bone in his body. So, I'm criticizing more the fact the ersatz environment in which aboriginal child are expected to grow up in. The dangers of the "blind leading the blind" are very real in this type of context, not just the Maori experience.
Having said that, in the few examples Barton provides, the possibility of miscommunication in a cross-linguistic environment never seems to cross his mind; nor the possibility that "plain-language" explanations may not be the best basis for curriculum development; nor the undertraining/under-resourcing of aboriginal teachers or non-aboriginal specialist teachers teaching aboriginal children, for that matter. I mean, I totally appreciate all teachers in Nunavut and the work they do is noble in my estimation but these possibilities are all too real for Nunavut.
There is also the superficial treatment of profound ideas and insights (both linguistic and mathematical/philosophical). Says Barton in many spots: one language may be so "different" as to make different mathematical worlds possible; one language may be the best and most appropriate language for maths discourse. He smatters half-baked arguments around then in the end states in most definitive terms that his research supports his thesis. What that thesis is is never made clear so I'm wondering if this book was intended for a gullible, uncritical, indoctrinated audience rather than as an honest academic discourse. The whole project seems to be designed to discourage self-reflection, further investigation and political awakening of aboriginal education.
I know this last subject (ie, political awakening) is scary to a lot of people but that is to show mistrust and denial of the basic goodness, rationality and maturity in human nature in both aboriginal and non-aboriginal compatriots (ie, this bogeyman is a myth, as much a "fiction" as maths as the Middle Earth). We need each other, and nobody's going anywhere (ie, no one is getting deported) so let's try and make our institutions more humane and humanizing rather than perpetuate their alienating, dehumanizing aspects with "cultured" parochialisms.
From a John Dewey critical perspective statements like below would never be tolerated:
Children do not need to have 3 follow 2, they do not need to have the 'correct' number of objects to refer to. They can suspend their dependence on reality if that is part of the game. All young children can do mathematics in this very real sense. All older people can too.
A relevant question to be asked is how this ability can be nurtured. How can I go about increasing my ability to think and act mathematically? A likely answer is to practice 'gossiping' with abstractions as often as possible, or, if I'm responsible for young children, to play such abstract games whenever the opportunity arises. (p. 147, The Language of Mathematics)
Even very young children sense when the supervisor/older person/teacher detects, even subconsciously, that something is not quite right in what they just said or offered as a response. This is how language is learned: through trial and error, and most importantly by feedback. This learning "technique" is embedded in the human consciousness. When they are not guided properly after realiizing themselves that they've made a mistake they quickly lose interest because they love playing within and with the rules of the game. When they do not get something out of it (ie, when no wrong or right can be measured or discerned) the reward system become meaningless.
In whatever language, in counting numbers 2 will always be followed by 3. Realiizing this is a great accomplishment for the child; their developing interpretation of the world is re-enforced, or if they got it wrong, they must be made to feel they have the creativity and wherewithal to figure things out (with proper guidance, mind). They love doing this: figuring things out. Anyone who has children know this, and no bureacratic reality nor academic theory will ever change it: their eyes light up, they become effervescent when they've done something right, or figured things "all by themselves". Denying young children the fact that 3 follows 2 in the counting system is to deny their innate intelligence.
Clearly, Mr Barton is a voice of authority in Maori education but like most self-appointed experts on alien cultures he has neglected to mitigate that pomposity and is now dancing like a fool for the world to see.