Joe N. posted Jun 14, 2014 4:22 AM (http://mathforum.org/kb/message.jspa?messageID=9486480) - GSC's remarks interspersed: > > >(GSC): There probably is much that could be argued in > >support of Liping Ma's and Mark Saul's respective > >arguments (and no doubt many have done exactly that, > >as you are doing in support of Liping Ma's thesis). > > (Joe N.): I have confessed sympathy with her viewpoint > but > haven't really tried supporting her arguments, ... > OK > > ... other > than it seems self evident to me that arithmetic is a > coherent subject. For Mark Saul to take that on as > "problematic" is not a good place to go. As I've just > pointed out, he pretty much flubs it from an > argumentation standpoint: 2 strawmen followed by a > change of subject. > As noted earlier, Liping Ma's contention that "arithmetic is a coherent subject" is something I've never contested. (I don't know about Mark Saul - he lost me when I found that he had not articulated any practical means to go about doing the one sound suggestion that I saw from him, namely: to seek to 'synthesise' the positive (worthwhile) aspects of the 'Chinese approach to elementary math education' with those of the perceivedly 'incoherent' US approach to elementary math education).
I do claim that Liping Ma has rather incoherently put forth her arguments for adopting the 'coherent' Chinese approach on elementary math education! > > But going a bit deeper, I also confess I'm not sure > I've pegged his 2nd "strawman" accurately. What he's > really questioning is whether the standard algorithms > are useful to teach, even *if* they are internally > coherent. That's an oft-debated question, so calling > it a strawman is inaccurate. The way he presents it > is flimsy though, so its like a strawman. This sets > up his shift of attention -- he wants his readers to > reject, or at least question the notion that > arithmetic (in his view, standard algorithms) is > central to elementary math education, because > arithmetic is just a delivery system for teaching > logic (like a cigarette for delivering nicotine.) > > Perhaps we could debate that single point first, if > there are any takers for Saul's view. > > My view is pretty much that arithmetic is not just > standard algorithms, but I wouldn't neglect those. It > is in fact a "coherent subject" par excellence. > Indeed, that it probably is. The heart of the matter is that neither Liping Ma nor Mark Saul has (insofar as I've understood them) clearly articulated that there is a significant difference between:
- -- 'arithmetic' as a discipline, coherence of; and - -- the 'teaching of arithmetic' as a discipline, coherence of.
Once they get there, most of the argument as it is now being conducted is over.
At that point, the real issue is:
Do students develop a 'fear and loathing' of math by the time they graduate from school? The seeds for this 'fear and loathing' of math are actually sowed in the teaching of elementary math. Implant a 'fear of numbers' in a child when he/she first looks at math, and you've lost him/her for any serious effort to learn math after that. The 'fear and loathing' takes over.
As I understand - on the basis of my little exposure to tutoring a US student in high school math several decades ago; and from what I've come to understand from my reading here at Math-teach and elsewhere - most US students have indeed picked up this 'fear and loathing of math' by the time they graduate school. (Recall President Barack Obama's somewhat shame-faced confession that he had been 'poor at math' while he was in school. He's clearly a very intelligent man indeed - notwithstanding 'israeliteknight! - so he doesn't fit the profile of those whom Robert Hansen claims should be packed off to 'vocational school'. By the way, that 'vocational school education' is also, most likely, crying out for radical change).
If Chinese students generally do NOT develop such a fear and loathing by they time they graduate school, then there probably is a strong case for carefully studying the 'Chinese system' and learning how to adapt it for the USA.
Both Liping Ma and Mark Saul have - IMHO - equally failed to identify just what the real problem with US school education in math, and how to tackle the problem. > Here's a couple questions I might ask an elementary > school teacher who professes a solid understanding of > elementary arithmetic: > > * How would you characterize those (rational) > fractions that can be represented by a non-repeating > decimal number? > > * As a function of n (whole number) what percentage > of all fractions with denominator < 10**n do such > numbers comprise? > > Is knowledge of standard algorithms used? No. > Would most elementary math teachers be able to answer > these simple question easily? I wonder. Would be > being able to discuss such question easily and > naturally be indicative of at least some familiarity > with arithmetic? I think so. > Well, I have approximately zero knowledge of 'elementary school teaching, so I guess I'm exempted! > > Arithmetic is a very old subject, and arguably along > with geometry is one of the oldest branches of > mathematics. Its coherence embraces much more than > standard algorithms. > Indeed. But, as noted, it's not the 'coherence of arithmetic' (as a discipline) that is the real issue.
The issue is the coherence of the way knowledge of elementary math imparted.
Here I claim that the underlying problem is simply that the educators have been focusing (for years; indeed, for generations - even a reading of Dickens makes this clear) on 'teaching math' as their concern, while their real concern shoul be with the dyad of 'learning + teaching' (math and, indeed, everything else). I claim that a little *practical* understanding of 'systems' would help significantly. > > Its usefulness goes beyond answers that can be found > with a calculator. > No arguments at all against this.