Joe N. posted Jun 12, 2014 11:07 PM (http://mathforum.org/kb/message.jspa?messageID=9485154): > > Let me start picking apart Mark Saul's critique one > point at a time. He sees the notion of coherence > talked about my Ma as problematic. He seems at a loss > to know really what she's talking about. > > Can it be he does not see arithmetic as a coherent > subject? (It seems wild, but that could be the case.) > It really is not the 'coherence of arithmetic (as a discipline)' [A] that is at issue, and this should be entirely obvious to all of us.
There IS some doubt about the "coherence of the 'discipline of the teaching of arithmetic'" [B].
'A' and 'B' are entirely different animals. > > After posing and knocking down a couple strawmen in > quick succession, he puts up his "real" argument: > some kids may not get a point in arithmetic because > of differing underlyingreasons, arguing that in fact > distinctly different cognitive abilities may be to > blame for different sorts of misconceptions (pg. > 505). > The strawman, if any, is only in seeking to conflate 'A' and 'B'.
I'll grant that this strawman is probably not being created deliberately (as was that created by Haim and Robert Hansen when they claimed "OPMS is just list-making and nothing else!'
Here it is (more likely) a simple confusion between two closely related but definitely quite different 'systems'. Such confusions are fairly common when people aren't accustomed to 'systems thinking'.
There are analogies of sorts in the 'machine world' to which we've already grown pretty well accustomed over the past couple of centuries.
For example, I believe that when automobiles first came out onto the roads, some people believed they were manifestations of the devil because there were no horses pulling them along!
The "Cargo Cults" of the South Pacific (http://www.sjsu.edu/faculty/watkins/cargocult.htm) may also be appostie in this context. > > Now, how does that support his claim that Ma's > "coherence" is in fact illusory or problematic? I > don't think it does in the least. A coherent subject > does not imply that a single cognitive ability > underlies or supports it. > > In fact, Saul quickly abandons his claim of > "coherence" being problematic, and instead jumps to > the conclusion that one was really teaching > arithmetic in order to strengthen these underlying > cognitive skills. We teach arithmetic in order to > teach logic, to paraphrase him. > I'm not at all supporting Mark Saul's arguments; in fact, I've pointed out elsewhere (http://mathforum.org/kb/message.jspa?messageID=9477972) a grave flaw in his suggestions. QUOTE .... However, (Saul) hasn't shown us any practical means of just HOW to fit together these disparate views, HOW to create his suggested 'synthesis' (in a systematic way). UNQUOTE But his view that it may well be useful to learn how to 'synthesise', if possible, the claimed 'coherence' of the 'Chinese system' of education in elementary math and the perceived 'incoherence' of the US system.
The rest of Joe N.'s post is pasted below my signature.
GSC The rest of Joe N.'s post: > > People say things like this all the time: we teach > sports in school because it teaches other socially > desirable qualities, yadda yadda. But why make this > claim about arithmetic? We all use arithmetic > everyday in our lives. Do we need to justify it on > other grounds? Why? > > So, is arithemtic a coherent subject or not? Why do > we teach it? Is it really just a delivery system for > logic? > > Cheers, > Joe N > > ------- End of Forwarded Message