Joe Niederberger posted Jun 19, 2013 7:50 AM - http://mathforum.org/kb/message.jspa?messageID=9139295 - (GSC's remarks follow). [These remarks also cover, implicitly, many of the points raised by Robert Hansen in his post dt.un 19, 2013 5:14 PM - http://mathforum.org/kb/message.jspa?messageID=9139927 - in response to Joe Niederberger]: > > Domenico Rosa posts: > >http://michel.delord.free.fr/toomwars.pdf > > This is very good, superb even, though though I view > it again as mostly a complaint about the baby being > thrown out with the bathwater. > I've commented on Andre Toom's article "Wars in American mathematical education" at http://mathforum.org/kb/message.jspa?messageID=9139928 . > > Points of agreement (with NYT piece): > (Page 17) > The most evident point of confrontation is whether > children should be taught paper- > and-pencil arithmetical algorithms or use calculators > instead of that. The dierence > of opinions can be illustrated by two quotes, both > included into the mathematicians' > letter. One is from an article written by Steve > Leinwand, a member of the Expert > Panel (and one of directors of NCTM), entitled "It's > Time To Abandon Computational > Algorithms" and published on February 9, 1994, in > Education Week on the Web: > 12 > "It's time to recognize that, for many students, real > mathematical power, on the one > hand, and facility with multidigit, pencil-and-paper > computational algorithms, on the > other, are mutually exclusive. In fact, it's time to > acknowledge that continuing to > teach these skills to our students is not only > unnecessary, but counterproductive and > downright dangerous." This is just a personal > opinion, but this person was selected by > the government to make an important decision about > mathematical education." > > That's rather strong, and wrong. > > Cheers, > Joe N > I believe Mr Steve Leinwand's "strong" suggestion that you have quoted might have become slightly less "wrong" if modified (made slightly 'weaker'?) to something along the following lines:
"It should be recognised that real mathematical power is not *necessarily* synonymous with facility with multidigit, pencil-and-paper computational algorithms. The insistence that 'mathematical power' is synonymous with skills of working 'multidigit, pencil-and-paper computational algorithms' may well needlessly drive many away from math. However, we should recognise that facility with performing computations COULD CONTRIBUTE QUITE SIGNIFICANTLY to mathematical power. Also, understanding of the power of mathematics COULD CONTRIBUTE SIGNIFICANTLY to enable an individual student to get himself/herself into the proper frame of mind to do all the hard work of learning how to do 'multidigit, pencil-and-paper computations'".
[The above statement has been written 'off-the-cuff', so to speak - and almost certainly could be made much more accurate and 'true' with some more thought about it. In order effectively to discuss such relationships in complex systems it would be useful to work in what I've called 'prose + structural graphics' (p+sg_ instead of the 'pure prose' we conventionally use in our debates].
There is at least one bi-directional "CONTRIBUTION" relationship between 'mathematical power' and such 'computational skills'. The underlying issue is to enable the 'mind' to 'understand'. It seems clear that a great many 'recommendations' are made without adequate understanding of underlying issues. Many such underlying issues would be clarified if we were to construct some simple models predicated on the relationship "CONTRIBUTES TO" in the situations being discussed.
We unfortunately do not know anough about the 'brain' (and its postulated 'associate', the 'mind'; and just how that 'association' operates in specific circumstances). For instance, we know rather little about the relative strengths of these relationships in each specific direction - we know even less about how these relationships may change over time, in a variety of circumstances.
It is entirely possible that a specific student's "lack of facility with computations" may well change quite significantly over time (given appropriate circumstances).
I place my own personal instance in evidence: +++ I recall that, at a quite early stage of my school career, I really LOATHED math, primarily because it seemed to be ALL just 'enforced, by-rote learning' (of 'times-tables', and the like). Sir Walter Scott and Robert Louis Stevenson, the classic stories of the Mahabharata and the Ramayana - all these were much more exciting.
[What was operating at the time must have been something along the following lines: "math as conventionally taught by-rote" CONTRIBUTED SIGNIFICANTLY TO my "boredom with math", which in turn, CONTRIBUTED SIGNIFICANTLY TO my "loathing math". And so on. (Most of the above argument would become abundantly more clear if I were able readily to use what I call 'prose + structural graphics' (p+sg) instead of the pure prose to which we are restricted at Math-teach)].
A couple of years later, we had a math teacher who did not insist on mindless, 'by-rote' mugging, who tried to demonstrate that math could be very different indeed. I soon came to realise that math was, in fact, very beautiful and, in fact it was quite as exciting as any of the 'adventure stories' that I loved. In just a few months after that, I taught myself (with considerble help from that teacher) to pick up all the skills I needed to perform those 'multidigit, pencil-and-paper computations' that are involved in much 'math learning'. At this point, I began to find it a breeze - and I often did not even require pencil or paper: I could do a great many of the computations in my mind, often MUCH faster than my math teacher(s)! +++