Domenico Rosa posted Jun 18, 2013 7:23 AM: > > Andre' Toom's truly superb analysis of the Math Wars > is available at: > > http://michel.delord.free.fr/toomwars.pdf > I've quite carefully read through Andre Toom's quite competent analysis discussing the 'Math Wars' syndrome. While it is adequate as an 'analysis' (and does provide several very useful insights), I obseve that it does not actually develop a 'synthesis' of all the sound insights contained in it that could have helped to develop an effective 'action plan' to enable the 'math community' (or even the 'education community' at large) to resolve the many issues identified. It does not even pretend or attempt to do that!
I observe that the study was published in 2002. It probably was a pretty good effort for its time. I find it utterly astonishing that no further development has occurred of the insights Toom had provided way back then, and that the math community (and indeed the education community as a whole) seems to have gotten no further on the matter today - MORE THAN 10 YEARS LATER!
I have extracted below just a very few of the many useful insights that Toom had provided in his study, and observe that it would have been very easy indeed to create an effective Action Plan to resolve most (if not all) of the issues that could be identified in the 'math wars'. (Or at least, to 'progress towards resolution' of these issues).
[Alas, this was not done at all - but we did have many individuals shouting out "PUT THE EDUCATION MAFIA IN JAIL!", "BLOW UP THE SCHOOLS OF EDUCATION!" and so on and so forth].
(I must clarify that, while Toom has actually focused on 'math education', many of the points/issues he has discussed are most relevant to 'education as a whole'. I have tried to extend my commentary below in this direction).
Some excerpts, from Andre Toom ("Wars in American mathematical education") - with a few comments from GSC: =============================== >... mathematical education provided by Russian public schools is better than American and Brazilian and it has been so for several decades including the Communist period. This sounds like a paradox, but you will see that it is more than just my personal impression. Why this is so? This article contributes to the answer. > The claim (that math education in the Russian public is/was then better than that in US and Brazilian schools) was probably true. I recall that when I was in the US in graduate school (researching math), this was an issue of considerable concern all round. The article does indeed "contribute to" the answer - unfortunately the math (/ed) community as a whole seems to have done absolutely nothing with the sound insights provided! (That this is true is clear if you look at some of the fatuous 'recommendations' we have seen from time to time here at Math-teach).
(In general, I would guess that what was true for the quality of 'math education [in Russia]' may not have been the case for the whole of education in Russia). > >Toom: Several years ago the Department of Education of USA, helped by analogous offices of many other countries, conducted the Third International Mathematics and Science Study (TIMSS).
>Its purpose was to compare the average quality of mathematics and science education at several levels in as many countries as possible. The most shocking result was the relative decline of US students while attending schools: .... > This alarming result has been covered in many commentaries, so I shall refrain from commenting - except to observe that neither mathematicians nor anyone else in 'math education' knew just what they should do about this measured decline! (I observe that Haim's and Professor Wayne Bishop's suggested prescriptions were exactly the wrong ideas for the situation). > > Toom: I think that the real situation in American mathematical education is even worse than TIMSS shows because TIMSS followed the anti-theoretical bias of American educators. > By \theory" I don't mean anything too advanced. > Profesor Toom is probably correct in his main suggestion - though unfortunately he has been rather vague in identifying just what US education should do (in real life) about halting/ reversing the decline! We still have ridiculous suggestions coming up like "PUT THE EDUCATION MAFIA IN JAIL!" and "BLOW UP THE SCHOOLS OF EDUCATION!"
Professor Toom has provided a number of specific 'math examples' - I observe he apparently has not adequately understood that the deficiencies he recognises are in fact indicative of the deficiencies of "education as a whole and of critical thinking" provided in schools (not just of 'math education'). > >Toom: Study of mathematics in school is useful because it teaches children to understand complex, rigorous or abstract matters. > Actually, the underlying issue is "that the purpose of studying math should be to help teach and train children to understand complex, rigorous, abstract 'critical thinking as a whole' - not just in math!!
There's ample evidence that US education is much lacking in 'critical thinking' as a whole:
i) Several of the 'non sequiturs' that arise in practically every discussion that we find right here at Math-teach. (Likewise, the discussions in most forums - e.g., the New York Times; the Senate; the House of Reps; etc, etc, are all generally less than effective as 'analyses' and 'syntheses' of the situations discussed).
ii) The fact that Toom's worthwhile analytical study seems to have had approximately zero effect on math education in the US since it was published in 2002 - despite it being widely recognised as a "superb work".
This is truly an AMAZING FACT (actually deserves to be in Ripley's Believe It Or Not!)!!! (How come you, Domenica Rosa - or anyone else at Math-teach, have not done this at all???) > ... ... > > Toom: The authors of "standards" want to reform American mathematical education, but actually only aggravate its main shortcoming: contempt for consistent, systematic and thorough teaching. Absence of any organized curriculum made neglect for prerequisites a family disease of American educators. > How very true! Here is one important consideration that the NCTM seems to have left out entirely in the 'standards' it suggests. >
>Toom: In October of 1999 the US Department of Education headed by Richard W. Riley approved ten K-12 mathematics programs by calling five of them "exemplary" and other five "promising".
>This decision was based on conclusions of an Expert Panel, most members of which have neved published a research article in mathematics.
>This is not an accident. Although there are plenty of bright mathematicians in USA, for a long time they were not invited to participate in making important decisions about education. Sincerely speaking, they did not especially object.
>Like all people, mathematicians are prone to avoid extra >work and sometimes say: "Why should I bother myself with > public education? There are special people to care > about it." Toom mistakes the real reason for the failure. The underlying reason is NOT because "like all people, mathematicians are prone to avoid extra work". It is simply that mathematicians did not then (and probably do not even now) know just how they should go about doing something effective - in practice on the ground - with "public education" (as a 'system'). The crucial aspects of these are interacting with stakeholders, taking their inputs, integrating it all into real Action Planning to get over the Math Wars. Mathematicians ARE indeed prone to avoid working in ways that they have not previously done! (As are we all). > When I started this post, I had intended to do a fairly complete and thorough workout using Toom's article as a basis.
I've not done that, as I have other urgent commitments. I do hope the above may have convinced a few US people interested in the state of US education to take up some appropriate project "to change the face of US education - within, say 5 years". > >Toom: Having read this article, somebody may think that I connect poor education with democracy. I do not. What I do think is that democracy has many aspects and free elections of political leaders is just one of them. Quality of education is not determined by quality of political structure and can deviate from it for better or worse. > The above is partially true, but by no means is it entirely true. The connections between 'democracy' and 'education' are far deeper than what Toom has suggested.
The underlying fact that Toom ignores is that 'true democracy' (as opposed to the 'electoral democracy' that is in place in the US - and in most other nominally democratic nations) can be a powerful enabler of 'effective education'. However, it is essential that the people in the democracy do need to take a great many needed steps to ensure that happens.
The underlying idea is: "Real democracy" COULD CONTRIBUTE (VERY SIGNIFICANTLY) TO 'effective education' AND 'effective education' also COULD CONTRIBUTE (VERY SIGNIFICANTLY) TO real democracy. (The above relationships are much more convincing in the 'prose + structural graphics' (p+sg) that I recommend for discussion of complex issues.
I believe that, in his discussion, Professor Toom has lost sight of these very significant bi-directional relationships.
In conclusion, the major loss is that others interested in education have utterly failed to do something practical, on the ground, with Professor Toom's very worthwhile insights into education (specifically 'math education').
The attachments to my post heading the thread "Democracy: how to achieve it" - http://mathforum.org/kb/thread.jspa?threadID=2419536 - describe simple tools that can help develop the kind of useful insights that Professor Toom has put up into effective Action Planning to do something, in practice on the ground, to bring about real change in math education (and, indeed, in your education systems as a whole).