Talk:Math wars

message: My own personal bias is more toward the "traditional" teaching methods, if you want to call them that, but nonetheless I feel that this article is very slanted. I feel that "someone" (that someone will be me if I find myself with more free time available) ought to try to present the "reform" (also not a very good label) perspective. There are legitimate points to be had, such as that the traditional methods overemphasive algorithm and underemphasize actual understanding of the material.
Even though I did it here, there's got to be a better way than to use these labels and sanitize them with quotation marks.
Pepper2000 03:26, 16 January 2007 (UTC)
replies: text: Unfortunately, the problem is bigger than you may think. Even facts of what a curriculum consists of is often not agreed upon. People on one side will say a certain curriculum consists of something or other while those on the opposition will insist otherwise. When I read through articles like math wars or traditional mathematics, it's very clear that the bullk of the information is written using propoganda pieces. There are a number of statements that are passed of as fact that should not be. One thing that would drastically improve the quality of these math education related articles is to remove everything that is not backed up by multiple reliable sources. --C S (Talk) 16:42, 3 March 2007 (UTC)
thread_title: My

message: This looks like a rehash of stuff from the early '60s, where every year would start with a sequence on elementary set theory... Has anyone else made the connection? --71.126.50.220 (talk) 18:13, 22 September 2008 (UTC)
replies: text: No connection. They come from different parts of different spectra. The New Math folk were concerned with making the math more rigorous, that we weren't turning out good enough engineers to send our own fellow travelers into orbit. Not all new math sucked, but it was too hard for lots of kids, and it got mangled by teachers who didn't necessarily get it, and certainly didn't buy it. This stuff comes from folks who are concerned that poor and minority kids don't get to the advanced topics in math, blended with ed professor folks who like to think about what math means, rather than perform calculations. The result are programs that have content removed, diluted, or chopped up, and that don't prepare kids well for harder math later. Once again, it gets mangled by teachers who don't necessarily get it, and certainly don't buy it, but that similarity is superficial. Jd2718 (talk) 01:29, 23 September 2008 (UTC)
thread_title:  Any connection to the [[School Mathematics Study Group|School Mathematics Study Group (SMSG)]]? 

message: This section was wholesale removed, despite the documentation of a TERC study which acknowledges that standard subtraction is simply not taught in that curriculum. Also the common complaint that textbooks which either contain no standard methods, or no explanation or solved examples of standard methods are difficult for parents to help. NPOV means presenting ALL sides of an issue, not presenting one and dismissing another. Though reform books continue to be adopted, many districts have decided that they are awful and are moving on, making "reform" the method of the current that is moving into the past. Bachcell (talk) 04:34, 22 October 2009 (UTC)
replies: text: See my response on my Talk page. Inclusion of both sides is more than welcome - it is necessary. IMO, this could also be considerably shortened. But it must be presented as a neutral report, not a debate. The language above is not NPOV. --seberle (talk) 05:05, 22 October 2009 (UTC)
thread_title:  POV removal of large section 

message: I started reading this article by an accident, but found it necessary to intervene, at least through this talk page. I agree with CS that the current text seems based on propaganda sources rather than on real documents of Math Wars, and reflects more the "wars" between the editors of this text rather than real "Math Wars".
First, it's unclear from the text why NCTM started the reform. As far as I know, various classroom recordings made in the 80-ies (in particular by Alan Schoenfeld) showed that math instruction in the US had degenerated into formal and dogmatic manipulations with memorized formulas. So, there is no argument between the sides if some reform was justified. However, one should not confuse the sad situation in the US math education in the 80-ies with traditional math education in general. It is the direction of the reform that caused the protest, not the satisfaction with the previously existing situation.
Next, there were some real events in the history of math wars that followed creation of NCTM standards and implementation of reform curricula. This is not the history of a debate between
two brands of "math educators" but the history of a grass-root movement (political, if you wish) against the reform, and it was started by some parents and mathematicians. Some events I am familiar with include:
* creation of Mathematically Correct,
* endorsement of 10 programs by the US Dept of Education,
* open letter to US Secretary of Ed. written by Klein, Askey, Milgram and Wu, and cosigned by 200 mathematicians and physicists including 7 Nobel laureates and Fields medalists,
* importing of Singapore Math, which has become a measuring rod, in view of TIMMS reports
* Wu's criticism of the new California standard,
* involvement of mathematicians (Milgram, Askey) into editing of the CA standard which eventually resulted in the dismantling of the reform in California,
* report of Milgram to a congressional committee,
* Math Wars in Israel, when a California-modelled math reform was stopped by a report of Aharoni to the Israeli Ministry of Ed. and by efforts of others; translation of SM in Israel,
* Math Wars in France and the grass-root movement there led by Fields medalist Lafforgue (see his speech "Why the Schools" in the English translation by Raimi)
There could be events on the other side (I am a mathematician, so my bias is clear), such
as development of specific curricula, support from NSF, establishing of Mathematically Sane,
and events in MA, NY, and other states, of which I am poorly informed.
Next, presenting the position of advocates of the reform through the paper of O'Brien is unsound.
First, the link to his paper is broken. I located the beginning of the paper by its title,
and it indeed contains the charges quoted in the present article, but the style is pure propaganda, not supported by any evidence. And it can't be supported, because his whole claim is outright ridiculous - as it is already clear from the list of activists mentioned above (all are
mathematicians, and Aharoni also has substantial experience of teaching in elementary school).
So, why is O'Brian's paper mentioned?
Next, in the current version of the article, the portrayal of the critics of the reform is
grotesque. No serious critics ever proposed "memorization of formulas" or that "practicing
algorithms" should come before their conceptual understanding. In the contrary, Madge Goldman
in her preface to teacher's manual for the 1st grade of the US edition of Singapore Math writes:
"The central idea of all of mathematics is to discover how it is that knowing some few things will, via reasoning, permit us to know much else --- without having to commit the new information to memory as separate facts. Mathematics is economy of information, not its unnecessary proliferation. Basic mathematics properly presented conveys this lesson. It is the connections, the reasoned, logical connections, that make mathematics manageable. Understanding the structure of mathematics is the key to success."
Ideally, the only things to be memorized are addition and subtraction facts within 20 and multiplication facts within 100 - the rest is based on reasoning. And of course, in the traditional math education, practicing the algorithms must begin with learning why they work.
What opponents of the reform claim is that the standard algorithms *are* among main concepts of elementary school math and hence neglecting them leaves math education ungrounded. And the lack of teaching algorithms is not the only or main charge of the critics - it is only an example. Another example is neglect with teaching fractions (e.g. Connected Mathematics was criticized for relying on calculators instead of full treatment of fractions.) The most serious charge was that, by suggesting that children can reconstruct elementary math from hands-on activities, proponents of the reform underestimate the depth of the subject, the complexity of its structure, the degree
of systematization needed to guide the students through all the stairs of the pyramid: from first exposure to whole numbers, to basics of the decimal system, through operations with fractions, decimals, to problems on percentages, ratios and proportions, etc. Aharoni wrote a book Arithmetic_for_Parents about all this and the preface of it was published in American Educator under the title "What I learned in elementary school?"
Finally, the mention of TERC's "Investigations" and especially the reference to supporting "research" prompted me to make some changes. Regardless of how ridiculous is the curriculum, the research paper supporting it is actually self-defying. I added a link substantiating this point of view and moved a couple of sentences around to accommodate the change. Borisovich (talk) 09:33, 27 December 2009 (UTC)
replies: text: Thanks for for informative post here and your changes to the article. Any work on this article is much appreciated as it is a poor state. Adding some of the event you mention would help make the article more encyclopaedic especially if references can be found. I'm based in the UK so don't really know much about the reform in the US.--Salix (talk): 19:52, 27 December 2009 (UTC)

text: Dear Seberle,
Returning to the article in general. It seems that you personally understand "math wars" as an academic debate between two brands of math educators. My point was that such wars exist only in imagination of the authors of the current version of the article. Look at the references: who the NCTM, TERC, EM, Mathematically Sane are at war with? Two concerned math professors plus a bunch of faceless critics?
In reality (read, e.g. Klein's paper) "math wars" did not start in 1989 as an opposition to NCTM Standards - noone would care - but almost a decade later, when many reform curricula were implemented, and mathematically educated parents (and many professional mathematicians and scientists among them) noticed that their children are not getting meaningful math education at all. It was not a debate, but a rebellion of educated public againts
educaional establishment. And there was no parity there, as on one side there were all the resources, including
(dozens of?) billions of dollars spent on development and implementation of reform currcila and NSF incentives, beuraucracy of Boards of Education and School Districts, and the authority of Schools of Education, and on the other only Internet and good names of some of the leaders.
So, assuming that this wikipedia article is intended not for internal consumption of a group of math educatiors, but for informing the general public about real events, it should be rewritten to reflect and document such events as they happened. Why wouldn't you let the opponents of NCTM to have personal names and speak in their own words - e.g. the way I quoted Madge Goldman?
You will see then, that what you consider as my middle-of-the-road position is what they (i.e. mathematicians involved into math wars) were saying all along. And if you say that many math educators now think the same - then, who'd care what they think - if they continue to supply our children with mathematically incompetent programs?
It's not a clash of opinions, but a fight, for their children's sake, of those who care about mathematics per se against those who care about education per se.
In particular, your interpretation of "traditional math education" as imported from the respective wikipedia article, may be accurate in that article, but is inedequate for the purposes of this article. "Math worriers" never proposed to return to the lousy teaching practice of the 80-ies, but to the well-tested tradition of meaningful math education as exists (or used to exist) in some other countries - hence the interest to Singaporean, Japanise, Korean, and Russian math programs. Thus, using the words "traditional math education" in your technical sense is misleading; one should either refrain from using this term in this article, or state clearly that it used here in its common sense, and not as a technical term from internal debates between educators about math education in the US in the 80-ies.
Borisovich (talk) 19:35, 25 January 2010 (UTC)
thread_title:  Is this real? 

message: : Dear Seberle,
Thanks for your comments. I'll come back to the more important and general issues about the whole article and your interpretation of its subject and of "traditional mathematics", but for now let me straighten the record with Givental's review.
1. I quote from Goodrow's paper: "When regrouping was required, the Constructivist group performed better than either of the other two groups". So, Givental's understanding of graph 5 is correct.
:Yes, that quote is correct. However, Goodrow states that the difference was statistically significant only between the Constructivist and Mixed groups, not the Traditional.--seberle (talk) 16:15, 25 January 2010 (UTC)
replies: text:  Are you saying that for the purposes of the present wikipedia article, this piece of date from Goodrow's paper cannot be used to justify the disputed claim since her data are statistically insignificant? I agree.Borisovich (talk) 19:23, 25 January 2010 (UTC)

text: Academic conferences usually require that papers go through the same peer-review process as journals. Conference papers and journals are the two main channels for peer review.--seberle (talk) 16:15, 25 January 2010 (UTC)
replies: text:  "Usually" is not good enough. Has the paper actully been ever made available in a printed form (what is ISBN of the proceedings volume of the Symposium? Pages in that volume?) Judging by what I see on the website, it was presented as a talk, or poster, or distributed at the conference as a manuscript. I am not aware of any way how such materials can possibly go through a normal, independent, anonymous peer-review process. What is your evidence that this particular paper was ever peer-refereed? Borisovich (talk) 19:23, 25 January 2010 (UTC)

text: Posting a PDF to your web site is not the same as peer-review.--seberle (talk) 16:15, 25 January 2010 (UTC)
replies: text:  It is not a result of a normal, anonymous peer-review process, but it is a review, and by a fellow-scientist (a peer), and by a mathematician (and not child-development expert), which is closer to the target, since mathematical competencies of the students are being evaluated, and it is nether anonymous, nor secret like a usual (non-existing in this case, I suppose) peer-review would be. So, your dismissal of a review because it is more responsible than a usual peer review is strange. Borisovich (talk) 19:23, 25 January 2010 (UTC)

text: Goodrow's paper may indeed be faulty, but that is not for Wikipedia to decide. It stands until the expert community decides otherwise, namely by someone publishing a peer-reviewed paper showing it to be faulty.--seberle (talk) 16:15, 25 January 2010 (UTC)
replies: text:  Not necessarily - there are other methods. By the way, I've made another change: the mention of the WWC report on EM was inaccurate at that "moderate to large" was not the impact but the extent of the data, the impact being "potentially positive". Note however that out of 61 published researches on EM, only 4 met the WWC evidence standards, albeit, with reservations. I am sure most of those 57 that did not, were properly peer-reviewed. This should tell us something about the standards of rigor in this branch of research. It is up to Wikipedia editors to select those sources of evidence that are credible, and using eyes for this is not a sin. Borisovich (talk) 19:23, 25 January 2010 (UTC)

text: That is why there is a peer-review process. In order for Goodrow's paper to be accepted, it had to be reviewed by neutral parties not associated with TERC.--seberle (talk) 16:15, 25 January 2010 (UTC)
replies: text:  Not true. For a manuscript, to be distributed at a conference it would suffice that a member of the organization committee reads the title and decides that it not crazy, or just trusts the recommendation of the thesis adviser. What is your evidence that a formal written review was souhgt for each poster/paper at this symposium, and that reviews were examined by any editorial body? Borisovich (talk) 19:23, 25 January 2010 (UTC)

text: I am not claiming anything at all. If you believe the Goodrow paper is inappropriate in the Math Wars article, then delete it. I did not insert this sentence and I don't think I would object to your deleting it if you feel it does not belong. It is rather too specific for this article and better references are available. I do, however, object to putting a non-peer-reviewed opinion paper against a peer-reviewed paper as if they were on equal footing. This is my only disagreement with you, Borisovich. I agree with you that Wikipedia writers should not insert their own opinions and should use their expertise. Most academic conferences I know of use genuine peer review, not someone simply looking at the title of a paper. This is why researchers cite papers from conferences as easily as they do from journals. However I am not familiar with the conference in question. If you suspect this conference is bogus, by all means check it out and correct the Wikipedia article accordingly. Or simply delete the reference for other reasons. --seberle (talk) 02:30, 28 January 2010 (UTC)
replies: text:  Sorry - I thought you insist on including it, and din't want to delete anything until there is an agreement.
So, I'll delete the senstence as too specific.
I completely agree with you that articles published in scientific sources are not to be dismissed on the basis of
media publications (and Givental's essay is rather in this category). For instance, when Marilyn vos Savant, a journalist with spectacular IQ, published a book objecting the prof of Fermat's Last Theorem, Andrew Wiles had no obligation to respond to that crap - for if she found an error in his proof she had to report it in refereed mathematics journals. However, if A. Borisovich founds "The Milky Way Academy", appoints his friends as fellow academicians, and initiates a fully refereed (by them) electronic journal (that's easy to do these days) I doubt that Wikipedia would have the obligation to quote its opinions. So, the issue which sources are "scientific" is not so formal and obvious. For the topic of "math wars", this issue is particularly non-trivial, since one side claims that its proposals are based on research, while the other side maintains that research in education has no scientific value.
I think, the situation with Goodrow's thesis is somewhere in between Fermat and "The Milky Way Academy" and falls exactly into the dichotomy about research in education. Referrying has little to do with this. I am not sure we have the same expericence with refereeing: To my knowledge, journals and proceedings of symposia are refereed because the editors risk their reputation. So, Goodrow's paper was not refereed not because the symposium was bogus, but because the paper was not published in any proceedings. However, it was endorsed by 3 faculty members of Taffts University. Let's leave it to their consciousness that they awarded a PhD degree for 2 days of routine work with inconsequential output. My position is: since they did, it is inappropriate to discard this work just because there is an internet essay saying that it's inconsequential. But it is likewise inappropriate to discard an internet essay just because it is non-refereed. This is not Fermat Theorem or rocket science - Wikipedia editors should be able to apply ctiteria based on common sense and intellectual merit.
Anyway, it's good that we have reached an agreement about the practical issue. Borisovich (talk) 02:37, 28 January 2010 (UTC)
thread_title:  Goodrow's thesis 

message: Should be some mention of the 60's-era "new math", since some see reform math as a kind of revival of this... AnonMoos (talk) 08:49, 10 March 2010 (UTC)
replies: text: Who? --seberle (talk) 11:46, 10 March 2010 (UTC)
thread_title: "New Math"

message: My opinion is that both what this article calls "traditional" math and "reform" math are no good; What the article calls "traditional" is outdated, and what is billed as "reform" is nothing but a get-rich-quick scheme for some textbook-sellers (this is my opinion, as a mathematician who recently graduated high school and was exposed to both math styles). While "Math Wars" in the literature may only refer to conflict between these two sides (Does it? Citation please!), reading this article leaves the impression that "traditional" and "reform" are the only ways to teach math. They're not. Look at The Art of Problem Solving (for advanced students) or JUMP Math (for all students) - methods both sound and modern, improving on the teaching tradition. As America is overrun with an epidemic of math-phobia, issues of math education are of great importance, and this article should be improved. It's oversimplifying to present the context for the Math Wars as a setting in which all alternatives are on one of two sides (especially the way the two sides are generalized so strongly in this article).
I think discussions of math education in the US also ought to internally link to discussions of single-sex math class research. Even though I find the suggestion of kicking girls out of the boys' math class offensive, it's a current and relevant discussion. —Preceding unsigned comment added by 147.9.66.82 (talk) 06:48, 5 November 2010 (UTC)
thread_title:  The truth is more complex 

message: In recent years, I occasionally read criticism that reformers want a vast, shallow curriculum and that traditionalists are fighting against this. I think most traditional educators are well aware of the fact that both sides have been wrestling with this issue and that only a few people are under the mistaken impression that this issue is part of the Math Wars. One issue that reformers and traditionalists generally agree on is that the American math curriculum is "a mile wide and an inch deep" (an expression first used by William H. Schmidt and enthusiastically repeated by just about everyone). NCTM was one of the first to propose a solution to this problem with their 2006 Focal Points, which clarified which parts of the Standards deserved the most emphasis. The National Mathematics Advisory Panel extended this work to define what parts of the curriculum should be most emphasized to support algebra.
It is great to add more information to this article, but I undid the three additions below because they did not accurately reflect the Math Wars debate (which was at its peak in the 1990s) and include the "mile wide" misconception (which is rather more recent). Some of the information is correct and the sentences could perhaps be rewritten?
:With about 45 states (acting individually) basing their No Child Left Behind Act (NCLB) mandated Math assessments on the National Council of Teachers of Mathematics’ (NCTM) Standards of 1989 and 2000, these standards became a de-facto national semi-curriculum in Math.
NCTM Standards only indirectly affect state assessments, which are directly based on state curricula, not NCTM Standards. This could be reworded to mention how the Standards greatly affected state curricula. This is quite important, though I think the rest of the article already makes this clear?
:These NCTM type Math curriculum have all these overarching topics in each grade: Arithmetic, Algebra, Geometry, Measurement, probability, Data analysis and problem solving; this greatly reduces the time available for arithmetic.
As explained above, the "mile wide, inch deep" problem in the American curriculum is a common criticism of both reformers (like NCTM) and traditionalists. The Standards did not add new subject areas, but only tried to reform how they should be taught and what lessons in each subject should be emphasized or de-emphasized. The 1989 Standards did not de-emphasize arithmetic, it only suggested which methods for teaching arithmetic should be emphasized (e.g. developing number sense) or de-emphasized (e.g. excessive drill). The 2000 Principles and Standards for School Mathematics did much to calm the Math Wars and did not, in fact, call for emphasizing or de-emphasizing anything, an oversight NCTM corrected in 2006 with their Focal Points.
:Critics of reform point out that the reform curricula flood each grade (K-8) with so many topics, that the curriculum is incoherent and very difficult to teach and before any topic reaches deep memory, the teacher must change topics. It has resulted in many students entering college with serious deficiencies in Arithmetic and Algebra.
Again, it is a misconception that reform curricula introduced these subjects. These additional subjects have simply creeped in to the curriculum over decades. These topics were nothing new when the 1989 Standards came out. Furthermore, the Standards themselves say very little about how much time should be devoted to each subject (arithmetic, statistics, etc.), only what should be emphasized within each subject. NCTM's 2006 Focal Points corrected this problem by being very explicit about what topics should be emphasized in the Standards at each grade level. They have been generally applauded by traditionalists as placing a proper emphasis on important topics such as arithmetic. Before the Focal Points, the Standards were basically silent as to the relative importance of the different topics that make up mathematics. This could be reworded to mention that some people are under the mistaken impression that the NCTM Standards created this problem, but it would need to be balanced by the fact that NCTM itself has been fighting this problem too and did not create the problem with its Standards. Also, it is not clear to me how many people are really under this misconception. Just a few? More? --seberle (talk) 22:08, 10 March 2011 (UTC)
thread_title:  "Mile wide, inch deep" misunderstanding 

message: The latest (and probably last) "Recent development" in the "Math Wars" is the Common Core State Standards, which have adopted the same mediating position as the NMAP (combining procedural fluency and conceptual understanding), though they explicitly avoid issues of teaching method. The "Recent developments" section should be brought up to date. As the article stands, it sounds as if the NMAP were the final word on the Math Wars, though the Common Core has overshadowed the NMAP completely and has made the mediating position more or less "official" for most states.
I have twice attempted to add a few sentences to bring the "Recent Developments" section up to date, but both times my edits have been deleted, once for lacking citations (which is true, though a tag would have sufficed) and once for being unrelated to the Math Wars, for being personal opinion and for having bad references. I do not agree with any of these reasons, but I don't want to start an edit war. I would be quite happy for someone else to write the closing sentences for this article, but someone does need to complete the article. As it stands, the "Recent developments" section is out of date. --seberle (talk) 21:06, 7 September 2016 (UTC)
replies: text: Good points. I'd like to see some discussion of the content that was removed. I'm not sure its removal was justified. TimidGuy (talk) 14:10, 8 September 2016 (UTC)

text: My explanation was clear as a mud-free river.  I'm miffed that you "don't understand".  Any editor on Wikipedia can tag or remove material they feel is unsourced, poorly sourced, or original research.  I chose to remove it.  Magnolia677 (talk) 11:34, 10 September 2016 (UTC)

text: I agree with you; I think Common Core should be included to bring the article up to date. This article is otherwise incomplete. TimidGuy (talk) 10:35, 12 September 2016 (UTC)
thread_title:  Bringing article up to date 

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