Talk:Math wars/Archive 1

Archive 1

My

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)

I agree with your sentiment. All the same, neutral does not mean presenting views equally, it means presenting the views impartially.

To improve the article, the stories of "traditional" and "reform" maths need to be told fairly, but that doesn't mean that the story will favour each equally. Reform math threw the baby out with the bath-water when it deemphasised the skills in early grades that are needed to do algebra and other things that require a basic level of skills that aren't being emphasised. It has gone on for so long, that too many teachers themselves were trapped in this thinking. There are some good things about reform maths, which basically advocated a kinder, more gentle and exploratory approach to maths. The big problem that reform maths had was that it dropped the drills, which were, in fact, vital.

I think the shape of the article should be to describe the wars, and how inflamed they were/are, and the current attempts to rescue maths, keeping what is good about reform maths, combined with the indispensible drills of traditional maths. Trishm 22:48, 1 February 2007 (UTC)

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)

I've reworked the article so that most statements are backed up by sources. Roseapple (talk) 15:32, 11 March 2008 (UTC)

Any connection to the School Mathematics Study Group (SMSG)?

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)

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)

POV removal of large section

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)

Those who disagree with the inquiry-based philosophy maintain that students must first develop computational skills before they can understand concepts of mathematics. These skills should be memorized and practiced, using time-tested traditional methods until they become automatic. Time is better spent practicing skills rather than in investigations inventing alternatives, or justifying more than one correct answer or method. In this view, estimating answers is insufficient and, in fact, is considered to be dependent on strong foundational skills. Learning abstract concepts of mathematics is perceived to depend on a solid base of knowledge of the tools of the subject.<ref>[http://www.ed.gov/about/bdscomm/list/mathpanel/pre-report.pdf''Preliminary Report, National Mathematics Advisory Panel, January, 2007'']</ref>

Supporters of traditional mathematics teaching oppose excessive dependence on innovations such as calculators or faddish technology, such as the Logo language used by Connected Mathematics, which was largely obsolete by the late 1990s. Student innovation is acceptable, even welcome, as long as it is mathematically valid. Calculator use can be appropriate after number sense has developed and basic skills have been mastered. Constructivist methods which are unfamiliar to any adult, and books which lack explanations of methods or solved examples make it difficult to help with homework. Compared to worksheets which can be completed in minutes, constructivist activities can be more time consuming to understand, time consuming to cut, color, paste, or play games with other family members, and does not practice anything recognizable as arithmetic. Emphasis on reading and writing also increases the language load for immigrant students and parents who may be unfamiliar with english, but familiar with the universal notation of mathematics.

The largest supporter of reform in the US has been the National Council of Teachers of Mathematics, a group largely concerned with promoting new curricula, not the actual practice of mathematics. Traditional methods are still universally and exclusively used in industry and academia where all but the youngest adults and parents from all cultures who have completed elementary school were trained in, and still familiar with standard methods. Yet even college trained parents were unprepared to help their children with constructivist homework which did not use familiar arithmetic methods. Contrary to claims that opponents of reform are unfamiliar with mathematics, many leading voices in groups such as Where's the Math and Mathematically Correct such as David Klein come from such academic and mathematical backgrounds who actually practice arithmetic, algebra and advanced mathematics. While critics have been accused of intolerance of new methods, they are appalled that some or most of the "reform" curricula appear to have no tolerance for standard mathematics.

Some curricula such as TERC Investigations were built largely around research by Constance Kamii and others that concluded that teaching traditional paper and pencil methods is not only unneccesary, but harmful to deep understanding of math. Standard methods are completely replaced with constructivist activities. Students who demonstrate proficiency in a standard method are asked to invent another method of arriving at the answer. Decimal addition is accomplished with color pencils and a 10,000 chart in Investigations. "Supplementation" is required as teachers were asked to also cover the standard methods which were always included in traditional textbooks. Not only are the methods of teaching different, such inclusion of sheet music for "happy birthday" in a unit on addition, or writing about a "favorite number" in a math journal, but the very mathematical methods are radically different as parents are unaware that students are not taught or allowed to use regrouping, long division, common denominators, or memorized formulas for computing averages. The NCTM would later revise its standards to explicitly call for continuing instruction of standard methods, largely because of the negative response to such radical curricula, while reform advocates would later claim they never meant to discard standard methods or modify their curricula in revised editions to re-introduce them.

A study based on students using "Investigations" asserts that students performed better despite not receiving any instruction in the use of the standard subtraction algorithms.<ref>[http://investigations.terc.edu/impact/impact-studies/modesofteaching.cfm Modes of Teaching and Ways of Thinking Anne Goodrow TERC/Tufts University]</ref> Many critical reviews noted the absence of coverage of any methods familiar to parents or people with mathematical backgrounds. Connected Mathematics is a comprehensive, problem-centered middle school curriculum based on the NCTM standards, developed by TERC and funded by the National Science Foundation. While students are expected to master traditional decimal and fraction arithmetic, its unusual design leaves out any descriptions of methods, formulas and solved examples from the student textbook. Instead, it is expected students will learn more when they must "discover" the methods through investigation, and write their "conclusions" in a notebook rather than simply reading the same method. Such curricula have been called "a mile wide and an inch deeep" which deemphasize basic skills in favor of exposure to more topics using an integrated mathematics approach which includes statistics and linear algebra in high school text such as Core Plus.

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)

Is this real?

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)

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)

Yes, thank you, Borisovich, for your contributions. This article used to be much worse and is slowly getting better. I am also not comfortable with the O'Brien paragraph. But because I have not read the O'Brien article, I have hesitated to delete this. I will take your word for it and delete the O'Brien references. As far as I can tell, the mathematics community seems evenly split over reform issues (those that take a position at least).

I will take issue with your reference to the Givental review however. If you read the original TERC paper, you will see that Givental has misunderstood it rather seriously. For example, Givental clearly misunderstood the graph (Figure 5); Goodrow only said it showed the difference between constructivists and the mixed group (which it does), not the traditionalists (which it doesn't). Far more importantly, Givental is incredulous that an average second grade classroom could turn out such poor students. However, Givental is a mathematician and probably not really aware of the current state of education in most public schools in the U.S. Educators know that the work reported by Goodrow is quite typical. Much research shows that students do not master material nearly as well as teachers think they do. Wait a month and interview an average child on the fraction unit he passed so well last month and you will probably discover a large amount of erroneous concepts and wrongly remembered algorithms. Wikipedia is not the place for original research, so I won't pick apart the rest of Givental's paper here. Suffice it to say that Givental's PDF is not peer-reviewed. It is just an opinion paper he posted on his faculty website. The TERC paper is peer-reviewed and is quite sound. What is Wikipedia policy on unpublished opinion pieces that criticize peer-reviewed published research? I really don't think Wikipedia should put the two on the same footing, but please correct me if I am wrong.

As to "confusing" the sad state of math education in the 80s with "traditional" math education, we are actually dealing with terms as they are being used by the two sides of the Math Wars debate, and again, it is not really up to Wikipedia to redefine the way terms are being used. The Wikipedia article on Traditional mathematics describes very well what might be called the extreme traditionalist position in this debate. Your own position, Borisovich, actually sounds rather middle-of-the-road, and would accord rather closely to the centrist position recommended by the 2008 National Mathematics Advisory Panel. Their conclusion is that conceptual understanding and procedural fluency should go hand in hand, a position that most would accept. Believe it or not, there are still a few serious critics and textbook authors who believe quite strongly that certain things like formulas and algorithms should be memorized first and understood later. Saxon math sometimes takes this approach. The "A Beka" textbook series is entirely in this camp. In fact, there were more people who believed this in the early 20th century, so I think calling this pedagogical philosophy "traditional" might be accurate. However, if you see this extreme position as "grotesque", please feel free to correct the parts you feel are inaccurate.

The reason NCTM started the reform was really for the reasons that you seem to believe in. It had become quite common to spend most of the class time drilling algorithms and there was quite a neglect of conceptual understanding. Even teachers who believed in teaching understanding first would gloss through the reasoning much too quickly for all but the brightest children to really understand it. The NCTM proposed reforms were a summary of a growing mass of research showing (1) exactly why certain "traditional" educational methods were not working very well in the U.S. and (2) that children really did learn better using certain constructivist-based principles emphasizing reasoning and conceptual understanding. Unfortunately the proposed reforms were often poorly understood by teachers and even textbook authors. Even today, research shows that proper implementation of the reforms is not easily or quickly achieved by most teachers. The reforms have only been proven to work when correctly implemented, so this is probably the biggest problem they have faced. In the case of California, they had not been implemented at all by the vast majority of teachers before they were rejected. (Simply giving a textbook does not fundamentally change how a teacher teaches, and giving a textbook with poorly understood pedagogical principles only creates problems.)

One last thing to be careful of. Reformers are commonly misunderstood to be against procedural fluency: learning the standard algorithms and memorizing formulas and basic math facts. This has never been the position of the NCTM or of any reform researchers I know of. Reformers would agree with you that neglecting these things would leave math ungrounded. The usual reform position goes back to research showing that children who explore and come up with their own ways of calculating first, and then learn the standard methods later, master the material better than with "traditional" methods. In other words, the standard methods are "withheld" only until the child really understands what is going on. The ultimate goal for reformers and traditionalists alike is mastery of standard methods. Unfortunately, even some reform-minded teachers often misunderstood this and believed standard algorithms were never be to taught to children. Many reform textbooks usually made it clear to the teacher that the ultimate goal was to learn the standard methods, but unfortunately a few did not. Those textbook editors may have also been under the impression that non-standard methods were the goal, rather than a means. This was a problem in the 90s and probably one of the more serious reasons for the Math Wars. The situation has considerably improved during this decade and nearly all reform textbooks today are clearer about their approach and the explicit inclusion of standard methods. The Math Wars have cooled considerably since the 90s. --seberle (talk) 06:18, 29 December 2009 (UTC)

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)

Goodrow's thesis

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)

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)

2. Goodrow's paper was not published in a peer-reviewed journal; it was a talk based on her PhD thesis. I quote from TERC website: "Paper presented at the International Society for the Study of Behavioral Development. Bern, Switzerland, July, 1998. (Summary of: Children's Construction of Number Sense in Traditional Constructivist, and Mixed Classrooms. Unpublished dissertation for the degree of Doctor of Philosophy in Child Development."

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)

"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)

Well, now - thanks to Givental's PDF - it is peer-reviewed, and the review is not anonymous but publicly available, google-indexed, etc. According to this review, the paper does not qualify for scientific evidence. It is an opinion, but it is well-argumented (after all, 9-8 is not -1, is it?); so to dismiss it one needs to argue with it, not just erase.

Posting a PDF to your web site is not the same as peer-review.--seberle (talk) 16:15, 25 January 2010 (UTC)

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)

In particular, that "constructivist group performed better" is merely Goodrow's opinion - Givental derives the opposite from the same data (and he is a mathematician, while her speciality is child development). But even if Goodrow's opinion is accepted as correct, with respect to this particular group of control students (according to you, it is easy to find such a group in the US), this is irrelevant for judging about "TERC Investigations", because the control group and the tasks were chosen, modestly speaking, inadequately.

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)

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)

Anyway, it is a formally correct statement that "A study of "TERC Investigation" asserts ...", but I personally think that it is inappropriate to quote this study in an encyclopaedia article, because it is clearly a phony PhD, and moreover, smells corruption (as Goodrow is affiliated with TERC).

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)

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)

However, if you insist on mentioning this claim, you should keep the reference to Givental's review as well. The two together may tell the reader of "Math Wars" more about the nature of math wars than the rest of this article. Borisovich (talk) 05:11, 25 January 2010 (UTC)

Dear Seberle,

I think you are misinterpreting the tasks of Wikipedia writers. It is not for them to decide which opinion is right and which is wrong, but it is their obligation to apply their expertise in the subject (and, I believe, they are expected to have some) to select (and not to delegate this decision to a possibly non-existing anonymous refree) those materials that are reputable and supported by evidence, and reject those which are irrelevant or contradict the truth.

The question at hands is not whether "A study based on students using TERC Investigations asserts that students performed better despite not receiving any direct instruction in the use of the standard subtraction algorithms" is correct. It is correct, since there is such a statement in Goodrow's paper. Moreover, Goodrow's data, although statistically insignificant, confirm that this particular group of 10 constructivist students gave more correct answers to the 12 subtraction problems with regrouping than this particular group of 10 "traditionalist" students did. But what's the reason to mention this fact in the paper on math wars?

Whatever the reason, the statement conveyes the impression that there exists some "objective scientific evidence" that in general, students can be expected to perform better if exposed to "Investigations" in lieu of normal math education. Goodrow herself didn't claim this. We don't have a referee report that claims this.

Do you claim this? Then show me which piece of data in Goodrow's paper supports this claim.

If not, the true statement how particular exercises were solved by a particular group of 10+10 students is irrelevant for this article, and should be removed.

Borisovich (talk) 19:23, 25 January 2010 (UTC)

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)

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)

Reform Curricula

Dear Seberle, I understand why you removed the clause on the total amount of research. However, your understanding of the results of WWC as example supporting the claim of reform educators is POV. They always claimed - long before WWC - that reform curricula and the whole reform are based on research, while the opponents claim that this research has no scientific value. The information about the portion of research that did not meet WWC standards rather supports this second claim. So, I rewrote this paragraph to reflect this controversy in a more explicit way. Borisovich (talk) 12:36, 10 February 2010 (UTC)

I partially disagree. I do not understand the WWC to support the claims of reform educators. On the contrary, the WWC is usually seen by reform educators as supporting the claims of traditional educators, though in theory it is set up to be neutral. (The disagreement between the WWC and reform educators is over the WWC's very limiting criteria for accepting research.) The example we are discussing is therefore all the more striking because the WWC actually favors the reform textbook in this case.

The WWC rejects most research for MOST programs, not just these two. Therefore it is misleading and POV to mention the amount of rejected research as if this were somehow unusual and an indication of the poor state of research for these two programs. The WWC itself does not rank research by the number of rejected programs, but by the size of accepted research. In this particular case, the evidence for Saxon Math is rated "small" and it would be fair to include that fact. You are right to point this out, but we should do this the way the WWC prefers to report its conclusions. --seberle (talk) 17:29, 11 February 2010 (UTC)

I have no idea - and it is immaterial - who WWC usually favors, and in whose view. As far as I understand, WWC does not do research but just evaluates credibility of existing research and summarizes it. The selection criteria are formulated somehow (and from my POV are *very-very-very* mild compared to, say, FDA requirements, but of course "very limiting" in the view of the party being limited). The fact that most of research (about all programs, of course, not only EM or Saxon) does not meet these standards is much more striking (and alarming!) than the specific conclusions on EM and Saxon. So, by reversing my edits, you removed essential information about the very point of debate: One side claims (long before WWC!) "there is research" - the opponents say "it's not credible".

Besides, by duly undoing my edits you also restored incorrect characterization of SM and Saxon: There is no such thing as "algorithmic mathematics", and SM does not emphasize calculations over conceptual understanding (in the contrary, it takes upon itself to explain every little conceptual twist and turn). So, I'll try to reverse your changes; please edit the wording if you think it's POV, but don't remove bare iformation, such as the amount of research not meeting the standards. It does not say anything about EM or Saxon, but says a lot about research in education in general. WWC reports this, and the reader may decide himself which conclusions to draw.Borisovich (talk) 18:54, 12 February 2010 (UTC)

I am sorry if I misunderstood you to be saying that the WWC favors the reform position. Yes, you are correct that the WWC summarizes research and does not conduct research itself. I am not sure what "'very limiting' in the view of the party being limited" means in this case. Everyone's research is being limited by the WWC, as the Saxon and Everyday Math examples show. It is not a question of bias in eliminating research from a particular point of view, but rather the types of research the WWC criteria eliminates, which many claim can give a skewed view of education. Most research eliminated by the WWC is rejected, not because of its quality, but because it does not match the very particular type of research the WWC is looking for. But that is too long to get into here. I am not sure who is saying that some research is not credible. You gave no citation in your newest edit, Borisovich. With WWC's stringent criteria, it is fairly safe to say that the research that gets accepted is very good. No one is saying the WWC accepts any bad research, only that it eliminates even much good research.

I still strongly disagree with including the amount of research included or excluded without further explanation. This gives the distinct impression that the research was not good, whereas in fact the WWC rejects most research everywhere, traditional and reformed. Without making this fact clear, the statement is giving a false impression about this particular research.

Rather than let this devolve into an edit war, I will simply replace the entire paragraph with a different reference making a similar point. —Preceding unsigned comment added by Seberle (talk • contribs) 06:20, 15 February 2010 (UTC)

Dear Seberle, You are right at that I did not provide a reference where research in education is not credible. This is easy to correct. Way 1: Insert the link to [Barry Garelick's "An A-Maz-ing Approach to Math"] , Way 2: restore the reference you recently removed to Givental's essay on Goodrow's thesis.

"Very limiting in the view of the party being limited" means that mathematicians and mathematically educated parents who object the reform don't do research in education - it is educators who do. WWC found overwhelming majority of submitted research not credible. Educators whose research was found not credible disagree (naturally). You are right that numbers I quoted give "the distinct impression that the research was not good". This is the right impression - accrding to WWC. What's unclear to me is why you object telling the truth about it. Furthermore, the research being accepted by WWC does not mean it was "very good" - it merely means that some minimal steps were taken (such as randomly assigning students to intervention and control groups) to make a fair comparison, and meeting evidence standards "with reservations" does not mean even that. The distance between meeting such requirements and scientific credibility (i.e. reproducibility!) of results is still infinite. We are touching here only a tip of the iceberg - the actual situation with what's called "research" in education is apparently much graver. A simple examination of WWC reports shows that these reports themselves are riduculously incompetent in the very area where they are supposed to control quality of reseach, namely - statistics.

Now, see what you did with the text: You removed true information and replaced it with a false claim - that reform curricula work just as well or better. What is this supposed to mean? There are many reform curricula and many other curricula in the US. Some of the reform curricula (e.g. "Investigations", according, e.g. to WWC, but not TERC)perform really bad. Most curricula - reform or not - feature mathematical nonsense on every page, perhaps with the exception of SM only. Tell me a single one reform curriculum which is known to "work better" than SM when taught by a teacher who knows elementary mathematics. Then the claim you quoted will become legitimate. Until then it's just false. The fact that someone wrote this does not make a false claim true. Borisovich (talk) 18:57, 15 February 2010 (UTC)

I do not "object telling the truth" about the WWC. The fact is simply that I was the original author of that paragraph. I was not happy with it for other reasons and this little debate was kind of a last straw that convinced me to change it. Furthermore, if I do not agree with your views about the WWC, that is hardly the same as "objecting to tell the truth" about something. I think the new paragraph explains much better what the reformers are saying. The goal of this encyclopedia article is, of course, to explain what the two sides are saying.

But in any case, thank you for your clarifications. I think I am starting to understand your point of view better. Basically you are saying that the WWC rejects a lot of research because educational research is of poor quality. Can you tell me who else is making this claim? (I ask out of genuine curiosity. "Math Wars" is far from my area of expertise and I am trying to learn more about this phenomenon. My contributions to this article are very few. As you pointed out in a previous post, I focus on research too much and I need to come to a better understanding of the social and political events that this article is supposed to be reporting on.) Garelick does not mention the WWC, so who exactly is making this point? I can, in fact, well imagine someone making the claim that WWC rejections imply that the general state of research is bad -- I just have not come across it yet, unless you count the implied support for WWC criteria by the positivist philosophical position often held by traditional educators. If you hold to a strict positivist position, then of course any type of research not adhering to the strictest empirical standards is of poor quality. But because most social researchers are not positivists, the whole question of what the WWC rejections imply becomes a philosophical debate. In any case, please tell me more about what traditionalists are saying concerning this and who is saying it. I want to learn!

Garelick's article is similar to the Givental article. Garelick was a math major in college and has done a bit of tutoring recently in his spare time. By his own admission, he has no classroom experience, and of course no experience with research. Furthermore, Garelick's initial argument is that America scores low on international tests, apparently unaware that this is the same argument used by reformers as showing a need for change. Again, I strongly object to using such a link as a serious critique of millions of hours of serious, peer-reviewed research. But here I am in research mode again! Garelick's piece might serve as a good representative of the popular voice of the traditional side of the Math Wars debate. Please note that not all educators are reformers. Just as there are many mathematicians who support the reform view, there are quite a few educational researchers who are more or less in the traditional camp. If we are trying to balance out certain debates (at least between researchers), then we should cite what traditional educators have said in peer-reviewed publications in response to the reform movement. At least that's my opinion. Researchers answer researchers; pop articles reply to pop articles. This is not to deny the importance of pop articles -- they are an important reflection of a social phenomenon -- it's just I think it's confusing to mix the two.

In summary, I need to stop focusing so much on research, and we all need to keep in mind that this is an encyclopedia article whose function is not to hold a debate, but to report on a socio-political phenomenon in a way that will simply inform readers about what has happened. --seberle (talk) 16:27, 16 February 2010 (UTC)

Dear Seberle, To learn about WWC, and what it's results mean, you should read its reports. I can't help you beyond that, since I myself learned about existence of this organization from that very same paragraph that we are editing. And I don't know any "traditionalist" (in your sense); I only know what some mathematicians think, but they don't discuss WWC.

It was not my opinion but a fact of life that WWC was charged with the task to determine which research in education meets certain standards and found (e.g.) that 57 out of 61 did not. It were you who said that this suggests that research was not good. And you were right - outside the wall of Chelm (using Givental's metaphor), that's what it means if 57 out of 61 projects can't serve the purpose they were made for. So - unless you change the meaning of the words good and bad - if you are looking for a source that said WWC found that research was not good, the source is you - your common sense (are you a positivist?)

This is exactly what Wikipedia asks for - facts that speak for themselves. And I believe, you removed this relevant fact because it does speak for itself, and you didn't like what it says. But - to remind you - you said you removed it because it was out of context. So, I added the context - that critics say research isn't credible. You asked for references - I gave you two: Garelick and Givental. Garelick *says* (read his article further) that he is suspicious about research on which the reform is based on; Givental analyzes a PhD report in great detail. Now you are trying to discredit these sources - not for the essense of what they say, but for formal credentials. Frankly, I think you should re-examine your motives, but OK, let's discuss the credentials.

Garelick, you say, has "only" BS in math and math tutoring experience. Are you aware of the fact that most academic math educators have neither?

Garelick does not attempt to discredit research in education - just expresses his doubts - it is Givental who does. So, your hesitation to use the link as "a serious critique of millions of hours of serious, peer-reviewed work" applies to his essay. You have to reconsider your requirement, and that's why.

None of the references in this article is peer-reviewed - and should not be, since the article is about social struggle and not about scientific results.

Moreover, credibility of research in education is one of the battlefields, and it's absurd to demand that critique be approved by those who are the target of it.

As we could see in Goodrow's case (and that's one of Givental's points) a PhD degree in education can be awarded for efforts worth of 1 (one!) day of work at the qualification level of a baby-sitter (who then can serve as a referee or even editor in a peer-reviewed journal).

The truth is that Goodrow's thesis is not an extreme case, but most likely the norm. Why do you think WWC was needed? Why not just take "peer-reviewed research" and use what it says? That's why: because most of it does not meet elementary scientific standards. The very fact that a governmental organization such as as WWC was established is the incontrovercial evidence that there are serious doubts about credibility of respective research. Like it or not, the result 57/61 confirms the doubts - "millions of hours of serious, peer-reviewed work" turned out to be self-serving.

Concerning the need to include opinion of traditionalist math educators - may be, but I don't know who you mean and why their opinion should be presented. So far, whenever "traditional math educators" are mentioned, they are always anonymous and always for one purpose: to present a grothesque picture of the world-wide experience of strong, traditional mathematics education and thereby achieve symmetry with (similarly primitive) views of reform math educators. Let's agree that Math Wars is not an academic debate but a real history of opposition to a reform that costs billions of dollars, and affects millions of children and dozens of millions of their future offsprings. Let's agree to report real facts and events, and try to characterize them with opinions of those individuals who played an important role in them. Borisovich (talk) 20:41, 17 February 2010 (UTC)

Gosh, Borisovich. There is not a single paragraph in that response that I can agree with. You have seriously misunderstood some things I've written. I'm afraid most of your assertions about research and researchers are extremely misinformed. I think we better stop here. If I were to respond, it could get very lengthy, but Wikipedia is not a forum for debates. --seberle (talk) 22:25, 17 February 2010 (UTC)

It's OK, if you don't want, you don't have to educate me about the fine state of affairs and high standards of education research. But what should we do with the paragraph you wrote? You stated as a fact that reform curricula seem to perform better, and that students achieve better conceptual understanding not at the expense of computational skills. However, the reference you added says quite the opposite:

"Substantively, it is striking to note the similarity between the patterns findings reported in the Senk and Thompson (2003) volume and the findings of the larger-scale comparative studies conducted by external reviewers. In both instances, students taught using standards-based curricula tended to hold their own on tests of computational skills and to outperform students taught with conventional curricula on tests of thinking, reasoning, and conceptual understanding. This pattern of findings—not the findings of any one study—has prompted some to point to the overall efficacy of standards-based curricula (e.g., Schoenfeld 2002).

But, efficacy for what? It is important to note that students tended to perform best on tests that aligned with the approaches by which they had been taught, repeating the well-worn finding that students learn what they are taught. Combined with the findings from the analyses of curriculum materials cited earlier, the research examined here suggests that students taught using conventional curricula can be expected to master computational and symbolic manipulation better, whereas students taught using standards-based curricula can be expected to perform better on problems that demand problem solving, thinking, and reasoning."

Two questions: 1. Will you correct it youself, or let me do this? 2. I understand it is your expectation that reform math education should provide "better conceptual understanding not at the expence of computation skills," but shouldn't we, regardless of expectations, stick to the facts of life? Which are: there is no (and for many general reasons cannot be!) any conclusive research that can confirm this. 193.55.10.104 (talk) 04:01, 18 February 2010 (UTC)