Talk:Math wars

"New Math"

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)

Who? --seberle (talk) 11:46, 10 March 2010 (UTC)

"Mile wide, inch deep"

Thread retitled from ""Mile wide, inch deep" misunderstanding".

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)

Bringing article up to date

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)

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)

Please let me respond with an explanation of why I deleted three edits made to this article by User:Seberle.

First, with this edit I removed the sentence "the Common Core Standards, adopted by most states since 2011, also adopts a mediating position". This was the source cited, and within that source I was unable to find the term "mediating". Perhaps this term was used by User:Seberle as a personal interpretation of information found within the source, but editors need to stick to the source.

Then, with this edit I removed one sentence reading "the Common Core Standards avoid endorsing any particular teaching method, but do suggest children should initially solve arithmetic problems using a variety of representations, which some parents have found controversial, though not educators". Two sources were cited, here and here, and the only part of the sentence supported by either of the sources was "the Common Core Standards avoid endorsing any particular teaching method".

Finally, with this edit I removed one sentence reading "since 2011, most states have adopted the Common Core Standards for mathematics, which require curricula to promote procedural fluency, conceptual understanding and good mathematical practices". This was the source cited, and it lists the "varieties of expertise" that mathematics educators should seek to develop in their students, which include:

• processes and proficiencies:
  • problem solving
  • reasoning and proof
  • communication
  • representation
  • connections

• strands of mathematical proficiency:
  • adaptive reasoning
  • strategic competence
  • conceptual understanding (comprehension of mathematical concepts, operations and relations)
  • procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately)
  • productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

First, I was unable to find within the source cited the specific summary User:Seberle had included in their edit. More importantly, as I stated in my edit summary, "this category is unrelated to "math wars" without a reliable source explaining its specific connection". If I am in error with my edits please respond and I will revert them. Thank you. Magnolia677 (talk) 16:02, 8 September 2016 (UTC)

I have to admit I really don't understand any of this. What is it in the list of mathematical practices that makes this reference lacking for showing that the Common Core supports "procedural fluency, conceptual understanding and good mathematical practices"? Or perhaps it is the first part of the sentence "since 2011, most states have adopted the Common Core Standards" that is not supported by the reference? In that case a simple "citation needed" tag ought to suffice? Or perhaps it is the presence of the word "good"? Then simply delete that word. Is it the fact that my exact sentence does not appear in the reference? I didn't put my sentence in quotation marks. Or, as the comment indicated, is it just that some don't see the connection with the Math Wars? Since a large part of the Math Wars concerns procedural fluency versus conceptual understanding, the connection seems obvious to me, but if not, another "citation needed" tag could have been added for more clarification. Or maybe it's something else I am not seeing? I am similarly confused by the other problems mentioned. But I really don't want to argue it out. I am just suggesting that someone write a short summary to bring the article up to date. It doesn't have to be my edit; anyone could do this. --seberle (talk) 06:25, 10 September 2016 (UTC)

@Seberle: 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)

I understand that edits can be tagged or deleted. But I think deleting is an extreme option for edits without value. Even with the accompanying explanations, I don't see how the entirety of the edit merits deletion, unless one truly believes that the Common Core has no bearing on the Math War issue of procedural fluency versus conceptual understanding. (Perhaps that is the case?) But I'll leave my edit deleted for now because Magnolia677 feels so strongly about it, or let someone else restore and edit those parts they feel are helpful.

For now, I suggest we work this out with multiple input. A two-sided argument probably won't accomplish much, but if several of us can put our heads together, perhaps we could make suggestions on how best to bring the article up to date. Should the NMAP really be the final word? Should the Common Core be mentioned, and if so, what aspects of it should mentioned and why? Are there other aspects of the Math Wars that need mentioning in order to bring the "Recent developments" section up to date? I've given my input. It would be good to see TimidGuy and others contribute their ideas, as well as a positive statement from Magnolia677 on what might be appropriate for the "Recent developments" section. --seberle (talk) 08:24, 12 September 2016 (UTC)

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)

Nothing was ever done with this, so I have changed the heading on this section to "Later developments," since it does not include recent developments (such as the Common Core). I still think it would be good to either include something, or at least discuss on the Talk Page what should be included to bring this article up to date. --seberle (talk) 11:51, 9 July 2022 (UTC)