Twistpunten in math wars in VS en ons verzet tegen de constructivistische aanpak in de ‘NCTM Standards’ (VS, 1989) en in de visie van het Nederlandse Freudenthalinstituut  &strijd van Onderwijskrant tegen dit soort wiskunde-onderwijs

De publicatie van de constructivistische ‘NCTM Standards’ in 1989 heeft geleid tot een wiskunde-oorlog in de VS. De recente Core Standards beklemtonen nu meer de klassieke waarden en aanpakken. In het Nederlands taalgebied was het vooral Onderwijskrant (Raf Feys & Co) die van meet af aan (1989) afstand nam van de ‘Standards’ en van de visie van het Nederlandse Freudenthal Instituut dat eveneens een constructivistische visie propageerde. We spanden ons ook in om te voorkomen dat de constructivistische visie ingang vond in het Vlaams wiskunde-onderwijs - en met succes. Zo komen in het leerplan wiskunde (katholiek onderwijs) geen enkele keer de term constructivisme en uitdrukkingen als 'het kind construeert zijn eigen wiskunde-kennis' voor. Jammer genoeg sloop het constructivisme wel binnen in de leerplannen voor de eerste graad s.o.

In een bijdrage in Education Next van 2012 werden een aantal twistpunten binnen de Math Wars in de VS nog eens op een rijtje gezet. We citeren even:

There will always be people who think that calculators work just fine and there is no need to teach much arithmetic, thus making career decisions for 4th graders that the students should make for themselves in college. Downplaying the development of pencil and paper number sense might work for future shoppers, but doesn’t work for students headed for Science, Technology, Engineering, and Mathematics (STEM) fields.

There will always be the anti-memorization crowd who think that learning the multiplication facts to the point of instant recall is bad for a student, perhaps believing that it means students can no longer understand them. Of course this permanently slows students down, plus it requires students to think about 3rd-grade mathematics when they are trying to solve a college-level problem.

There will always be the standard algorithm deniers, the first line of defense for those who are anti-standard algorithms being just deny they exist. Some seem to believe it is easier to teach “high-level critical thinking” than it is to teach the standard algorithms with understanding. The standard algorithms for adding, subtracting, multiplying, and dividing whole numbers are the only rich, powerful, beautiful theorems you can teach elementary school kids, and to deny kids these theorems is to leave kids unprepared. Avoiding hard mathematics with young students does not prepare them for hard mathematics when they are older.
There will always be people who believe that you do not understand mathematics if you cannot write a coherent essay about how you solved a problem, thus driving future STEM students away from mathematics at an early age. A fairness doctrine would require English language arts (ELA) students to write essays about the standard algorithms, thus also driving students away from ELA at an early age. The ability to communicate is NOT essential to understanding mathematics.
There will always be people who think that you must be able to solve problems in multiple ways. This is probably similar to thinking that it is important to teach creativity in mathematics in elementary school, as if such a thing were possible. Forget creativity; the truly rare student is the one who can solve straightforward problems in a straightforward way.

There will always be people who think that statistics and probability are more important than arithmetic and algebra, despite the fact that you can’t do statistics and probability without arithmetic and algebra and that you will never see a question about statistics or probability on a college placement exam, thus making statistics and probability irrelevant for college preparation.
There will always be people who think that teaching kids to “think like a mathematician,” whether they have met a mathematician or not, can be done independently of content. At present, it seems that the majority of people in power think the three pages of Mathematical Practices in Common Core, which they sometimes think is the “real” mathematics, are more important than the 75 pages of content standards, which they sometimes refer to as the “rote” mathematics. They are wrong. You learn Mathematical Practices just like the name implies; you practice mathematics with content.

There will always be people who think that teaching kids about geometric slides, flips, and turns is just as important as teaching them arithmetic. It isn’t. Ask any college math teacher.

Math wars erupted as a result of the unfocused and mostly math-less 1989 NCTM standards. NCTM rewrote those terrible standards in 2000, yet much of what mathematicians found objectionable remained in place. Only in 2005, with the publication in Notices of the AMS [American Mathematical Society] of “Reaching for Common Ground in K–12 Mathematics Education,” did the two sides make a serious attempt to bridge the chasm. NCTM followed shortly with its 2006 Curriculum Focal Points, a document that finally focused on what mathematics is all about: mathematics. Since then, NCTM seems to have regressed, as evidenced by its 2009 publication Focus in High School Mathematics, a document that is full of high-minded prose yet contains little rigor or specificity.
(The Common Core Math StandardsEducation SUMMER 2012 / VOL. 12, NO. 3Education Next talks with Ze’ev Wurman and W. Stephen Wilson)