A good reality check on several of the assertions made in the article, or in the comments here, about Finland is to look at another country high in international educational rankings, namely Singapore. I have known people from Singapore (mostly students at my state's flagship university) since the mid-1970s. Always, they have been amazingly smart people. I have been curious about how schooling is done in Singapore since well before the first time that Singapore was included in an international education study.

Chapter 1: "International Student Achievement in Mathematics" from the TIMSS 2007 study of mathematics achievement in many different countries includes, in Exhibit 1.1 (pages 34 and 35)

http://pirls.bc.edu/timss2007/PDF/T07_M_IR_Chapter1.pdf

a chart of mathematics achievement levels in various countries. Although the United States is above the international average score among the countries surveyed, as we would expect from the level of economic development in the United States, the United States is well below the top country listed, which is Singapore. An average United States student is at the bottom quartile level for Singapore, or from another point of view, a top quartile student in the United States is only at the level of an average student in Singapore. I have lived for years in one of the other countries that regularly outperforms the United States in those studies, Taiwan, and will also comment on the Taiwan educational experience as a reality check on the comments on Finland in this thread.

I am amazed that persons from Singapore in my generation (born in the late 1950s) grew up in a country that was extremely poor (it's hard to remember that about Singapore, but until the 1970s Singapore was definitely part of the Third World) and were educated in a foreign language (the language of schooling in Singapore has long been English, but the home languages of most Singaporeans are south Chinese languages like my wife's native Hokkien or Austronesian languages like Malay or Indian languages like Tamil) and yet received very thorough instruction in mathematics. Singapore is very diverse linguistically--the MAJORITY of the population in my generation spoke NONE of the four official languages (Mandarin Chinese, Malay, Tamil, or English) in standard form at home, and certainly not the main language of school instruction, English, but Singapore has become part of the "outer circle" of use of English internationally and now maintains a high degree of multilingualism. I hope that all of us here in the United States can do at least that well both in language learning and in mathematics learning in the current generation.

The article "The Singaporean Mathematics Curriculum: Connections to TIMSS"

http://www.merga.net.au/documents/RP182006.pdf

by a Singaporean author explains some of the background to the Singapore math materials and how they approach topics that are foundational for later mathematics study. The key aspect of Singapore's success is a MUCH better curriculum in primary school mathematics than is used in the United States. Homeschoolers in the United States, including quite a few parents of top-scoring students on the American Mathematics Competitions tests, have become aware of the Singapore curriculum materials,

http://www.singaporemath.com/Primary_Mathematics_Stds_Ed_s/1...

and those are generally helpful for American families who are looking for something better than the poorly organized, often mathematically incorrect materials used in United States schools.

Professor Hung-hsi Wu of the University of California--Berkeley has written about what needs to be reformed in United States mathematics education.

http://math.berkeley.edu/~wu/Lisbon2010_4.pdf

http://math.berkeley.edu/~wu/Lisbon2010_2.pdf

http://math.berkeley.edu/~wu/NCTM2010.pdf

http://math.berkeley.edu/~wu/NoticesAMS2011.pdf

http://math.berkeley.edu/~wu/CommonCoreIV.pdf

Other mathematicians who have written interesting articles about mathematics education reform in the United States include Richard Askey,

http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf

http://www.math.wisc.edu/~askey/ask-gian.pdf

Roger E. Howe,

http://www.ams.org/notices/199908/rev-howe.pdf

Patricia Kenschaft,

http://www.ams.org/notices/200502/fea-kenschaft.pdf

and

James Milgram.

ftp://math.stanford.edu/pub/papers/milgram/milgram-msri.pdf

ftp://math.stanford.edu/pub/papers/milgram/report-on-cmp.html

All those mathematicians think that the United States could do much better than it does in teaching elementary mathematics in the public school system. I think so too after living in Taiwan twice in my adult life (January 1982 through February 1985, and December 1998 through July 2001). I have seen (and used) the textbooks from Singapore and from Taiwan. They are much more clear in their presentation and much more conceptually accurate than the typical United States textbooks. Moreover, elementary mathematics teachers tend to specialize in teaching mathematics while other elementary teachers teach other subjects, at much younger ages than when United States pupils typically encounter specialist teachers. The United States model of elementary education is to have teachers who are jacks of all trades and masters of none, and who do equally poorly (by reasonable international standards) in teaching reading, mathematics, science, and all other elementary subjects.

The United States could do a lot better and reach the level of Finland by staffing reforms

http://edpro.stanford.edu/hanushek/admin/pages/files/uploads...

and by using best practices

http://www.amazon.com/Teaching-Gap-Improving-Education-Class...

in provision of elementary education.