OP references an article by Elizabeth Green about Japanese math instruction and how wonderful it it. To put in a counterpoint, consider the following paper which completely refutes the Green article: http://www.brookings.edu/research/papers/2014/08/07-new-york-times-math-loveless.
If you don't want to read the whole article, here's a summary (taken from the article). Japan does score better than the US in math scores, which she attributes to the difference in the public schools instruction technique, but her argument is flawed in several important ways:
1) Green argues that Factors Outside School Are Unimportant to Japanese Math Success.
There is no discussion of Japanese parents drilling children in math at home or of the popularity of Kumon centers that focus on basic skills. And juku gets not a single mention in Green’s article. Juku, commonly known as “cram school,” is the private, after-school instruction that most Japanese students receive, especially during middle school as they prepare for high school entrance exams. Jukus are famous for focusing on basic skills, drill and practice, and memorization. Japanese public schools have the luxury of off-loading these instructional burdens to jukus.
2) American Kids Hate Math, Japanese Kids Love It.
Green’s article depicts American math classrooms as boring, unhappy places and Japanese classrooms as vibrant and filled with joy. She cites no data other than her own impressions from classroom observations and the assertions of advocates of reform-oriented instruction.
It is odd that she didn’t examine the Program for International Assessment (PISA) or TIMSS data on enjoyment because both assessments routinely survey students from randomly-sampled classrooms and ask whether they enjoy learning mathematics. American students consistently report enjoying math more than Japanese students. In response to the statement, “I look forward to my mathematics lessons,” posed on PISA, the percentage of U.S. 15-year-olds agreeing in 2012 was 45.4%, compared to 33.7% in Japan. To the prompt, “I do mathematics because I enjoy it,” the percentage agreeing was 36.6% in the U.S. and 30.8% in Japan. The differences between countries are statistically significant.
3) The History of International Test Scores Supports Math Reform.
Japanese and American math scores are headed in opposite directions, but the trend is not what you’d guess after reading the New York Times article. Japan’s scores are going down, and U.S. scores are going up.
If the scores on international test scores are converted to standard deviation units (SD), Japan scored 0.9 SD higher than the U.S (all scores in this section refer to eighth grade) in 1964. Jump ahead about five decades. On the 2011 TIMSS, Japan still outscored the U.S., but by a smaller amount: 0.61 SD. Most of the narrowing occurred after 1995. From 1995 to 2011, the average scale score for Japan’s eighth graders fell 11 points (from 581 to 570) while the U.S. eighth graders gained 17 points (from 492 to 509). Japan’s decline and the U.S.’s increase are both statistically significant.
4) The Failure of 1990s Math Reform was the Failure to Change Teaching.
Green holds up the 1985 California math framework as an example of that era’s push towards “teaching for understanding.” The 1985 and 1992 California math frameworks were indeed crowning achievements of progressive math reformers, but as new textbooks and programs began trickling into schools, a coalition of parents and mathematicians arose in vehement opposition.
The notion that classroom teachers’ blind devotion to procedures or memorization led to the failure of 1990s math reform in the U.S. is ahistorical. Indeed, Green cites no historical accounts of that period to support the claim. Moreover, the suggestion that teachers were left on their own to figure out how to change their teaching is inaccurate. Throughout the 1990s, the NCTM standards were used as a template for the development of standards and assessments in states across the land. Education school professors in the late 1990s overwhelmingly supported math reform.
Contrary to Elizabeth Green’s account, history shows that math reform movements have repeatedly failed not because of stubborn teachers who cling to tired, old practices but because the reforms have been—there are no other words for it—just bad ideas.[1]
1 - http://www.csun.edu/~vcmth00m/AHistory.html and http://www.amazon.com/The-Schools-We-Need-Dont/dp/0385495242.
The OP is also wrong about constructivist learning methods versus tradional methods. See Paul A. Kirschner, John Sweller, and Richard E. Clark. “Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential and Inquiry-Based Teaching.” Educational Psychologist. 2006. That review shows a balanced approach works best.