Alex Reinhart

The more important difference between mathematics education in Japan and mathematics education in (say) the United States is how hard the problems are and the encouragement to pupils in Japan to try to figure things out for themselves.

I put instructional methodologies to the test by teaching supplemental mathematics courses to elementary-age pupils willing to take on a prealgebra-level course at that age. My pupils' families come from multiple countries in Asia, Europe, Africa, and the Caribbean Islands. (Oh, families from all over the United States also enroll in my classes. See my user profile for more specifics.) Simply by benefit of a better-designed set of instructional materials (formerly English translations of Russian textbooks, with reference to the Singapore textbooks, and now the Prealgebra textbook from the Art of Problem Solving),

http://www.artofproblemsolving.com/Store/viewitem.php?item=prealgebra

the pupils in my classes can make big jumps in mathematics level (as verified by various standardized tests they take in their schools of regular enrollment, and by their participation in the AMC mathematics tests) and gains in confidence and delight in solving unfamiliar problems. More schools in the United States could do this, if only they would. The experience of Singapore shows that a rethinking of the entire national education system is desirable for best results,

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

but an immediate implementation of the best…

I keep a notebook with a list of references on pedagogy, including active learning:

https://www.refsmmat.com/notebooks/pedagogy.html

The Peer Instruction section features a great deal of research in introductory physics courses, where well-implemented active learning methods can double or triple student learning of core concepts. (I also blogged about this research long ago: https://www.refsmmat.com/posts/2012-10-19-shutup.html)

Students in intro physics classes tend to memorize the formulas but don't have any conceptual understanding, and active learning seems to dramatically improve the conceptual understanding without harming the ability to solve typical calculate-the-force problems.

Happy to discuss or send PDFs if you're not able to obtain them. My email is in my profile.

One of the best articles covering this issues is Meehl[1][2]. You can find discussion in various places like Gelman[3] and Reinhart[4].

[1] Meehl, Paul E (1990). Why summaries of research on psychological theories are often uninterpretable. Psychological Reports, 66(1), 195–244.

[2] http://meehl.umn.edu/files/144whysummariespdf

[3] http://andrewgelman.com/2015/03/23/paul-meehl-continues-boss/

[4] https://www.refsmmat.com/notebooks/meehl.html