What I hate about this article is the way that it plays on American parents' educational anxiety, implying that these very mild linguistic effects on cognition may impair Anglophone children relative to Asian children unless American parents invest in all these educational board games. The article specifically frames it as a problem of English linguistic deficiencies, which is incredibly naive. With math, children are essentially learning a new and unfamiliar symbolic language.
All of these correlations between language and cognition are interesting, but if you're interested in Sapir-Whorf, you're still looking at overall effects that are weak and small, overall. This correlation between linguistic/mathematical behavior may be stronger in a language like Piraha, but Daniel Everett would argue that what's going on there is less linguistic determinism and more of a cultural bias against the abstract or non-concrete. http://www.slate.com/blogs/lexicon_valley/2013/10/16/piraha_...
And look here at this paragraph in the OP: "The U.S.-Asian math-achievement gap—a sensitive and much-studied topic—has more complicated roots than language. Chinese teachers typically spend more time explaining math concepts and getting students involved in working on difficult problems. In the home, Chinese parents tend to spend more time teaching arithmetic facts and games and using numbers in daily life, says a 2010 study in the Review of Educational Research by researchers at the Hong Kong Institute of Education and the University of Hong Kong." Yet overall outcomes are taken as evidence of English's "linguistic disadvantages".
East Asian languages DO handle base-10 math in a simple, direct way that is easy to learn. This is especially true in Chinese, but begins to fall apart in Japanese. Japanese uses simpler words for higher numbers: ni-juu-hachi (two-ten-eight) for 28, for example. But Japanese also has two series of words for numbers under 10: 1 may be ichi or hitotsu, 2 may be ni or futatsu. These combine with a large series of counter words that makes counting in Japanese much more complex. Might this impact Japanese children's acquisition of numeracy? Plausibly, but it's easier to just elide over the differences in Asian languages handling of numbers.
There are just a plethora of linguistic differences between Asian languages and English, that necessarily impact education. Take the writing system, where Japanese has probably the most complex written system in the world, that takes over a decade to read proficiently even for native speakers. English has a terrible orthography, whose irregularities and inconsistencies make it difficult for children to learn and exacerbate economic inequality and linguistic privilege.
We really could spend a lot less classroom time on learning reading and writing the differences between plough, dough, and cough and more time on STEM if we improved the English orthography, but I don't exactly see the WSJ reporters calling for spelling reform =/ http://www.theatlantic.com/education/archive/2015/02/how-the...