Mathematicians can definitely be opinionated, but a lot of the problem lies elsewhere. The "suspicion of empirical methods in the social science" is actually pretty well justified, for example the recent replication studies flap in psychology.
In education, I haven't seen any studies showing a marked superiority of a particular teaching method. Sometimes a new idea shows promise, but the effects evaporate when someone else tries it. So Boaler's results were enormously surprising, and it was reasonable to ask for verification. And then it turned into ugly politics.
You might be interested in skimming the following paper:
njrp.tamu.edu/2004/PDFs/Collier.pdf
This is a entry-level paper investigating dual-language instruction. These researchers are looking at student outcomes and how dual-language instruction improves those outcomes more than other approaches. It's also not particularly advocating an instructional method that the researchers are claiming ownership of.
The abstract:
"Our longitudinal research findings from one-way and two-way dual language enrichment models of schooling demonstrate the substantial power of this program for enhancing student outcomes and fully closing the achievement gap in second language (L2). Effect sizes for dual language are very large compared to other programs for English learners (ELLs). Dual language schooling also can transform the experience of teachers, administrators, and parents into an inclusive and supportive school community for all. Our research findings of the past 18 years are summarized here, with focus on ELLs’ outcomes in one-way and two-way, 50:50 and 90:10, dual language models, including heritage language programs for students of bilingual and bicultural ancestry who are more proficient in English than in their heritage language."
More germane to this discussion, in the paper there are links where the methodology, data collection, and data analysis are discussed in-depth. The authors also call for more specific and follow-up research on "program evaluation research, to refine what particular forms of dual language programs are most effective."
The TL;DR results: "Enrichment dual language schooling closes the academic achievement gap in L2 and in first language (L1) students initially below grade level, and for all categories of students participating in this program."
That's a pretty bold claim, that dual language instruction can bring below grade level student test performance up even for native language speakers.
If we can isolate pedagogies or aspects of dual language instruction that lead to better student outcomes, it would be nice if those approaches could be used in math education.
Thanks for the link. It seems like the bold claim is supported by a ton of data, as it should be. If this was what Boaler was offering, I think she would have a much stronger case. I skimmed some of the papers on Boaler's site as well, and they are almost completely unlike this one. They are full of anecdotes and quotes from students and very little data. To be fair, her study that is cited her later papers is not available on her web page so I have not read it.
Look at applications of Sweller's theory of cognitive load. Suspicion of methods of social science in contested areas doesn't justify coming to any conclusion whatsoever on empirical matters of social science in general.
In education, I haven't seen any studies showing a marked superiority of a particular teaching method. Sometimes a new idea shows promise, but the effects evaporate when someone else tries it. So Boaler's results were enormously surprising, and it was reasonable to ask for verification. And then it turned into ugly politics.