It's difficult to argue with the thesis of the book that mathematics should be taught in a more holistic way, focused on real-world problems, and helping pupils to make connections and to verbalise their thinking, rather than as a purely formal or rote exercise where pupils don't have any real idea what they're doing. So much so, in fact, that I thought this was a bit of a straw-man argument, as no maths teacher worth their salt would be opposed to such an approach on principle.
I was increasingly frustrated by several aspects of Boaler's argument, which I'll sketch here as others may find it useful. Firstly, her rather cosmopolitan worldview, which she shares, quite ironically, with her bete noire in this book, the former UK Education Secretary Michael Gove. The idea that teaching practices can simply be transplanted from one country (e.g. South Korea, Japan) and used in another (the UK, the USA) absent any discussion of background culture and history of public education in those countries is debatable, to say the least.
Much of the book seems to bemoan the fact that the educational culture in the USA is not what it is Boaler's preferred contexts. That may be true, but, absent a complete shift in social attitudes and educational priorities, it's not at all clear what the point being made here is. It would have been more useful for Boaler to sketch a road-map for piecemeal educational reform, but none appears in the book. Instead all we get is her final cry of "Viva la Revolution!" which, while no doubt tongue-in-cheek, exposes the flaw in her argument.
Secondly, Boaler's approach seemed to be geared towards more extroverted learners. Getting students to talk about their thinking is useful and can help with mathematical cognition. But I was left with a lingering suspicion that students who are more introverted, and just want to be left alone to get on with maths work and figure things out for themselves, would be quickly frustrated with her approach and even come to regard maths classes as a waste of time. For someone apparently sensitive to the plurality of ways of learning, I thought her approach was remarkably 'one size fits all'. There's also a question of how to manage group dynamics in a classroom, which could be very demanding. Boaler touches on this but, again, there isn't much detail.
Thirdly, I thought her remarks on gendered learning were rather odd. She makes the argument that girls seem to be more philosophical than boys, as the former want to understand the conceptual background to maths and stop to ask more profound questions, while the latter just get on with the task at hand. While I found it fairly amusing that, under Boaler's categories, from my own school experience I tended towards the more 'female' end of the spectrum, I think this highlights that if this difference does exist, then it's more of a spectrum than a sharp division. And it's not clear what we should do about it, practically speaking, other than run different maths classes for different genders, which would be hugely problematic for all kinds of social and moral reasons.
Overall, it's an interesting, well-written book and contains a lot of good resources. It could be that some or all of the points I've raised here are dealt with in more detail on her website or in her other research and publications. But the book itself is more a work of advocacy rather than a balanced analysis. While there's nothing wrong with that, it doesn't really consider the broader questions or make any fine-grained policy proposals, and therefore is limited on its own terms.