Interesting article.
Ms. Bialystok’s research shows that bilingual children tend to have smaller vocabularies in English than their monolingual counterparts, and that the limited vocabulary tends to be words used at home (spatula and squash) rather than words used at school (astronaut, rectangle). The measurement of vocabulary is always in one language: a bilingual child’s collective vocabulary from both languages will probably be larger.
I haven't seen this with FI DD9, although it's impossible to measure, really... how do we know what her English vocab would have been if she'd been in an English program? Her English vocab has never been tested against her English-stream age peers. She'll ask her brother sometimes "do you even know what that means?" and when she explains it to him, 9 times out of 10 she's right.
FI (and language disorder) DS8 interestingly seems somewhat ok as well, although it's safe to assume there's a deficit. He has other language deficits involving pronunciation and sequencing, but strangely his grammar seems ok, and he uses a reasonable variety of English words.
On a related note, though... I remember I was at the school one day and overheard a grade 4 boy in the FI program who needed help to spell "school." I was stunned. FI DD was 6 and in grade 2 at the time and could have spelled it for him.
At the same time, bilingual children do better at complex tasks like isolating information presented in confusing ways. ... a fact researchers attribute to a more developed prefrontal cortex (the part of the brain responsible for executive decision-making, like which language to use with certain people).
This is a benefit also mentioned by our psychologist.
I think, as far as vocab is concerned, what and how much a child reads outside of school, as well as the way language is used by their parents, is going to have an impact regardless of which program they're in.
Re: home time Vs. school: My husband has very poor grammar. He says things like "you don't want nothing?"
I make a point of taking this literally and pointing it out to my kids. "I don't want no broccoli" ...results in broccoli being served. Both kids think it's funny, and even my language disorder son has better grammar than is dad.
“The flexibility of their thinking helps them in nonlinguistic abilities like science and math,”
Three of the four kids in DD's gifted math program are from the French side of the school, and DS8's best marks were in math and science 
On a related note, DH was English-only at school and he has the worst vocabulary I've ever encountered. It's shockingly bad (for example, he'd never heard of the word "introvert" and thought I'd made it up). He's very mechanical and is clever with formulas and math - in fact he scored higher than one of the company engineers on a recent test at work, but his language skills are in the toilet.
I think that acquiring multiple languages definitely shapes cognitive development, but the aptitudes the child was born with have a big influence on the outcome.
