Inside the Al Huda Institute’s Canadian chapter, the hijabis are earnest and exuberant. Get them going about their shared passion and they start speaking fast, finishing each other’s sentences and consulting their smartphones.

That passion is the Koran, and if you ask them a provocative question about it – say, “How do you reconcile conflicts between Islamic law and Canadian law?” – fingers fly in search of a scripture app.

“We all have it,” one student says, explaining how the text of all that was revealed in 7th-century Arabia is now just a few swipes on a screen away. But she can’t find her phone, so she wings it instead. “I don’t know what the verse is exactly. But it says, ‘Obey Allah, and obey the Messenger and obey those who are in power….’”

“Those who have authority over you,” corrects a friend who, like the others, is in her late 20s or early 30s.

“Unless there is injustice occurring,” someone else says a minute later. “There are always ‘ifs,’ right? But basically what we’re trying to say is that being here does not make us any less Canadian. We follow Canadian rules and laws and that’s as per the Koran.”

The mood turns sombre, however, when another subject arises. Al Huda, a female-focussed Islamic study movement with centres in Canada, the United States and Pakistan, has seen thousands of Muslim women move through its courses over the years. But last month, one of them became notorious: Tashfeen Malik, 29, was one-half of the husband-and-wife team, wielding assault rifles, who killed 14 people in San Bernardino, Calif. She had taken the Al Huda course in her native Pakistan.

Another report alleged that, separately, four students who had studied at this very centre in Mississauga, Ont., tried to make their way to Islamic State in the Middle East. No names were revealed. But one was said to have gotten through, while another three were redirected back to Canada after being intercepted by authorities overseas.

The women at the centre say they are not like Ms. Malik and don’t know anyone who wants to join a violent jihad. “To say that just because this one person passed through the doors of Al Huda … means there’s a causation … I think to make such a claim is completely absurd,” says one student. “This is not what happens at Al Huda.”

She grows adamant. “There is no problem here,” she says, “it’s just media hype.”

What does happen at Al Huda, in Canada and around the world, is this: Muslim women dive deep into the Koran – so deep that they treat study as if it were a full-time job, for up to 18 consecutive months. Many are young mothers whose husbands support them over that span.

Working in groups, they break down each verse, word for word, in unfamiliar classical Arabic, before coming up for air to discuss the larger life lessons with fellow students. This is intended to give them the mental tools to figure out, for themselves, what it means to be Muslim.

Such back-to-basics approaches to Sunni Islam are hardly unique; in fact, in Canada and globally, they appear to be gaining ground. But literalism can also be controversial – critics say it sits at a crossroads where well-intentioned fundamentalism meets disquieting zeal.

Within Islam, the Koran is indisputably the cornerstone of the faith. But different sects debate whether an overly rigid reading of it can create discord and intolerance. Some scholars warn that scripture, taken in isolation, can transport believers back to the polarizing politics of ancient Arabia, where the founders of Islam were a small band at constant risk of being wiped out by enemies.

Today there are 1.6 billion Muslims, one million of them in Canada. For a few, a self-styled caliphate in the Arab world can still exert a pull. Dozens of Canadian extremists have now been publicly accused of migrating, or trying to migrate, to the territories in Syria and Iraq now controlled by Islamic State.

The majority of the accused are male, but there have been accounts of some female travellers too – including the four Toronto women, according to the CBC. That December report came only hours after other news tied the female San Bernardino shooter to the Al Huda school in her native Pakistan. Ms. Malik enrolled in 2013 and stayed until the following year, but left the course as she got a visa to join her new husband in the United States. More than a year later, the couple went on their shooting rampage, before being killed by police.

For Al Huda, the fallout was immediate. The Canadian centre closed for a day, as administrators called upon police to protect students and their children – there is an Al Huda elementary school at the same location – from any potential Islamophobic backlash. And they say they still don’t know who the CBC is talking about.

“The institute has no knowledge as to the identity of these individuals and, as such, cannot confirm whether or not they were enrolled,” reads a statement from Al Huda Institute Canada.

The parent school in Pakistan has issued a statement saying it bears no blame for San Bernardino. “No organization can be held responsible for personal acts of any of its students,” says the Al-Huda International Welfare Foundation in Islamabad. Such violent acts, it adds, “invoke the anger of Allah Almighty.”

The Al Huda movement is the brainchild of Farhat Hashmi, a 58-year-old Pakistani. The niqab-wearing daughter of a conservative Islamic scholar, she boasts a PhD in “hadith sciences” – the sayings of the Prophet Mohammed – from the University of Glasgow in Scotland. In 1994, she launched Al Huda by teaching courses out of her Islamabad house.

Before long, Pakistan’s chattering class was buzzing about the early adopters – the well-heeled women who had never before appeared outwardly Islamic, but who walked into the Al Huda course in designer jeans and came out wearing high-end hijabs.

Ms. Hashmi insisted to the Urdu-speaking masses that the Koran is best read in its original classical Arabic. Technology helped spread the message: Al Huda’s embrace of PowerPoint was considered remarkable in the early days, but the centre now circulates its own branded Android and iPhone apps.

Transforming Faith, a 2009 book about Al Huda, profiled several graduates of the Pakistani course who said their personal metamorphosis didn’t start and stop with a head scarf. Many students said a close read of the Koran taught them to be more gentle and loving, better wives and mothers. Others talked of jettisoning electronic gear as materialist trappings – ridding themselves of CDs, DVDs, TVs and, in a few cases, even cameras (because they felt digital images were akin to idolatry).

The book also criticizes Ms. Hashmi and some of her Pakistani followers for speaking harshly about countries in the West, for describing them as sex-crazed, decadent, even “devilish” at times. “How will the positive values of love, kindness, simplicity and spending time constructively … play off against the intolerance and rigidity?” writes Sadaf Ahmad, a Pakistani professor, in the conclusion to her book.

Just over 10 years ago, Ms. Hashmi lived in suburban Toronto as she opened the Canadian chapter. This was around the time an epic earthquake killed more than 80,000 people in Pakistani Kashmir.

“The people in the area where the earthquake hit were involved in immoral activities,” Ms. Hashmi was quoted as saying at her Mississauga centre, “and God has said he will punish those who do not follow his path.”

The centre is housed in a converted laboratory-equipment factory tucked amid the plazas where Highway 401 meets Highway 403. Its focal point is a classroom where dozens of women raised in Canada gather to stumble through the Koran in Arabic, before discussing the meaning together in English.

Around this central hub radiate many amenities. There’s a prayer hall, with a wheeled partition that usually allots more spaces for females than males. There’s an adjacent Al Huda-branded kindergarten-to-Grade 6 Islamic elementary school, and a row of rooms filled with playmats and Dr. Seuss books for an affordable “child-minding service” for babies. And when it comes to kids, Al Huda administrators say they place their faith in the Montessori method of self-directed learning.

“Creating a space for women means creating a space for mothers,” says Imran Haq, the centre’s operations manager. He speaks of how the students are constantly popping out of class to change diapers.

What Al Huda teaches is not dogma, he says: Koranic passages are taught in historical context, tailored for students who grew up in Canada. The course takes more than a year, he says, because it can be time-consuming for students to break down verses into Arabic root words.

He bristles at reports that have drawn a connection between the Al Huda Institute in Canada and travellers to Islamic State. “Is there any worse slander in the world you could put on somebody right now?” he asks. He says he hasn’t the foggiest notion which past students have supposedly tried to run off to join extremists in Syria and Iraq.

But he says Al Huda is now losing traction in Canada’s Muslim community. A few parents responded to media reports by pulling their kids out of the elementary school, while even some staff members have started asking whether it would be prudent to wipe their affiliation off their LinkedIn pages.

When The Globe visited in mid-December, classes had finished for the day. There was just enough time between the afternoon and evening prayers to spend an hour in Mr. Haq’s office speaking to three women who were taking the core course, or had recently completed it.

Fearing backlash, they asked that their names not be published. Rumour had it, some fellow students were already having trouble crossing the Canada-U.S. border.

“Noor” is a 27-year-old in a peacock-blue headscarf who recently worked as a chartered financial analyst, before going on maternity leave last year. She decided to use the time to enroll in Al Huda. Now, she wonders whether she will ever go back to her day job.

“I felt like I was leading a very selfish life,” Noor explains. Focused more than ever on God and family, she has convinced her mother to take classes too. “My mom is coming with me everyday,” she says, adding that her one-year-old daughter is spending the day there as well.

“Aisha,” also 27, introduces herself as an expectant mother pursuing a PhD in psychology. She points to the verses underpinning her decision to wear a floral hijab. You need to read each verse in context, she says, arguing that people who criticize Islam for female modesty should study the verses about male modesty too.

“It says for the believing men to ‘lower their gaze’ … so that’s basically their way of covering,” Aisha says. She adds that “a Muslim man can’t be walking around in a Speedo.”

As for women, the Koran says to “draw your veils over your chest,” but there is no consensus on which specific kinds of garments, she says. As she speaks, several niqabis – women wearing fuller face coverings, though colourful ones – chat in a cluster in the prayer hall. A toddler runs around there in a veil too, which seems unusual – the head scarf more typically arrives on a young girl’s head with the onset of puberty.

This is the daughter of “Miryam,” who says her two-year-old is playing dressup. “I don’t tell her to wear it,” she says. “She actually sees me, and she has been asking me for months and months and months: ‘Can I please have one, like you? … It’s her first day that she is wearing those clothes.”

Miryam, 30, wears a peach-coloured hijab, and putting the garment on was no small matter for her. She hails from a Hindu family who immigrated to Canada from Sri Lanka. Her conversion estranged her from her family for years.

That was all before she joined Al Huda, and she credits the course with giving her the self-confidence to successfully reboot relations. “I spoke directly to my dad and I told him: ‘This is what I learned, this is how I feel, this is not any kind of judgment against you. I’m not saying that you’re going to hell – I’m not saying that, I’m saying this is what is working for me.’”

The women say they know nothing about anyone in Canada leaving for war zones. They say they came to the centre seeking a spiritual reawakening – not a jumping-off point to a religious utopia.

“There is no ideal Islamic state. Where would I go?” Miryam says, adding: “There is no ideal Muslim state that exists in the world in the way that it did at the time of the Prophet, at the time that it did when Islam was really flourishing.”