A group of girls just one week away from starting Grade 10 giggled over tea and cupcakes Monday morning in a small second-floor apartment. Rather than whiling away their last hours of summer freedom, the teenagers were getting a jump start on the school year at a math bootcamp.

Mathematical knowledge fades with disuse over the summer holidays. This can be problematic as math concepts are cumulative and teachers often struggle to find enough time for review. Tutoring services are responding by introducing back-to-school review sessions.

"No one wants to do badly at math, but they don't know where to start so it's easier to just say, 'Math sucks,' " said Vanessa Vakharia, founder and director of The Math Guru, the Toronto tutoring service that offered the bootcamp for the first time this year.

Tutors, parents and students are finding that a shaky foundation can make math grades tumble, and by the time fall report cards are sent home it's already too late.

Math Tutor Network, another small tutoring service based in Vancouver, also introduced back-to-school reviews this year. Henry Chow, the service's director, says that he often sees parents expecting a turnaround after they sign their children up for tutoring mid-year.

"In math you build from one concept to the other," he said. "If they miss a concept [early in the school year], it's going to be a huge uphill battle for them."

Mr. Chow started his tutoring company just two years ago, and it has grown rapidly to include close to 100 students. Ms. Vakharia has also seen a rapid rise in enrolment. Since she started tutoring full time in September, 2010, her business has grown to include six full-time tutors and about 150 students.

Both describe an alarming number of smart kids who are convinced they can't do math. A widely held belief that humanity can be divided into those who can do math and those who can't leaves students vulnerable to a single failure or a bad teacher.

They have a crisis of confidence and give up.

That's what happened to Shayne Stilman, who two years ago as she started Grade 10, was getting marks in the 60s and counting the days until she could drop math forever.

"I would sit in my room and have meltdowns," she said. "I'd be staring at a math textbook without any idea what to do."

Now, after two years of one-on-one tutoring at The Math Guru, she's getting As in math and aiming to get 90s in her Grade 12 calculus and vectors courses at Lawrence Park Collegiate. She says in hindsight she had been paralyzed by her fear of math – it made her reluctant to do her homework and shook her confidence on exams.

Ms. Vakharia says it's no surprise that so many smart teens like Shayne are convinced to give up. She points to shirts marketed to teenagers by major vendors such as Forever 21 and JC Penny that read "Allergic to Algebra" and "Math Sucks" as evidence the problem has more to do with culture than IQ.

It's a frustration that plagues math teachers at every level, according to Harley Weston, a retired University of Regina professor of mathematics and coordinator of the Canadian Mathematical Society's summer camps.

"You never hear anybody say they can't read, but somehow it's socially acceptable to say you're no good at math," he said.

The consensus is that math education needs a makeover, but there is little agreement over what that should look like. In Canada, the debate has centred around real-world applications and conceptual learning versus foundation-building drills, but Ms. Vakharia takes a different approach.

She has turned her apartment into a sort of math café where she serves baked goods and tea lattes. Students work at a hodgepodge of vintage-style café tables and she has covered her apartment with whiteboard paint so that students can write equations on the walls.

One of her staff members has 13 math-themed tattoos, and another uses an arsenal of foreign accents to make his students laugh.

"We try to embody the notion that it's not a binary thing, that you're not either cool or you do math," Ms. Vakharia said. "It's a switch in thinking."