With half of students failing or quitting, university calculus hitting Manitobans 'like a ton of bricks'

Manitoba students are so unprepared for university calculus that half of them are either failing the first-year class or withdrawing long before the final exam takes place.

And how well they did in high school pre-calculus doesn't seem to indicate whether they'll succeed in university calculus.

Darja Barr, a University of Manitoba math professor, analyzed 15 years of marks for students who took pre-calculus in a Grade 12 Manitoba classroom and introductory calculus at her university. 

She found high school grades were a poor indicator of future success, which she said is disturbing, since Grade 12 pre-calculus is designed to prepare students for university calculus. 

"It really does hit students like a ton of bricks when they get to university," Barr said.

In the last year of her study, she found high-achieving students in one Winnipeg school division — who earned an A or A+ in pre-calculus — were as likely to fail calculus in university as they were to earn another A or A+.

A professor for 13 years, Barr knows it's common for A students in high school to drop one grade point when they enter post-secondary.

Students baffled

But too many students in her classes are barely treading water — and she argues Manitoba's education system deserves some of the blame.

"I want to figure out why the disconnect is happening," said Barr, who turned her research into a PhD thesis in education this year.

"I would have students come to me after a midterm and say, 'I don't understand what's happening. I got 90s in high school.'"

Barr's work aligns with other Canadian research showing deteriorating math scores countrywide. Students also struggle in other subjects, but the problem is most pronounced in mathematics and the sciences, she said. 

In response to her own research, Barr asked the commission reviewing Manitoba's kindergarten-to-Grade-12 school system to improve the pre-calculus curriculum so students are prepared to continue their math education.

She worries the status quo is discouraging people from careers in mathematics and the sciences.

Barr analyzed the grades of more than 12,000 students who took first-year introductory calculus at the U of M from 2001 to 2015, excluding students who voluntarily withdrew from the class and who did not go to high school in Manitoba.

She found the percentage of students with a final grade of C or better went to around 50 per cent of the class in 2015, from 65-70 per cent of students five years earlier.

Her data shows students who scored well in calculus also did well in pre-calculus. However, there was no correlation between students who struggled in university math and their previous pre-calculus mark.

In fact, students with good grades in pre-calculus (4.5 GPA) were almost as likely to fail as students with poorer grades (2 GPA).

"I'm teaching calculus and seeing such high failure and withdrawal rates; it's very clear that the problem is a big problem," Barr said.

Since calculus builds upon a student's previous knowledge in math, it is obvious the province's education system isn't adequately preparing students for university, she said. 

Barr argues curriculum changes have made high school math worse; for example, the topic of conic sections has been removed from pre-calculus when it's considered a prerequisite for most first-year calculus courses.

More standardized tests are needed to gauge where students are at, she also said. 

School divisions and teachers realize there's a problem, Barr said. 

Her findings were concerning enough to the Winnipeg School Division that their math teachers met with Barr and other university math professors, said program lead Thomas Locke, who was previously the division's grades 7-12 math consultant.

School division representatives sat in on a university calculus class, he said. 

"The ideas the students need for success in calculus, we felt, were within the [high school] curriculum. They weren't necessarily in the best order, though," he said.

Lagging behind

Anna Stokke, co-founder of WISE Math, a numeracy advocacy group, said Barr's findings are in line with what she already knew. She's seen it first-hand as the head of the University of Winnipeg's math department.

Curriculum changes in the last few decades have delayed the teaching of essential subjects, such as adding fractions, she said.

"The thing with math is, you need a lot of practice to get good at it," she said.

"If our students are seeing things two or three grades later than they should be, it's going to affect where they're at by Grade 12."

Like Barr, she's optimistic the province's education review will improve the teaching of math.

In the latest Programme for International Student Assessment, the province's 15-year-olds scored dead last in math in comparison to their Canadian peers, Stokke said. 

"Most people do recognize that there is a problem."

The Manitoba government said the province isn't considering changes to the math curriculum, but the kindergarten to Grade 12 commission may make recommendations. 

Barr's research doesn't compare other faculties or post-secondary institutions, the province said in a statement.

"Although the study shows a decline in students' averages over a decade, it does not establish a long-term pattern that is different from what is already known — that calculus has always been a challenging course with a high dropout rate."