# Big drop in math skills of entering students

#### On that point there’s no argument, but educators don’t agree about how much it matters.

Deteriorating math skills among high school graduates is not just a North American phenomenon, experts say. |

The math skills of students entering Canadian universities have declined sharply in recent years, with many students unable to do basic arithmetic. Whether this is a learning crisis with dire implications for Canada’s citizenry and its future science and engineering base or simply an inevitable result of the ubiquity of calculators and computers is a matter of debate.

The deterioration of math skills is apparent across North American, says Brenda Smith-Chant, a psychology professor at Trent University who specializes in the development of mathematical cognition. And it’s not merely a matter of students being unable to handle trigonometry or algebra, she says. “Even basic arithmetic is throwing them, and we’re talking about adding three two-digit numbers.”

Dr. Smith-Chant says that students’ deficiency in math is affecting their course choices and educational paths. For example, many psychology students decide to leave the field because they’re put off by the requirement to take a statistics course.

For the past 20 years, Carleton University psychology professor Jo-Anne LeFevre has been researching how well first- and second-year students solve simple arithmetic problems, such as adding 25+73+16. She has seen a marked decline in paper-and-pencil computation skills. In 1990, students were solving an average of 80 problems in a set time period; 15 years later that had dropped to an average of 60. “It’s a significant change, statistically,” she concludes.

Dr. Smith-Chant, for her part, has seen a similar decline, using similar methodology. In 1984, first-year psychology students answered an average of 80 questions correctly. In 2004, the number had dropped to 73 correct answers, and last year it was 56.

While most educators agree that numeracy has declined, there’s no consensus on how much it matters. Some argue that in an age of calculators, people don’t need basic skills to acquire higher level mathematical knowledge and that it’s more valuable for students to spend their time learning larger concepts.

But others say that the more fluent you are in the basics, the more easily you can grasp more advanced math. Sherry Mantyka, a professor of mathematics and statistics at Memorial University and director of the mathematics learning centre, has spent years helping students improve their core math skills. In a controlled experiment several years ago, Dr. Mantyka and a psychology researcher found that students who didn’t know basic numerical facts and numeric processes were disadvantaged when grappling with more complex math problems. “Their working memory was insufficient and they would start making mistakes,” she says. She adds that the need for remedial math courses at Memorial “seems to be getting worse,” with about 500 first-year students requiring remedial math in each of the last five years.

Many observers say this erosion in basic computation skills is a result of the mathematical reform movement spearheaded by the National Council of Teachers of Mathematics (NCTM) about two decades ago. This philosophical shift in math pedagogy to emphasizing conceptual thinking from what some saw as rote memorization brought about curriculum change across North America.

Now, many are seeing unintended consequences. Robert Mann, a professor of physics and applied mathematics at the University of Waterloo and president of the Canadian Association of Physicists, hears concerns about math skills from colleagues across a number of disciplines including economics, math, physics and chemistry. In his own classes he has found that, a decade ago, students were strong in technique and weaker at grasping concepts, but that has almost reversed. “Now, they know what to do but they don’t know how to do it,” he says.

“The changes [in teaching approach] paid off in one way but they also had this alternative impact that we didn’t really expect,” he says. “I think pedagogically teachers at all levels are not really comfortable with how to teach in the computer or calculator age.”

Gordon Robinson, a biologist at the University of Manitoba, believes that the level of math skill being seen at universities across Canada is of widespread concern. “I think the answer you would get from anybody who teaches first-year math at a university is that they are just aghast at the quality of the students they are having to deal with. We’re talking baby calculus, not rocket science.”

The deterioration of math skills is far from just a Canadian or North American phenomenon. “There have been a number of wide-ranging studies out of OECD countries that have found that preparedness for math in postsecondary education is really bad and it’s getting worse,” says Dr. Robinson.

So how is it, then, that Canada ranks highly in math in the international Program for International Student Assessment (PISA), which compares skills of 15-year-old students in OECD countries? In the most recent scores for math assessment, administered every three years, Canada placed fifth out of 30 OECD countries.

That’s because, say Drs. Mantyka and Smith-Chant, the PISA tests “math literacy” or how to apply math knowledge in the real world, and there is no correlation between “math literacy” and the level of basic math fluency found in students entering university.

In fact, the leading Aalto University School of Science and Technology in Finland, the country that came first in math under PISA, recently sought Dr. Mantyka’s advice after noticing that Finnish students are entering university with weaker math skills than expected. Dr. Mantyka is now collaborating with the Finns on developing remedial programs and has joined them in an on-line remedial software project for the European Union.

While the debate continues about the importance of numeracy, researchers in the field aren’t ready to concede that the need to perform math in our heads has become obsolete. Dr. Smith-Chant says the lack of math skills may have even contributed to the recent recession in North America, with people getting themselves into risky financial situations, including mortgages with ballooning payments, because they didn’t understand how interest rates work.

Dr. Mantyka agrees. “How can you make a sensible decision about a mortgage or your ability to pay back that mortgage if you have no ability to work with percents, other than punching numbers on a calculator and hoping you get the decimal in the right place? Yes, it’s very scary.”

**Want to know more? Alan Slavin poses the question that sparked this news story:** **Has Ontario taught its high-school students not to think?**