Complex mathematics isn’t for everyone (but maybe it should be)

by Marilyn Achiron
Editor, Directorate for Education and Skills

Put a complicated algebraic equation or geometry problem in front of a 15-year-old student (or, for that matter, just about anyone) and you can almost see the brain at work: I. Can’t. Do.This.

Most of us have found ourselves in this situation at one point or another. But many students, particularly students from disadvantaged backgrounds, have never seen these kinds of mathematics problems; their teachers have decided they’re not up to the challenge.  Some might call these students “lucky”; but this month’s PISA in Focus argues otherwise.

Results from PISA 2012 show that while weaker students report higher anxiety when confronted with complex mathematics problems, if their teachers work with them individually, without “dumbing down” the mathematics lesson, these students tend to develop more positive beliefs in their own abilities to solve mathematics problems.

PISA 2012 finds that, on average across OECD countries, about 70% of students attend schools where teachers believe that it is best to adapt academic standards to students’ capacities and needs. Teachers in disadvantaged schools are more likely than those in advantaged schools to agree that the content of instruction should be adapted to what students can do. In Germany, for example, 51% of principals of disadvantaged schools reported that teachers are willing to adapt their standards, while only 13% of principals of advantaged schools reported so.

Most of these teachers choose to adapt their instruction to their students’ abilities because they want to be sure that all students can follow the lessons. But differentiating course content, based on students’ abilities, could deny low achievers access to the same learning opportunities that their higher-achieving peers enjoy. And that, in turn, could lead to the same kind of segregation of low-performing students that is the usual result of early tracking or grade repetition.

The best way to avoid this outcome is to offer struggling students individual support so that they can “catch up” with the rest of the class – and gain some self-confidence along the way. If teachers believe that some differentiation is necessary, they can opt to use teaching methods that do not segregate weak students further, such as making students work in groups that are frequently reconfigured on the basis of students’ needs and progress.

We may not all be born mathematicians, but we all need to learn how to work hard and persevere to achieve our goals – whether those are solving difficult equations or writing a novel or repairing a car engine. We all need to be challenged – and we all, from time to time, need guidance and support from teachers who can help us meet those challenges.

Links:
PISA in Focus No. 65: Should all students be taught complex mathematics? by Mario Piacentini
Equations and Inequalities: Making Mathematics Accessible to All
Find out more about PISA:oecd.org/edu/pisa
Photo credit:  Male teacher writing various high school maths and science formula on whiteboard@Shutterstock