Every few years, the Organisation for Economic Development (OECD) assesses the mathematics level of hundreds of thousands of students around the world. In 2000, when the first tests were held, Australia ranked 6th for maths. In the most recent results, we had dropped to 19th. Here's why we need to be literate in maths, and why our failure to do so is spelling bad news for our careers, life choices -- and even our mental health.
Of all the primary academic subjects, mathematics causes the most stress and trepidation. Many students are genuinely terrified of maths, a sentiment driven by a culture that's consistently trying to convince us that maths is hard, or that it's useless.
But as we head deeper into a knowledge-based economy, and as our personal and professional lives become increasingly dependent on our ability to comprehend and process numbers, it's becoming increasingly imperative for us to have at least a rudimentary knowledge of maths.
More Than Just "School Maths"
Maths literacy, also called numeracy, doesn't imply proficiency in some of the more advanced areas of mathematics, like calculus or trigonometry. Rather, it describes the knowledge and skills required to effectively manage the mathematical demands of diverse situations. Numeracy doesn't require the knowledge of "school mathematics," but rather a minimal level of competency required to grasp and handle numbers.
The Organisation for Economic Cooperation and Development (OECD) offers a more precise definition, but one with a similar message. Numeracy is defined as:
an individual's capacity to identify and understand the role that mathematics play in the world, to make well-founded judgements and to use and engage with mathematics in ways that meet the needs of that individual's life as a constructive, concerned and reflective citizen.
Literacy in maths, therefore, is less about the hard skills and more about its ability to play a role in our lives, such as our ability to carry out mechanical operations with numbers and symbols. As noted by the Australian Council for Educational research, it:
encompasses the ability to put mathematical knowledge and skills to functional use as well as the ability to pose and solve mathematical problems in a variety of situations and having the interest and motivation to do so.
Numeracy can be divided into three specific areas, including the understanding of mathematical content (areas like quantity, space and shape, change and relationships, and uncertainty), mathematical processes (including the use of mathematical language, modelling, and problem solving skills), and situations (namely the ability to recognise any context in which maths can be applied, including personal, educational, occupational, public and scientific).
Numeracy can also involve what mathematician Sol Garfunkel calls "quantitative literacy" -- the ability to make quantitative connections whenever life requires (such as being confronted with conflicting medical test results, but we need to decide whether to undergo a further procedure) and "mathematical modelling," the ability to move practically between everyday problems and mathematical formulations (like deciding whether it is better to buy or lease a new car).
A Tool For Life
The need for numeracy has never been greater. It has a pronounced influence on our fiscal choices, literacy, and even perceptions of risk as it pertains to health. Perhaps surprisingly, it has even been associated with a reduced susceptibility to framing effects (a cognitive bias in which people react to choices depending on whether or not it's presented in a positive or negative light), the tendency to choose logic over emotion, and a greater awareness of risks that have a numerical component.
Just as importantly, numeracy also has a significant impact on our careers. Atif Kukaswadia says it's a necessary skill for the 21st century. Given that that the world is moving towards a knowledge based economy, he says the lack of mathematical literacy is a big concern: "Now more than ever the ability to critically evaluate information presented to us to draw our own conclusions, rather than have someone tell us what they mean, is of the utmost importance."
Indeed, many professions require people to have at least a rudimentary sense of numeracy, including accounting, actuarial work, risk analysis, finance, engineering, architecture, social sciences, urban planning, and many others -- including those jobs outside of specialised areas. Innumeracy reduces employment opportunities and promotions, resulting in unskilled manual careers, low-paying jobs, and unemployment.
Late last year, the Programme for International Assessment (PISA) survey -- which is organised by the Organisation for Economic Cooperation and Development (OECD) -- assessed nearly 510,000 students aged 15 to 16. The tests considered three primary areas, namely reading, science, and (especially) maths. The emphasis on maths was on account of it being a key indicator for post-secondary success. PISA says proficiency in maths is a strong predictor of:
positive outcomes for young adults, influencing their ability to participate in post-secondary education and their expected future earnings...The OECD's new Survey of Adult Skills finds that foundation skills in mathematics have a major impact on individuals' life chances. The survey shows that poor mathematics skills severely limit people's access to better-paying and more-rewarding jobs; at the aggregate level, inequality in the distribution of mathematics skills across populations is closely related to how wealth is shared within nations. Beyond that, the survey shows that people with strong skills in mathematics are also more likely to volunteer, see themselves as actors in rather than as objects of political processes, and are even more likely to trust others. Fairness, integrity and inclusiveness in public policy thus also hinge on the skills of citizens.
Each year, countries around the world invest over USD$230 billion in mathematics education in schools. OECD admits this is a major investment -- but the returns are many times larger.
Looking at the results of last year's PISA survey, Asian countries did the best, occupying the first seven spots in the rankings. Canada finished in 13th, the UK 26th, and the US 36th. Boys scored higher than girls in maths in 37 out of the 65 countries (more on this gender gap later).
The doom-and-gloom reports generated by these findings can be discouraging for students. Indeed, maths anxiety is actually a thing -- one with potential downstream mental health consequences.
According to Mark Ashcraft and Elizabeth Kirk, maths anxiety is "a feeling of tension, apprehension, or fear that interferes with maths performance."
Their work has shown that individuals with pronounced maths anxiety have smaller working memory spans. This reduced working memory capacity, say the researchers, results in a pronounced increase in errors when mental addition is performed along with a memory load task. Ashcraft and Kirk say it's likely caused by a disruption of central executive processes.
Previous studies have shown that maths anxiety is associated with poor maths performance on tests, negative attitudes about maths, and outright maths avoidance.
Trouble is, maths avoidance results in less competency and confidence, resulting in even greater levels of anxiety. Further, Ashcroft says an empirical dilemma arises as a result of this avoidance; it presents a chicken-and-egg scenario. His work shows that there's a correlation between accuracy and maths anxiety.
There's also the self-reputational threat to consider when it comes to poor maths performance. Studies have shown that women do better on tests when they fake their names. By assuming an alias -- whether it be a male or female name -- women can overrule the self-reputational threat -- the fear of doing poorly when they're concerned that it will be taken as proof of a stereotype. Removing this pressure appears to alleviate the fear and the distraction.
Revealingly, research done by Sian Beilock and her group at the University of Chicago shows that maths anxiety is not simply about being bad at maths. Using brain scans, she determined that the brain areas active when highly maths-anxious people prepare to do maths overlap with the same brain areas that register the threat of bodily harm -- and in some cases, physical pain.
"For someone who has maths anxiety, the anticipation of doing maths prompts a similar brain reaction as when they experience pain -- say, burning one's hand on a hot stove," noted Beilock in a statement.
Indeed, it was the anticipation of having to do maths -- and not actually doing maths itself -- that looked like pain in the brain. The brain activation does not happen during maths performance, meaning that it's not the maths itself that hurts, but rather it's the anticipation of maths that's painful.
Fixing the Problem
So how do we alleviate maths anxiety? And how can we cast aside the prevalent anti-maths culture?
It all comes down to the quality of education and how maths is presented. Maths doesn't have to be boring. And as Sol Garfunkel has noted, different sets of maths skills are useful for different careers -- and maths education has to reflect that. He continues:
For instance, how often do most adults encounter a situation in which they need to solve a quadratic equation? Do they need to know what constitutes a "group of transformations" or a "complex number"? Of course professional mathematicians, physicists and engineers need to know all this, but most citizens would be better served by studying how mortgages are priced, how computers are programmed and how the statistical results of a medical trial are to be understood. A maths curriculum that focused on real-life problems would still expose students to the abstract tools of mathematics, especially the manipulation of unknown quantities. But there is a world of difference between teaching "pure" maths, with no context, and teaching relevant problems that will lead students to appreciate how a mathematical formula models and clarifies real-world situations. The former is how algebra courses currently proceed -- introducing the mysterious variable x, which many students struggle to understand. By contrast, a contextual approach, in the style of all working scientists, would introduce formulas using abbreviations for simple quantities -- for instance, Einstein's famous equation E=mc2, where E stands for energy, m for mass and c for the speed of light.
Garfunkel asks us to imagine replacing algebra, geometry, and calculus with such things as finance, data, and basic engineering. In other words, teach the maths within the context of the larger discipline or subject itself. So, in the finance course, for example, students would learn the exponential function, use formulas in spreadsheets and study the budgets of people, companies and governments. And in the basic engineering course, students would learn the workings of engines, sound waves, TV signals and computers.
"Science and maths were originally discovered together," says Garfunkel, "and they are best learned together now."