The great mathematician Euclid is said to have told his students “There is no royal road to geometry.” By this he meant that, as with most academic subjects, sports, music, or other worthwhile pursuits, key elements to success in math are persistence, exposure and practice.
Parents with school-aged children will be familiar with the rhetoric surrounding math education today. Children are immersed in hands-on learning for the 21st century, which will supposedly develop creative problem solvers and deep thinkers. Children are to discover their own techniques, pencil and paper math and extended practice are kept at a minimum and conventional math techniques are discouraged in favour of using objects like blocks and fraction strips. Teachers are told to encourage children to create their own math questions instead of assigning prescribed problems. It is argued that children will then feel successful even if their math skills are lacking. Much time is devoted to projects intended to keep children engaged in math, such as building gardens or creating posters that list examples of uses of math. Parents are told that these teaching methods have been well researched and will benefit their children in the long run.
If these methods translate to genuine learning, why are parents across Canada concerned about their children being unable to carry out the simplest mathematical calculations? Why are business owners, tradespeople, university and college professors and scientists concerned about the lack of skills in high school graduates? Why could only 28 per cent of eighth graders in one of our highest performing province – Alberta – correctly subtract two simple fractions on the 2011 international TIMSS exam, compared with 86 per cent in Korea? Shouldn’t creative problem solvers and deep thinkers be capable of, at the very least, subtracting fractions?
As a professional mathematician, I am familiar with what is required to think creatively in math and, as a parent of young children, I am also familiar with recent teaching techniques and math curricula across Canada. A few of my university colleagues and I felt the situation was so dire that we founded a non-profit math program to provide parents with an affordable option to address deficiencies in the math curriculum. My colleagues and I also lobbied the Manitoba government, which resulted in recent changes to the provincial math curriculum – a positive first step. However, more needs to be done in all provinces to correct the current direction in math education that is negatively affecting children across Canada.
In attempting to create an environment where children feel engaged in math, much of the math has been eliminated altogether. Performing one or two calculations while building a garden is not enough to ensure that a child knows how to multiply. Expecting young children to discover their own methods in math is unrealistic given that most do not have the tools to do so. Concepts should be taught with understanding, but there is nothing cute about an eighth grader who needs to use pizza pieces or fraction strips to add fractions. In addition to creating confusion, dependence on these objects cripples students for later math learning and works against the development of abstract thinking. Children need to move beyond these techniques and into the symbolic mathematics on which algebra – the bridge from elementary math to higher-level math and science – relies. Students who have not memorized times tables and cannot easily perform basic arithmetic with numbers or fractions cannot possibly become creative problem solvers.
Math is extremely cumulative, which is why teaching methods that do not promote practice and mastery of skills have a strong negative impact on math learning. When children are not given genuine tools to master concepts, they can quickly lose confidence in their ability to do math, which diminishes their chances of success. Many math educators incorrectly assume that children are not capable of finding math interesting and so insist that teachers incorporate recipes for inauthentic learning and false self-esteem into lessons, thus depriving children of important skills and of experiencing the satisfaction gained by true accomplishment through hard work and persistence. As with sports or music, repeated exposure and practice in math are imperative to mastering topics and to progressing to later levels and there is no magic formula that will alter this reality.
Anna Stokke is an Associate Professor of Mathematics at the University of Winnipeg, a co-founder of the non-profit organization Archimedes Math Schools and a co-founder of WISE Math. This commentary is part of a series. You can read the first part here.