Why maths should be fun and creative, not a test of rote learning
Mathematician and educator Solomon Garfunkel believes instructors should favour originality and creative problem solving
Many youngsters see little use for maths beyond how to add and subtract, multiply and divide. But that's largely because of the way the subject is normally taught. Curriculums worldwide have lost touch with everyday life and failed to rouse interest among students as a result, says Solomon Garfunkel, a leading American mathematician and educator.
Maths is a life skill that allows us to understand how the world works and make informed decisions on matters such as mortgages or balancing our bank accounts, he says.
But all too often lessons linger in the abstract and maths is taught with the sole purpose of preparing students to pass exams, move on to the next course and impress university entrance committees.
It's akin to running a carpentry course in which students are told to hammer nails and saw boards for years to equip them with the skills to build a house in the future - completely out of step with students today, who do not believe in delayed gratification, Garfunkel adds.
Youngsters should use their maths skills as they learn them. "Otherwise it's just a set of facts, algorithms, methods and techniques … it should be close to their hearts, plus it's more fun," he says.
"The students need to see a problem they might want to solve. For example, quadratic equations can help determine when it is more economical and time efficient to test blood samples for a disease or steroid use.
A long-time campaigner to re-establish the broken link in math education, Garfunkel was in Hong Kong this month to present awards at an international contest for high school and university students.
The Mathematical Contest in Modeling began 30 years ago in the US, and has since become a prestigious global challenge that this year attracted 7,600 teams from 17 countries.
Senior teams competed to create the best and most realistic models to tackle two problems that have gripped the world in the past year: fighting Ebola and searching for a plane that was lost over open water.
To extend its influence to secondary schools, the contest presented students from 10 countries with a problem on a smaller scale: working out a system to efficiently schedule filming of a movie, taking into account the availability of actors and equipment, filming time and order of scenes.
Garfunkel hopes school curriculums can be reformed so that teachers can present the subject in context, in a way that makes sense to students and which they can use throughout their lives.
But such transformations don't come easy.
"Educational change is like geological change. It takes a very long time," he says.
Many teachers pursue mathematics for the love of the abstract and theoretical, and tend to teach the way they were taught.
"I understand that people like to stay in their comfort zone. But it's not a very good justification," Garfunkel adds.
That's why it is necessary to "stir the pot" every decade so that educators are forced to rethink how they teach and reimagine how children learn, he says. Even if the direction taken is not necessarily the best, it at least brings about a shift within the education world. The mathematical modelling challenge has helped encourage such moves.
"The more important and prestigious the contest becomes, the more chance it has of affecting the curriculum," says Garfunkel. It has brought about "dramatic changes" on the mainland, while US universities have added more modelling courses and seminars. Having worked at the university level, the organisers believe it will have similar effects in secondary schools, too.
In the US, perhaps the greatest progress has been in the establishment of a "common core" of educational standards, which has been adopted by 43 states. The consolidated standards listed modelling as one of the eight essential mathematical practices to be emphasised at an early age.
Nonetheless, there is ongoing global debate on the best way to teach mathematics. When Shanghai topped the world for maths in the Pisa international education league table in 2012, it prompted a flood of educators from the West to try to emulate their teaching methods and classroom configurations in the hope of boosting results in their own country.
Britain for example, invested in an £11 million (HK$133 million) initiative this year to bring 30 teachers from Shanghai to work their mathematical magic in their classrooms.
However, a number of educators, including Garfunkel, remain sceptical about attempts to copy the Shanghai model because culture, as well as curriculum, determines success. "I don't say you can't learn from Singapore [another high-achieving city] or Shanghai, but are British parents treating their children the same way the Singaporeans are?" asks Garfunkel, who believes simple replication of successful models doesn't work.
"It's useful to study and learn what is adaptable. But this takes some experimentation. It's not one size fits all."
Instead, Garfunkel argues what the world could learn from Shanghai schools is their emphasis on precise mathematical language and logical reasoning, serious classroom discipline, strong and coherent teacher-student rapport, and strong collaborative culture among teachers.
"Teachers are given an hour or two a day which they can critique each others' lessons. It's been very successful."
Just because rote learning is often practised in East Asian schools, he argues it is wrong to conclude that this helps improve children's maths skills. Rather schools should move away from drilling because it does not help develop good communication skills and creativity in problem solving, which are valued by employers. "We over-drill. Speed and accuracy are overvalued," says Garfunkel.
Educators on the mainland may be coming to the same conclusion: "When the contest first started, Chinese teams were almost like a cliché. Their maths was always correct but with no creativity. The US teams were a little sloppy, but they did strange and crazy things. As time has gone on, the Chinese teams have become more creative because they understood the contests - and the society - rewards originality."