By Kevin Cheung, Associate Professor, School of Mathematics and Statistics
Any discussion on the merits of discovery math is potentially contentious. There are many stakeholders involved and a variety of views are strongly held. Nevertheless, judging from the math test results in recent years, one can sense that something is not quite right. But is it because of discovery math? This is probably the wrong question to ask. Instead, it might be more illuminating to take a more pragmatic view and ask, “Given limited time and resources, what should math teachers do to help the majority of the students attain the learning outcomes?”
Instruction methods, provided that they are theoretically sound, are only as good as their implementations. If a method takes a typical student 20 hours to learn something that needs to be learned in 10 hours, it will not work. If one sees elementary math education mostly as equipping students with a certain set of skills, then the efficiency of the acquisition of such skills needs to become an important part of the discussion.
Interestingly, in competitive sports and performing arts, which require development and mastery of skills, I rarely see the equivalent of discovery math being advocated. I do not know any parents who are happy to pay a violin teacher to let their children figure out how to play the violin by themselves. A gymnastics instructor that insists on letting budding gymnasts figure out how to do a backflip by themselves will likely get fired. In both domains, skills are taught directly and built up incrementally with graduated exercises. Yet students are not robbed of the chances of expressing themselves during performances. Teaching what works right from the beginning helps prevent developing bad or potentially injurious habits.
What then makes skills development in math so different from that in sports and performing arts? There is no substitute for practice and practice takes time. When time is limited, one needs to make choices. The late mathematician John von Neumann is often quoted as saying, “Young man, in mathematics you don’t understand things. You just get used to them.” Perhaps discovery math has gotten things backwards.