‘Discovery learning’ is failing our children
The C. D. Howe Institute’s recent publication of yet another lament on Canadian students’ declining mathematics skills criticizes a teaching philosophy esteemed by North American university education faculties. Advocated for decades by these educators, it has many names, such as discovery learning, inquiry-based learning and problem-based learning. The C. D. Howe critique, by mathematics professor Anna Stokke, suggests returning to predominantly direct instruction.
To the uninitiated, discovery learning has seemingly attractive features. Scorning direct instruction as “drill and kill,” it seeks to engage students by focusing on “real-world” problems having significant complexity, and by using group projects to foster participation. It encourages students to develop their own techniques for basic arithmetic, thus de-emphasizing prac- tice in the use of the efficient standard techniques evolved over the centuries. The hope is that students will thereby construct for themselves a deep understanding ostensibly missing from direct instruction. Educators repeatedly claim scholarly justification for their methods; for instance a 2002 article in the U.S. Journal of the National Council of Teachers of Mathematics asserts that compelling evidence supports discovery learning.
But this is not so. In 2006 the University of Virginia’s E.D. Hirsch observed that decades of classroom research has not been able to rid itself of uncontrolled influences, making the work unreliable and fruitless. A paper on mathematics education coauthored by the Nobel laureate H.A. Simon notes that evidence supporting discovery learning is lacking and that it is often inferior to direct instruction. Furthermore, even when successful, it wastes valuable classroom time that could have been spent practising.
Modern cognitive psychology, with its insights into the crucial distinction to be made between working memory and long-term memory, shows why. Capable of holding three to five items at any given time, the working memory can greatly interfere with learning if it is cluttered with extraneous details characteristic of discovery learning. Furthermore, as anybody trying to remember a telephone number will attest, if not repeatedly practised, the number will not be committed to long-term memory. Educators have been sharply criticized for ignoring the insights afforded by cognitive science research.
Simon and his colleagues note that criticism of practice is prominent in discovery advocates’ writings, observing that the assertion that practice is harmful contradicts 20 years of research. Instead of “killing” by demanding endless “drill,” the objective should be to find ways for students to practice while continuing to maintain their interest.
Why do educators keep pushing the discovery method? This question is especially important for mathematics, where progress in topics such as high school algebra crucially depends on automatic familiarity with basic arithmetic. As the 19th-century German mathematician Leopold Kronecker put it: “God created the natural numbers; everything else is man’s handiwork.”
In this respect, discovery methods advocate a top-down approach to instruction, which conflicts with mathematics’ bottom-up logical structure. As an example, one Ontario official Grade 6 text introduces the statistical concepts of mean and median of a population before discussing integer addition and subtraction. It claims to achieve this by requiring the use of calculators before the students have acquired basic numeracy!
Emphasis on discovery methods has created serious deficiencies; the C. D. Howe report cites a shocking example from a 2011 international test. One four-choice question asked Grade 8 students to compute the difference between 1/3 and 1/4. Whereas 86 per cent of South Korean students answered correctly, only 33 per cent of Ontario students did. This is barely above the 25 per cent achievable by random guessing. The decay in ability as demonstrated by such results is beginning to have serious financial consequences; a recent report observes that Ontario’s community colleges are spending millions on remedial courses.
In Ontario, both the curriculum and teaching guidelines need extensive revision, and textbooks need to be rewritten. Discovery methods have a role to play, but in the crucial Grades 1 to 6, direct instruction should dominate. This instruction form is much more than a “sage on the stage,” as it is commonly caricatured. It can include structured assignments of increasing difficulty together with group and individual tutorials, all of this being accompanied by appropriate feedback.