Error of Conventional Wisdom

Share Cognitive Science Implications for Teaching Mathematics
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Conventional wisdom informs us that if a fact has not been learned we must expend more energy to get that fact stored in long-term memory.  Consequently, the learner is directed to reread again and again, to underline, to highlight, and to engage in all manner of massed practice.

Scientific knowledge about the learning process tells us that it is more effective for the student to expend energy on activities which strengthen the ability to recall the fact from long-term memory.

Unfortunately, conventional wisdom relies less on scientific knowledge than on intuition, a collection of common misunderstandings or myths about learning, untested theories, marketing ploys by parties with a vested financial interest, and political pressure from organizations and institutions with a strong interest in maintaining the status quo.

In 1885, Hermann Ebbinghaus (discovered the forgetting curve) demonstrated that massed practice was an ineffective study technique.  In the ensuing 134 years many studies have attempted to disprove his findings, and all have failed.  Massed practice is among the most ineffective ways to learn and yet it remains the strategy most commonly recommended by teachers and most commonly used by students.

In my capacity as a mathematics professor, I have consistently tried, in classes and professional presentations, to discourage massed practice as a study technique.  My current writings will probably be my last effort to influence this issue in mathematics education. We don’t need 100+ exercises after each minor section in a math textbook.  Ten, or less, well chosen exercises should be sufficient in every case.

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