Share Cognitive Science Implications for Teaching Mathematics

**MASSED PRACTICE:** The process of massed practice usually takes the form of cramming, cram – test – dump, or practicing a certain event or act intensely over a short period of time.

Cramming for exams is a form of massed practice. It feels like a productive strategy, and it may get you through the next day’s test, but whatever learning is produced by massed practice is short lived. Massed practice is the least effective of all study strategies.

As early as 1885, Ebbinghaus showed that massed practice was less effective than distributed practice. Despite hundreds of subsequent studies his findings have never been refuted.

It has always baffled me that for 130 years we have known the disadvantage of massed practice and the advantage of spaced practice and yet all math textbooks and other study materials are based on massed practice. In fact, as evidence against massed practice mounts, mathematics education gives it more emphasis.

I have spent my entire career in education and it seems to me that students use cramming as their standard method of studying much more today than they did 15 or more years ago. Cramming does provide short-term learning sufficient to pass a test, but the learned information is rapidly forgotten. Unfortunately, students have learned from our educational system that passing the test is the only important thing. Learning the subject is of little importance. Teachers contribute to this distortion by constructing tests which can be passed by cramming for the test. In mathematics for example tests usually consist of problems for which getting the right answer is considered success. All the student need do is remember the process until the test has been completed. Cramming would not be successful if the test questions focused on concepts, deductive reasoning, critical thinking, creativity, patterns, etc.

Faith in focused, repetitive practice of one thing at a time until we’ve got it nailed is pervasive among mathematics classroom teachers and students. This is a form of massed practice. It is the least effective of all study strategies. Mathematics textbooks, classroom activity, and homework assignments explicitly encourage massed practice.

Working many problems of the same type at the end of a section is massed practice and is quite ineffective. It is more like training than learning.

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