Comments by Alan H. Schoenfeld on

 

PREVAILING CLASSROOM CULTURE FOR SCHOOL MATHEMATICS

 

Schoenfeld, Alan H. (1987). Cognitive Science and Mathematics Education, Lawrence Erlbaum Associates, p. 27. 

 

Suppose that during your entire academic career, every mathematics problem that you were asked was in fact a straightforward exercise designed to test your mastery of a small piece of subject matter.  You were expected to solve such problems in just a few minutes:  If you did not, it meant that you had not understood the material and the material should be explained to you again.  Suppose in addition that this scheme was reinforced in class:  Problems were expected to be solved rapidly, and teachers gave you the solution if you did not produce the answer quickly.  Having had that experience over and over again, you might eventually codify it as the following (implicit) rule:  When you understand the subject matter, any problem can be solved in 5 minutes or less.  The stronger form of this rule is even worse:  If you fail to solve a problem in 5 minutes, give up.  Unfortunately, this story is not hypothetical:  My research indicates that this belief and a number of equally counterproductive beliefs about mathematics are all too common among our students.