"Practice does not make perfect. Perfect
practice makes perfect.
- Taken from The Little Book of Coaching
One of the most frequent comments from students
when going over errors made on mathematics tests and assignments
is, oh that was just a stupid mistake. We do not allow students to
classify mistakes in this manner. We insist that the mistake be
acknowledged as something important that must not be repeated. We
seek to classify this error in a manner that will facilitate its
correction. So instead of calling it a stupid mistake, we offer
more useful categories like multiplication fact error, long
division process error, slip in concentration, or lack of
automaticity. Then we establish a practice procedure to avoid more
instances of that particular error.
One of our means for building automaticity is a piece of software we developed called Mathdrill (May, Rabinowitz, Hart, and Larson, 1995). This program was designed to drill students in algebraic principles in order to help students respond accurately, quickly and – ultimately – automatically. The program was based on the resource literature reviewed and mentioned in other sections of the book as well as on the memory findings summarized by Salisbury (1990) that are relevant to drill programs. These include using: small subsets of items to teach new concepts in order to reduce interference; spaced, rather than massed, practice to improve retention; and occasional review or reinstatements of earlier learned material in which the concepts are mixed to facilitate discrimination, retention, and appropriate use.
During the two-year interval between 1995 and 1997, we conducted a controlled experiment to test the effectiveness of Mathdrill in skills development. The results supported our hypothesis. (May, Rabinowitz and Mantyka, 2002, pp. 27-33)
Many math educators are content with a minimum level of competency in topic areas. Our experience has been that unless core algebraic skills are over-learned to the point of automaticity, errors in these skills occur in more complex problem-solving situations. Our experience supports the Blanchard and Shula principle cited earlier, "Practice does not make perfect. Perfect practice makes perfect" (2001, p. 46) and we require all our students to engage in perfect practice. If you want to teach or learn mathematics well, you must be prepared to do the same.