Mayfield, K. H., & Chase, P. N. (2002).
The effects of cumulative practice on mathematics problem solving.
Journal of Applied Behavior Analysis,
35, 105-123.
This study compared three different methods of teaching five
basic algebra rules to college students. All methods used the
same procedures to teach the rules and included four 50-question
review sessions interspersed among the training of the individual
rules. The differences among methods involved the kinds of
practice provided during the four review sessions. Participants
who received cumulative practice answered 50 questions covering a
mix of the rules learned prior to each review session.
Participants who received a simple review answered 50 questions
on one previously trained rule. Participants who received extra
practice answered 50 extra questions on the rule they had just
learned. Tests administered after each review included new
questions for applying each rule (application items) and problems
that required novel combinations of the rules (problem-solving
items). On the final test, the cumulative group outscored the
other groups on application and problem-solving items. In
addition, the cumulative group solved the problem-solving items
significantly faster than the other groups. These results suggest
that cumulative practice of component skills is an effective
method of training problem solving.
DESCRIPTORS: _cumulative practice, problem solving, application,
quantitative skills, algebra