cumulative practice, part 1

Steve's & Lynn's EM exchange has prompted me finally to get something put up about the cumulative practice study I read this summer.

It was life-altering (seriously).

Here's the abstract, more later:

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.

The Effects of Cumulative Practice on Mathematics Problem Solving
Kristin H. Mayfield and Philip Chase
Journal of Applied Behaviour Analysis Summer 2002, 35, 105-123

Cumulative practice is different from mixed review and from the embedded practice I see in the Dressler books, which were written in the 1960s. More later.

I'm now basing everything I do on 3 articles. This one, the one Concerned found on overlearning, and the article on "shuffling" math problems.

I have all 3.

I'm thinking of starting a Yahoo list for ktm, so I can post them there and people can download them if they like.

How illegal is that?

...................................

Increasing Retention Time Without Increasing Study Time
Doug Rohrer and Harold Pashler
Current Directions in Psychological Science, 2007
Volume 16, Number 4

The Effects of Cumulative Practice on Mathematics Problem Solving
Kristin H. Mayfield and Philip Chase
Journal of Applied Behaviour Analysis Summer 2002, 35, 105-123

The shuffling of mathematics problems improves learning
Doug Rohrer & Kelli Taylor
Instructional Science 2007