described how the use of means-ends analysis to solve conventional problems imposes high levels of cognitive load, and thus impedes learning. It is therefore likely that the emphasis given to "practice problems" described above will not result in efficient learning.
While the use of goal free problems provides an effective alternative to conventional problem solving its application is limited to situations where the problem space is "small". As the size of the problem space becomes "large" the increasing number of alternatives faced at each step in a solution render the technique impractical for teaching purposes.
An alternative technique may be found in reconsidering the nature and purpose of worked examples. Worked examples are presented to students to show them directly, step by step, the procedures required to solve different problem types. Worked examples contain explicit information that equates to schemas and automation.
That is, worked examples promote the acquisition of knowledge and skills required to:
.....identify problems as being of a particular type,
.....recall the steps (in sequence) needed to solve each particular type, and
.....perform each step without error.
Studying worked examples imposes a low level of cognitive load because attention need only be given to two problem states at a time and the transformation (rule operator) that links them.
A successful method for placing emphasis on worked examples is to present them with conventional problems in an alternating sequence (example type A, problem type A, example type B, problem type B and so on). Students are informed of the paired nature of the material and instructed to study each example closely because they will not be allowed to look back at it once they begin the associated problem.
Students thus focus their attention on the problem type and the associated steps to solution (the schemas). In solving the associated conventional problem they are testing themselves to determine if they have learnt the procedure. This may be a more genuine form of "practice problem solving".
The problem completion procedure has a similar rationale and effect to the use of worked examples (see Paas, 1992; Van Merrienboer and Krammer, 1987). Instead of providing an entire worked example followed by a problem, students are just provided with partially completed worked examples. For instance, in example 1 above, they may be provided with the first two lines and required to complete the third line themselves.