Planning knowledge

Any of the three parts of a Change situation may be unknown, and the planning knowledge will be used to identify the correct one and also to determine the operation needed. Consider this very simple example ... 

Planning knowledge is especially critical for problems containing multiple situations and/or multiple unknowns. It is by means of this knowledge that the solver determines the priority with which he or she addresses each situation. Thus, for the Change situation, if more than one component of the mental model is unknown, the plans must shift to include a search for another situation (or a repetition of the current one) that will allow determination of one of the missing elements. This may necessitate, of course, a call to one of the other schemas. 

Planning knowledge. Planning knowledge is particularly critical for the Compare situation because the situation most often occurs as the final stage of a multiple situation problem. Thus, the solver should recognize and order the various subgoals that must be satisfied before the comparison can be made. In many instances, the comparison is not directly stated and the solver must make several... 

Planning knowledge leads naturally to execution knowledge. One does not end problem solving with a plan for solution one carries out the plan. Presumably, students already have acquired at least some of the procedures that will be used with the schemas under instruction. It is probable that new ones will need to be developed as well or old ones modified for application in the new domain. These rules or procedures will be created in the context of... 

Schema knowledge. The instruction in this set of lessons assists the student in developing essential planning knowledge. Given the presence of more than one situation in a single problem, the student must acquire the necessary knowledge for selecting which one...

Both of these last two exercises represent an attempt to have the student step back from the immediate details of the problem and reflect on the more general framework of their problem solving. The objective here is to encourage the students to include some techniques for analyzing complex problems in their repertoire of planning knowledge. 

As already described, SPS focuses a part of its instruction on planning knowledge, just as it focuses on identification and elaboration knowledge. In its exercises, SPS requires the student to do one of three things indicate the relative importance of situations... 

These experiments provide evidence of students acquisition of identification knowledge, elaboration knowledge, and planning knowledge. They yield a great deal of information about how schemas for problem solving develop. 

It will be recalled that PSE was developed with two purposes in mind First, it was to be an environment in which students could practice using their newly acquired knowledge of problem solving, and second, it was to provide the setting in which to examine planning knowledge. Both objectives were realized. All students used the flexible computer environment easily and seemingly with enjoyment. Many volunteered how much they liked certain features of it. Thus, at least anecdotally, the first function of PSE was... 

What have we learned from PSE First, it is possible to isolate planning knowledge and to examine individual differences in how students develop plans. We can examine direct linkages between planning knowledge and other critical aspects of a schema, such as identification knowledge and elaboration knowledge. We can follow the student s execution of the plan and observe the order with which he or she carries out the necessary steps. 

Note ID = identification exercises, ELAB = elaboration exercises, PLAN ID = exercises requiring both planning and identification knowledge, PLAN ELAB = exercises requiring both elaboration and planning knowledge. 

S4 has a different profile of development. He did quite well on the individual exercises of identification and elaboration, but his performance fell on the exercises requiring these types of knowledge combined with planning. Almost certainly the best course of action for him is additional instruction about and practice in integrating planning knowledge with his other knowledge. 

Schemas are interrelated, and one schema may call on another or require the output of another. Typically, the call to another schema reflects planning knowledge. Complex problem solving almost always involves more than one schema, and the evaluation of whether the individual is able to shift easily from one to another as problem solving demands is an important ingredient of assessment. 

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