30.5 Induction, Modification, and Maintenance

Mathemagenic activities can be induced, shaped, and maintained by a variety of methods. A rather questionable trend in the literature is to treat individual control techniques such as adjunct questions, directions, learning goals, etc., as if they were pharmaceuticals that had to be evaluated for curative effectiveness. The empirical assessment of methods poses many well-known logical and practical problems, and this approach will not be used here. Instead, the nature of possible controls will be considered with respect to their influence on the functional topography of mathemagenic activities.

Mathemagenic activities are always analyzed with respect to some specific educational goals or some achievement reference. Effective functional topographies are likely to differ among various instructional media such as texts, film materials, computers, lectures, and so on. We know most about topographies that are effective with text because most of the relevant research was done with text.

Several useful distinctions need to be pointed out before' discussing the management of mathemagenic activities.

The first is between (a) general instructional material that is used for a particular purpose, and (b) specific instructional material that has been prepared for a particular purpose, These two types of material differ sharply in how selective the learner has to be.

Another useful distinction is between (a) materials in which the learner has relatively weak control over inspection, such as a film or videotape; and (b) material in which learners have strong control over sequence and timing, such as text or certain computer courseware. Weak control materials offer poorer opportunities for reinspection. This raises capacity limitation problems that may limit mathemagenic activities.

The third distinction that needs to be made is between operations (a) that directly elicit mathemagenic activities, and (b) those that shape and dispose towards such activities in future efforts. This distinction is similar to the contrast between the direct and indirect effects of adjunct questions (Rothkopf, 1966). One operation directly induces actions that will produce learning and strengthen memory or the ability to retrieve it, e.g., rehearsal. The indirect operation makes it more likely that instructional material will be processed in some particular way in the future (e.g., Sagerman & Mayer, 1987).