30.4 Characteristics of Mathemagenic Activity

General mathemagenic activities may be viewed as falling into two classes. The first of these involves gross activities that bring learners within physical reach of the instructive information. They are readily observable. The second class consists of covert mental processes, i.e., hypothetical internal processes such as the representation, collation, elaboration, and integration of information.

Overt mathemagenic activities include the gross body movements and postural adjustments that we usually associate with attendance, compliance with assignments, the procurement and inspection of information-bearing objects such as books, videocassettes, examining specimens, turning pages, keyboarding, and other gross information-gathering and exploratory activities. Also linked to overt mathemagenic activities are eye movements, changes in skin resistance, and other physiological responses, although these are mainly used to infer covert mathemagenic activities (e.g., Rothkopf, 1978; Rothkopf & Billington, 1979).

Covert mathemagenic activities are hypothetical mental processes that are characterized by their function such as, for example, selection, segmentation, rehearsal, etc. (e.g., Rothkopf, 1965). These processes control the flow and transformation of information during learning and comprehension. Their functions may include selection, analysis, or interpretation. The invisibility and importance of covert processes makes them ripe for speculation, but this temptation should be resisted. In doing a reading assignment for homework, for example, the gross mathemagenic activities might include taking notes about the assignment, picking up the necessary books, finding a quiet location, and looking at the assigned pages. The covert mathemagenic activities might include reading, interpreting what is read, and, perhaps, extrapolating from it. Of course, it is hardly possible to do this without engaging in gross activities, but the converse is easy. It is not uncommon to hold a book, even to turn the pages and move one's eyes across the lines of type, and still extract hardly any information from what is written.

Gross, overt mathemagenic activity for an accountant who does not know how to use a particular feature of a spreadsheet might be to find the relevant section of the Manual. The covert activity might be to extract the required information from the text and apply it to the task at hand.

In the laboratory, we make inferences about covert mathemagenic activities both through the manipulations by which we induce them and by the observable consequences that are Produced. For research purposes, antecedent manipulations, such as questions, are designed not to be instructive by themselves. They simply accompany a standardized instructional delivery. Therefore, if the antecedent experimental manipulation is found to influence learned performance, it can be inferred that the manipulation has altered the manner in which the instructional message was processed, i.e., that it has altered mathemagenic activities.

A distinction must be made between (a) the methods that are used to induce mathemagenic activities in the laboratory and to infer their effects, and (b) the methods that are used to manipulate them and to apply the concept in practical situations. In the laboratory, great pains have to be taken to ensure that the inducing operations are not informative or instructive with respect to criterion measurements. In practical situations, this is not necessary. It is wasted motion. Opportunities should be fully exploited that would combine interventions to enhance useful mathemagenic activities with operations that communicate substantive information, strengthen memory for information, or facilitate subsequent retrieval. Practical applications will be discussed in somewhat greater detail later in this chapter.

General characteristics of mathemagenic activities include lability, topography, and persistence. These will be briefly sketched below. A more detailed discussion follows later.

30.4.1 Lability

From a practical point of view, the most important characteristic of mathemagenic activities, whether overt or covert, is their lability. They can be changed by many situational factors including environmental conditions and task demands. They are adaptive in the sense that they are responsive to environmental pressures. Because they are labile they offer opportunities for instructional intervention.

30.4.2 Topography

Operationally this simply means that the effective processing induced by demand characteristics for certain materials or content is not necessarily transferred to other materials and topics. Demand characteristics shape mathemagenic activities. Association linkages occur if certain situations reliably produce the same demand characteristics. Subsequently these situations will tend to elicit particular topographies. This means that topographies may have specific linkages to content and instructional forms. Selection, elaboration, and rehearsal, indexed with respect to instructive sources, are examples of topography.

Our ability to infer the topography of covert mathemagenic activities is very limited. But a functional analysis of these covert activities is feasible, i.e., it is possible to infer to a certain degree what transformations the learner has performed on instructional information. The postulation of hypothetical mathemagenic functions and inferences about functional topography is useful in planning practical interventions. It is of particular value in devising adjunct techniques to induce effective mathemagenic activities and in avoiding procedures that will interfere with purposive learning.

Not all mathemagenic processes should be categorized as executive functions, i.e., as strategies that are purposefully focused on learning. It is not unlikely that the most effective mathemagenic activities involve the invocation of processes that incidentally produce the desired learning outcomes. The highest art in teaching is the skillful management of such processes.

30.4.3 Persistence

Mathemagenic processes can be maintained by incentives, and they can be eroded by difficulties and through effortfulness. It is very likely the case that some mathemagenic activities behave like operants in the sense that they require appropriate reinforcement schedules to maintain them. Such mathemagenic activities will deteriorate if reinforcement contingencies are haphazardly managed or are removed from instructional situations. There are also good reasons to expect that the law of least effort modifies mathemagenic activities and that effort itself can erode them. For this reason, it is not enough to teach learners how to handle information. Schools have to create environments that will sustain mathemagenic activities at vigorous levels by managing reinforcement contingencies and reducing obstacles. It must not be assumed that study skills or metacognitive strategies will be practiced once they are mastered.

The factors that shape and sustain mathemagenic activities are partially in instructional environments because such environments can model appropriate activities, create task demands, and provide contingencies between activities and consequences. Other shaping and sustaining factors can be found in intrinsic consequences of learning activities. Finding interesting information in books, lessons, or other instructive sources makes it more likely that these sources will continue to be consulted.