30.7 Dispositional Social Influences

30.7.1 Intrinsic Factors

It is something of a truism that the control of mathemagenic activities does not depend entirely on external interventions but may result from well-internalized dispositions such as interests and immediate or long-range goals. One has the impression that such controls function better if there are immediate concrete linkages between instruction and the disposition. For example, the instructional materials work better if they are interesting rather than if they were just logically related to the learner's career goals. It is a common observation that some students can be very articulate about the importance for their career of certain skills (such as programming or calculus) but consistently fail to pursue the appropriate studies in a serious vein. Afterward, they often express keen regret. Intrinsic controls can often be established by certain experiences that are calculated to create interest and establish the value of outcomes.

30.7.2 Modeling

Social modeling is probably the most powerful of several Possible learning-inducing mechanisms (Bandura, 1977). It is likely to have a direct influence on overt gross mathemagenic activities and is likely to shape covert mental activity indirectly through the modeling of values. Models have been shown to affect persistence (Zimmerman, 1979). Models of information gathering and intellectual preparation and models of positive attitudes towards such activities are also likely to induce these in others. If the models for information gathering and problem solving that are provided by family and neighborhood are sparse, public media such as television and films are likely to play an important role in shaping behaviors and attitudes towards the use of information. Television (and other powerful media) cultivates attitudes and influences behavior when other influences are weak. This has been demonstrated by a number of studies. For example, the perception of danger from crime and attitudes towards aging have been shown to be influenced by television watching (e.g., Gerber, Gross, Jackson-Beek & Signorelli, 1978; Gerber, Gross, Signorelli & Morgan, 1980). American students average over 1,200 hours per year before television sets-more time than they spend in school. Yet television fare is exceedingly short of models of behavior in which information is diligently gathered to master some skill or to solve a problem. Portrayals of success gained through hard study, the acquisition of useful knowledge, training, and problem solving have poor dramatic value and are therefore very rarely portrayed. The exceptions are sweaty preparations for sports, which appear both in news programs and in drama (e.g., Rocky), and the grunty travails of becoming a Kung Fu master. But mad and brilliant scientists and engineers in the movies seem to have arrived at work without preparatory schooling or labor, just as tycoons succeed by greed and cunning and rarely by the knowledge they have acquired. Cowboys learn to ride, shoot, and sing without much visible effort, and police drive their cars masterfully in hair-raising chases without any hint of schooling or frustrating practice. The studying and gathering of information for problem solving does not offer good dramatic possibilities. Preparation like the passage of time is often portrayed as the wind riffing through the calendar. It is therefore not too difficult to extract the message from the media that accomplishments are due mainly to special talent-a popular contemporary form of magic-rather than hard work and the diligent, judicious acquisition of information. For this reason, it is not surprising that Americans blame lack of talent for failures in mathematics, while Asians, both here and abroad, attribute such failures to lack of hard effort (Stigler & Barnes, 1988). The convergent theme is that success is achieved through magic and talent and not by marshaling information resources and molding them into a lever that will serve a prechosen purpose.

30.7.3 Mathemagenic Activities and Motivation

Insufficient motivation is often blamed when instruction fails, and success is often attributed to good motivation. Those attributions are probably incorrect in many cases. Of course, motivation is a fairly broad, portmanteau kind of concept. But it may frequently be the case that what is attributed to motivation should be attributed to the shaping and maintenance of mathemagenic activities. The purpose of this section is to contrast briefly mathemagenic activities with motivational concepts.

Psychology has evolved three kinds of explanatory engines to account for why people act. They are motivation, incentive, and the learned-skill dispositions, which behaviorists like Hull (1943) called habits. None of these concepts is very crisply defined when taken away from its original experimental contexts, and the boundaries between concepts are a bit fuzzy. Both motivation and incentive are frequently invoked to explain why students study. Habit-like concepts (e.g., study strategies, concept mapping) are used almost exclusively to describe how they study. When failures to study occur (e.g., compliance), regardless of how effective the available study skills are, the failure is usually attributed to lack of motivation or lack of suitable incentives. Yet the results from research on mathemagenic activities suggests that habit-like concepts should be assigned a more important role in descriptions of why students do or do not study.

Undoubtedly all three-motivation, incentive, and habit-like dispositions-influence study performance. Of course, most motivation relevant to human study activities is not directly derived from basic tissue needs such as hunger and thirst but rather stems from complex experiential factors that have largely social origins. It is safe to say that motivation in instructional situations is less under immediate environmental control than either incentives or habit.

We infer motivation both from what we know about people (a test, an attitude questionnaire) and what we tell them (that others will "hold their manhoods cheap" because they did not stand and fight on St. Crispin's day or that "the eyes of Texas are upon you"). Incentives, on the other hand, refer to objects or states of affairs that are associated with satisfaction of drivelike motivational states (a high grade, money, a smile from Texas, or even some wanted information obtained from study). Incentives can be thought of as exercising, both direct and indirect control on study performance. It is direct control when the incentive is present in the study situation and is reached for. Indirect control is exerted when the attainment of incentive objects in similar situations is remembered and serves as an internalized incentive.

The most complete theoretical statement about the relationships between motivation, incentive, and habit was offered by the latter-day behaviorist Clark Leonard Hull (1943). Habits as learned, skill-like entities are conceptualized as taking place when certain external or internal demands are made. Motivation and incentive are rather closely related. An object or event acts as an incentive only for particular motivational states. In practice, many motivational conditions are named for the incentives that are operative when a given motivational state is . in effect.

Furthermore, when the term incentive is used to include internalized representations of the goal object, the distinction between motivation and incentive almost disappears.

Habit, on the other hand (and with it mathemagenic activity), is quite distinct from the other two concepts. The growth and decline of habit depends either (a) on contingencies between the student's actions and events in the instructional environment, or (b) on modeling or mimicry. For this reason, growth and decline of habits occur only in the performance situation, whereas motivation can be thought to arise in many contexts. Motivation may increase gradually and with weak references to any particular external event. We say that Laura and Joanna study hard because they want college scholarships, or like to be praised, love mathematics, or because their mother has promised them a space shuttle if they get all Xs.

Study habits refers to whether students study at the same time each day, whether they shut off radio, TV, or CD while reading, and whether they paraphrase and write down what they have read. Covert mathemagenic activities.(as well as overt) also fall into the habit category that can be caused to change and to wax and wane as a consequence of instructional contingencies or through modeling.