30.6 Interventions

The major kinds of interventions to elicit, shape, and maintain mathemagenic: activities are task demands, modeling, and incentive manipulations. Task demands include adjunct questions and exercises, directions, and process-inducing tasks.

30.6.1 Adjunct Questions

The role of adjunct questions in the control of mathemagenic activities has frequently been misunderstood. The problem has been the obsessive concern of many educators with method and their unsound belief in a pharmacological model for the empirical evaluation of methods of instruction. As a result of these mistaken beliefs much effort was wasted in a flurry of experiments that were carried out to determine whether adjunct questions were instructionally effective.

It is historical fact that adjunct questions were used in the experiments that first demonstrated mathemagenic activities and provided existential proof for them. These adjunct questions were carefully designed to provide no information that could be directly useful in responding to a text-based criterion test, and this design feature was empirically checked before experimentation. Such questions, nevertheless, were found to improve criterion test performance. They shaped mathemagenic activities that yielded information needed to answer criterion test questions. The point of these early experiments (e.g., Rothkopf, 1966; Rothkopf & Bisbicos, 1967) was to show that mathemagenic activities were labile and adapted to environmental pressures. The adjunct questions shaped and maintained effective mathemagenic activities. Unhappily, this caused the methods addicts to pay attention. To make the misunderstanding worse, recall of the material actually covered by the adjunct questions was greatly improved, in part, because the questions also provided direct rehearsal of the relevant information.

Not enough people paid attention to the governing principles proposed by Rothkopf (e.g., 1982). First, adjunct questions have to be consistent with instructional goals to be effective. Mathemagenic activities are labile, and it is possible to write adjunct questions that will result in mathemagenic behaviors that will depress test performance. This was clearly demonstrated by Rothkopf and Coke (1963, 1966) using overprompting techniques.

The second principle is that beneficial mathemagenic effects will be produced by adjunct questions, chiefly when the mathemagenic activities of the learner are inadequate. Good learners hardly need a boost. This was demonstrated (Rothkopf, 1972) by having learners read a very long (96 page) passage on geology- Adjunct questions were never used before page 12. We kept track of whether (a) people accelerated their reading rate during the first 12 pages or not, and (b) if they remembered more than average about the first 12 pages. It is safe to assume that mathemagenic activities were not adequate to the task in the group members who did not learn much from the first 12 pages but who increased their reading rate. Our experiment showed that it was exactly this group that showed the greatest gain due to adjunct questions. Other subsequent reports that adjunct question are more likely to be useful to ineffective learners (e.g., Serethy & Dean, 1986) have similarly attracted very little attention.

The size of the "mathemagenic" effect produced by adjunct "Post" questions also depends on how representative the adjunct question set is of the criterion test and on the malleability of appropriate mathemagenic activity. In order to estimate the effect on the population mean, the experimental effect must then be multiplied by the proportion of the student population who bring inadequate mathemagenic activities to the learning situation. The gross effect of the intervention, however, is substantially larger when the criterion test is only a small sample of the total knowledge domain that was covered by instruction. This is commonly the case. As a crude estimate, if the experimental gain in incidental learning is only 4%, and the criterion test was derived from 50 out of a 1,000 sentences, then the expected gross gain from the intervention averages 40 sentences per person. It will average a lot more per inefficient learner if such learners represented only a small proportion Of the total student population.

Adjunct questions or exercises have several consequences. First of all, they are acts of rehearsal that strengthen memory, Prepare for future interrogation or use (Landauer & Bjork, 1978; Landauer & Ainslie, 1975; Glover, 1989), and provide context for future recall and use (e.g., Ross, 1984). Whether knowledge of results is made available or not, adjunct questions provide feedback that will strengthen or weaken

learning processes that have been applied in the recent past, depending on the results that they have produced.

Adjunct questions also influence selection mechanisms (e.g. Rothkopf & Bisbicos, 1967; Reynolds & Anderson, 1982; Reynolds, Standiprot & Anderson, 1979). Learners are sensitive to the tenor of the questions and any biases in the nature of the information that is asked for. Such bias shapes selective attention. It works on the instructive events that follow adjunct questions (see Rothkopf, 1966; Sagerman & Mayer, 1987). The selection mechanism is important when teachers are trying to adapt general instructional materials to their special instructional purposes. They are especially useful in the unhappy case when teachers are unable to state their purpose clearly but have a good intuitive sense of those goals. The questions the teachers then ask can provide an inductive basis for tuning the selective attention of the student to the teacher's intuitive aims.

The notion of selection implies that particular instructive elements (e.g., text elements) are favored with a different level or kind of mathemagenic activities than other instructive components. We may not be able to specify in detail what these activities are, but they seem to result in increased demands on cognitive resources. This has been shown through inspection time measurements (e.g., Reynolds et al., 1979) and by demonstration of threshold increases through ingenious secondary task monitoring techniques (e.g., Britton, Piha, Davis & Wethausen, 1978; Burton, Niles, Lalik & Reed, 1986).

Finally, another beneficial usage of questions is to communicate to the student that someone cares about what they derive from instruction. There is some evidence that suggests that social questioning is more effective than questions from inanimate sources. Questions directly relevant to the reading task that were personally asked by a teacher-like figure were found to result in more effective learning activities than automatically presented questions or than nonsubstantive questions (e.g., Is the chair at a comfortable height?) asked by a teacher-like person during a periodic visit to the workstation (Rothkopf & Bloom, 1970). Such contingent reinforcement procedures may be especially helpful in maintaining gross overt mathemagenic actions.

Questions that can be answered through information obtained through trivial processes will depress effective mathemagenic activities. Examples of such trivially based queries are adjunct questions made up preeminently from picture captions (which I have actually observed in the teachers' version of a prominent social science textbook) or questions that can be answered from short-term memory.

30.6.2 Goal-Descriptive Directions

When general instructional materials are used and the teacher can specify what students should accomplish with these materials, then the students should be informed as precisely as possible about these goals. That is the purpose of directions that describe goals. This fairly obvious point is worth reiterating. Adjunct questions can be used as inductive guides to goals that teachers consider important but cannot describe specifically. When teachers can describe goals in explicit language, then questions are still useful because they act as rehearsal. But when goals can be described, explicit direction can guide the student in selecting from the instructional material. This is especially useful if teachers wish to adapt general materials for specific purposes of their own. Directions have been found instructionally effective with text (e.g., Rothkopf & Kaplan, 1972; Ellis, Konoske, Wulfeck & Montague, 1982). Eye movement studies (Rothkopf, 1978; Rothkopf & Billington, 1978) have shown that goal-descriptive directions can effectively control selective attention in reading. There are indications that there is a fall-off in efficiency as the number of directions increases (Rothkopf & Kaplan, 1974). For text, this is most likely due to failures in the search set rather than from capacity stresses during reading, because the observed fall-off in efficiency was due to the number of directions rather than to the density of direction-relevant sentences in the text. It is highly likely that the density of direction-relevant material might play a role if exposure to the instructional material were externally paced,

Much of the work on directions seems to have been carried out with text. But Mager and McCann's (1961) elegantly simple use of goal directions with engineering trainees at Varian Industries demonstrates the broad usefulness of goal descriptions. Recently graduated, newly hired engineers were given short orientation assignments in various departments of the Varian plant. Their subsequent professional development was greatly aided if they were given descriptions of what they were to find out during each departmental assignment.

Goal-descriptive directions operate on mathemagenic selection. The major technical challenge is to understand the discriminations that must be made by the learners when they detect instructional elements (such as text components) that match the goals that have been identified through the directions. It seems clear that goals can be described too broadly or vaguely, so that the processing focus is scarcely narrowed or is described so badly that the focus is misdirected. Empirical techniques can be devised for determining whether directions highlight the appropriate instructional elements (e.g., Rothkopf & Kaplan, 1972). Asking a representative sample of students to identify instructional elements that are relevant to a particular goal provides much useful information about the effectiveness of the directions.

Several additional points should be made about goal-descriptive directions. First, some skill is required to identify the instructional components that are relevant to a goal. For example, trivial misidentifications occur when a sentence in a. text shares a word or two with the goal description. A particularly difficult situation arises when the goal-descriptive directions require concatenation of two or more elements that are widely dispersed in the text (e.g., Gagne & Rothkopf, 1975; Rothkopf & Billington, 1975; Rothkopf

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& Koether, 1978). Second, identifying goal-relevant instructional elements is not a sufficient condition for learning. Although cognitivists tend to overvalue the importance of intention, the incidental learning literature is replete with demonstrations that intention is nice, but not sufficient, and not needed (e.g., Mechanic, 1962; for a discussion, see Postman, 1964).

Finally, the clever experiments of Frase and Keitzberg (1975) have shown that the positive identification of goal-relevant elements, as well as other kinds of categorization, can be an effective mathemagenic act. Their experiments show that the processes required to identify a sentence as containing relevant elements may be sufficient for learning.

30.6.3 Other Task Demands

Students can be asked to carry out. tasks that involve elements of the instructional information. Such demands can result in mathemagenic processes that will lead to the acquisition of targeted information. The search for goal-relevant information, alluded to above-i.e., the examination of instructional elements to see whether they contained goal-relevant material-may internalize the information sufficiently to cause it to be understood and remembered. Sorting instructional information according to certain attributes can result in sufficient processing for important learning. Frase and Kammann (1974), for example, showed that sorting animal names according to a dual criterion resulted in better recall than sorting them according to a single feature. A number of tasks (other than the directions to learn) can be devised that will result in processes sufficient for learning.

Inventing tasks that will induce appropriate and sufficient mathemagenic processes to accomplish instructional goals, without necessarily revealing to learners that they are working to achieve these goals, is an exciting challenge. It is a challenge because of an intriguing mystery, which some ingenious researcher may help us understand some day, namely, that many people perceive efforts to learn as painful. Such pain prevents many learners from accomplishing what they are asked to do. Yet these very same people will willingly perform other tasks with the . instructional materials-tasks such as searching for content elements, classification or sorting, rewriting text, or explaining the instructional content to others - and thus process the material sufficiently to induce the desired learning outcomes. This is the reason why well-conceived task demands often result in effective mathemagenic activities, while hortatory directions to learn will only produce

modest results.

30.6.4 Control by Revealing Consequences

Since mathemagenic activities are labile, they tend to be responsive to environmental pressures. The incorporation of indicators of progress into the instructional stream therefore makes it more likely that these activities will be shaped into effective topographies. Two kinds of consequences of mathemagenic activities appear useful. One is essentially informative. It lets learners know if they are moving in the right directions and warns them of difficulties. The second involves consequences with hedonistic tone, for example the recognition or praise of study activities or of accomplishments. There are some suggestions in the literature (e.g., Dweck, 1986) that some learners may perceive information about their accomplishments as particularly pleasant and encouraging. Others flourish when their learning activities gain the attention of teachers or other persons. As pointed out earlier, we have observed that the effectiveness of adjunct questions can be enhanced by having them delivered (live) by a teacher-like person (Rothkopf & Bloom, 1970).

It is hardly worthwhile experimentally to evaluate the advisability of providing consequences, i.e., making the instructive environment transparent to results. Even if consequencing did not work all the time, gauges and mileage markers are usually installed without much cost, and they are unlikely to do much harm. Instructional materials that have been developed for very specific purposes ought to be transparent enough to provide learners with an accurate sense of progress. Interactive instructional systems offer many opportunities for providing consequences with which learners might evaluate their efforts.