30. 10 Research Issues and The Role of Mathemagenic Activities in New Instructional Technologies

Like any scientific conception, our notion of mathemagenic activities may change as new data become available and as theory becomes further elaborated and tested. There clearly are several open questions that are at present too broadly cast for systematic scientific solutions. An example of such is the relative contribution of instrumental and cognitive processes in shaping and maintaining mathemagenic activities. The following section deals with selected theoretical and empirical issues for which further research is required and for which, at least in principle, workable research resolutions can be foreseen. These include questions about the relationship between prior subject-matter knowledge and the disposition to process new information, about a wave theory of attention, and the support of effective mathemagenic topographies with newer instructional technologies.

30.10.1 e and m: Unsolved Riddle

In the macrotheory described earlier, the likelihood of successfully processing an encountered instructive event depends on three factors. It is inversely related to the disparity (d) between the representation of the relevant information in the instructional stream and the simple canonical representation of this information, i.e., it is inversely related to the complexity of the transformation

that the learner has to perform. Successful processing is positively related to instruction-relevant experience (e) and appropriate mathemagenic activity (m). For example, the likelihood of acquiring targeted knowledge from a group of written sentences depends both on degree of familiarity with the words in the sentences (e) and the topography and persistence of mathemagenic processes (m). Rothkopf and Billington (1979), in accounting for the effects of goal directions, have proposed the expression e + (I - e)m to describe the interaction between instruction-relevant experience such as previously acquired knowledge (e) and process (m). In other words, with respect to particular purpose, the contribution of mathemagenic, process to performance is greatest when e is small.

Theoretical problems arise because, for simplicity, the assumption has been made that e and m are independent. But there are circumstances when the independence of e from m is suspect. For example, strong interest in a particular topic may increase not only instruction-relevant knowledge but also the likelihood that information-bearing elements of topical interest will be attended. People are more likely to focus on information that is of interest to them and are more likely to try to understand it. One possible solution to this theoretical quandary is to collapse instruction-relevant experience and mathemagenic, activity into a single variable. This would work in many cases, since both e and m have positive effects on the likelihood of successful process. This solution is not appealing, however, because there are many situations where the determinants of e and in are clearly independent. Low e is an obstacle here against which m is played. The problem clearly needs a resolution. In general, issues relating the external control of mathemagenic activities to intrinsic control factors such as interest await careful analysis and formalization.

30.10.2 No Broad Wave Effects for m

It has been possible to develop indirect measuring techniques to study fluctuations in attention and engagement during purposive reading of text (Rothkopf & Billington, 1975). The measurement techniques are based on the assumption that, if engagement has systematic wavelike fluctuations in time, then the recall of contiguous items from text should be correlated. If engagement is strong, both of two adjacent items should be remembered. If engagement is weak, items from adjacent text segments should be failed together. The rationale behind this approach can be understood by imagining text going by the learner on an ever-moving tape. The learner sometimes closes his or her eyes (low m engagement), and sometimes the eyes are open (full m engagement). One way of deciding when the eyes were open and when they were shut is to look for clusters of test items (from adjacent sections of the text) that tended to be passed or that tended to be failed.

Using the correlational methods referred to above, it has been found that mathemagenic: engagement with text materials fluctuates fairly capriciously in time but is effectively entrained by task demands or by endogenous content factors (Rothkopf & Billington, 1975). Mathemagenic selection appears to become finely tuned quickly. In a study on the effects of goal-descriptive directions, inspection time and eye movement measures have shown sharp rises in inspection activities around goal-relevant instructional elements with little or no spread of this effect to other material within the same close text neighborhood (Rothkopf & Billington, 1979).

The sharp tuning may be due to the profound mathemagenic effects of the act of discovering that an instructional element is relevant to a learning goal. Frase and Kreitzberg (1975), in an important study, asked subjects to learn about aspects of Nathaniel Bowditch's life and career. They . gave them directions that referenced certain kinds of sentences (e.g., sentences that contain information about Bowditch's childhood, or that included certain words). They then told some subjects that: (a) their learning goal was the information in the referenced sentences, and directed others that (b) their learning goal was the information in the sentences that did not include referenced elements. The number of referenced and not-referenced sentences were the same in the passage. But subjects remembered more information from sentences that were both referenced and had goals than from the compliment sentences that were goals but were not referenced. This simple, elegant experiment suggests that the processes required to decide that a sentence contains referenced elements has more profound mathemagenic consequences than detecting the absence of such elements.

The following general principles are worth testing and may be testable. First, that the most dramatic and accessible aspect of mathemagenic activities is selectivity, i.e., high-process densities for some elements of the instructional materials rather than others. Second, the selection processes involve comparisons between learners' conceptions of their goals and elements of the instructional materials. These comparisons invoke mental activities that transform instructional materials in important ways and that must be considered effective mathemagenic acts. The Frase and Kreitzberg (1975) results as well as those of Rothkopf and Billington (1979) provide a certain degree of support for these conjectures.

The mathemagenic character of comparison processes does not depend on the intention to learn. Directions to search or to categorize the instructional information, without any intention to learn, may be useful teaching maneuvers. The comparisons involved in search (e.g., Do these materials contain any information about Nathaniel Bowdich's grammar school education?) or in categorization (Find any mention of food! Find any mention of fruit!) (Frase & Kammann, 1974) are also effective producers of learning. Clever search directions or requests to categorize are mathemagenic control maneuvers that are worth exploring further, Particularly since very powerful, new storage media such as CD-ROM will open vast challenging horizons for application of search and categorization techniques.