30.11 Mathemagenic Activities and Developments in Instructional Technology

30. 11. 1 Superhooks, Hypertext, CD ROM Databases

The development and instructional use of densely indexed information media allow students to embark on highly individualized explorations of subject matter. Automated cross-indexing of a quite sophisticated character permits extended searches that often lead to the emergence and pursuit of new search goals. This promises many new educational opportunities but casts the student in the often unaccustomed role of solitary explorer/adventurer.

Explorations in a hypertext or in a rich CD-ROM database is a class of mathemagenic activities that has not received much attention in the research literature. The first reaction of many educators will be to rely on intrinsic interest and curiosity, but this may not be enough to sustain and guide appropriate activities. Not only do ways have to be found to maintain the intelligent collection of information but, for practical reasons, some topical focus has to be fostered. Another problem that may be anticipated stems from technological means that are becoming readily available for recording the found information either on disk or by printing it out. This activity may supplant covert interpretive process. The student, rather than trying to understand and learn, collects information fragments and stores it in machine memory as a kind of digital amulet against ignorance. The phenomenon is already observable in the educational research community where the collections of reprints and photocopies sometimes serve as a surrogate for reading.

The basic problem with superbooks or hypertext is that following your nose into interesting crannies is nice and may lead to serendipitous discoveries. But using such text to accomplish a particular purpose requires judgment and discipline about selection, as well as persistence. Mathemagenic activities will have to be shaped and supported, perhaps with greater care and energy than is required for ordinary reading assignments. It would be a serious mistake to think that all students will be irresistibly charmed by an information wonderland. One possibility that might be worth exploring is the kind of task demand that requires productive reportage about specified and open subject matter. This is likely to engage the selection mechanism. Classification and restructuring may induce sufficient process. Information shopping lists similar to those used by Mager and McCann (1961) in the Varian Associates experiments described before may also be a useful control mechanism for mathemagenic activities with super- or hypertext.

Finally it should be noted here that. the theoretical modeling of structural and sequential text features (e.g., Kintsch & van Dijk, 1978) that has captured the attention of many researchers during the past decade will require very substantial revision before it can be applied to text that can be traversed in a very large number of ways.

30.11.2 Adaptive, Computer-Based Instruction

Sustained, "intelligent" interactions between learners and a shrewdly configured computer program are excellent opportunities for maintaining gross and covert mathemagenic activities at a high level. If the interactive program is conversationally dense, i.e., if frequent response demands are made, short-term memory support tends to reduce topographic shaping. Some processing fetch is required in order for feedback to have much selective effect on process. It seems advisable to require substantial elaboration and synthesis in the learner's responses to avoid too much recent memory support. Answers fresh out of the echo box usually do not shape -useful mathemagenic activities. It would pay to reach, from time to time, well back into the instructional scenario for elements that the learner must use to solve problems. There is some evidence that lengthening the acquisition-recall/exercise interval improves subsequent retention (Landauer & Bjork, 1978; Landauer & Ainslie, 1975).

The external management of instruction through the creation of an effort-sustaining environment is probably at least as important as the internal courseware structure for the effective use of sophisticated computer-based instructional systems.

30.12 SUMMING UP

The aims of this paper were to (a) review characteristics of mathemagenic activities, (b) disentangle the concept of mathemagenic activities from rather short-sighted concerns with the efficacy of adjunct aids to learning, (c) contrast the mathemagenic concept with cognitivist notions such as metacognition and with over-rationalized ideas about learning processes such as study skill training, (d) discuss the place of mathemagenic acts in a broad macrotheory of instruction, (e) consider some issues that invite research, and (f) explore the role of mathemagenic activities in the use of advanced instructional technologies.

Mathemagenic activities are labile. They can be shaped and trained. They are adaptive and are modified by learners according to information structures, task demands, and the transparency of results. Not all adaptive responses support the goals of instruction. Certain instructional circumstances can create undesirable mathemagenic activities.

The concept of mathemagenic activities stresses not only topography ("know how") but also maintenance. The latter is generally not the focus of concern for cognitivist and other skill approaches. The instructional situation must contain support elements to ensure the persistence of learning-related activities.

In a macrotheoretical instructional model, mathemagenic activities play two roles. First, degree of gross compliance. with instructional transactions, such as assignments, influences the number of encountered instructional events. Second, mathemagenic activities operate in a reciprocal trade-off with the number and "difficulty" of instructive events, to determine the likelihood of successfully processing an encountered instructive event. New technological instrumentalities afford learners many diverse paths through instructional information.

Goal-consistent guidance and maintenance of excursions through informationally rich paths pose new challenges for the control of mathemagenic activities.