30.2 Cognitive Models of Learning Processes

How does the notion of mathemagenic activity differ from cognitive models that have emerged from information-processing research during the past decades? Many of these cognitive approaches share psychological perceptions of man as an active, resource-limited transformer of information. Cognitive models of study processes differ on several important points of emphasis from the conceptions that have grown around mathemagenic activities.

Numerous cognitivist conceptions deal with learning and learning-related activities.' These include a cluster of similar or related notions such as metacognition, learning strategies, study strategies, networking, concept learning, mnemonic techniques, and constructivist conceptions (see 7.3). All portray the learner as an active agent who plays a critical role in acquiring information. Clearly, in this respect these views resemble mathemagenic conceptions. The difference is that the notion of mathemagenic activity includes dispositional elements as well-skilled acts acquired through experience. Disposition refers to the likelihood that learners will carry out acts that they are capable of carrying out. It refers to optional, and perhaps volitional, aspects of acts. Cognitive formulations tend to concentrate on know-how. The mathemagenic concept stresses the likelihood of execution as well. This is an important difference. If there is such a thing as a mathemagenic hypothesis 3 it is that mastering of learning activities is a necessary but not a sufficient condition for their execution.

One additional important difference between Rothkopf's (1970, 1976) approaches to mathemagenic activities and cognitive formulations such as that of Kintsch and van Dijk (1978), Frederiksen (1972), and Meyer (1975) concern the specifiability of the content of instruction." For example, it is assumed by the cognitivists that text passages have innumerable content. All measures of the successful use of the text, e.g., understanding or recall, are derived from characterizations of content. The major theoretical focus is the explication of understanding and recall. This position is fraught with logical complexities when it is applied to instructional expository text and, in fact, any other fixed instructional message.

The mathemagenic conception rejects the proposition that text or any other tangible instructional product has true specifiable content for which the reader signals receipts by demonstrating comprehension. The logic of this position is as follows. Assume that an operational definition of text content is the set of questions that a prudent and intelligent observer can generate about a passage. Generally, many questions can be produced for each text element. Additional unique questions can be generated from pairs of text elements and other multiples. As the text grows longer the number of questions that can be asked-with it our conceptions of content increase geometrically. As a result, content becomes much more difficult to specify as text length approaches the size usually found in school assignments. A basic assumption in our work is that the successful use of expository, instructional text or any other instructional product must be evaluated with reference to a criterion outside a text. The most likely of these outside criteria is derived from the purposes of instruction, i.e., a specification of what we want students to know when they are finished reading. This approach makes it possible, for example, to compare the value of several texts, a task that is awkward with text-centered, cognitivist approaches.

Cognitivist approaches have tended to be content centered. Accounts of mathemagenic activities, on the other hand, look to the pragmatics of teaching-to what we hope readers or learners will achieve-for criteria of successful use of text or any other instructional message. Mathemagenic activity is always considered with respect to a specific purpose. The characterization of instructional material that is of greatest importance, according to this view, is not the content but the relationship between material and instructional goals. The cognitivist-structuralist asks whether the instructional material is understood and how this is accomplished. We ask whether a particular purpose can be achieved with a text and what can be done to help learners achieve their goals.

Another difference is that cognitive models have tended to focus on relatively fixed components of learning processes that are used by expert learners and that can be taught like any other procedural skill. Research on mathemagenic activities, on the other hand, has concentrated on changeable processes that not only have flexible skill components but also include important dispositional elements. There has been an inclination in much information-processing research (see 5.4.1) to regard reading processes as the same or very similar in all readers, or that, at most, they may vary in the time constants associated with each processing stage. Work on mathemagenic activities has emphasized process differences among learners, and within learners from time to time.

The matter of fixed versus changeable, and of uniform versus diverse, learning processes is of course not only a matter of emphasis but also involves questions about empirical facts. These empirical issues have often received cavalier treatment by information-processing researchers. The preferred form of their theoretical models is the decomposition of information flow into component stages or the postulation of algorithmic processes that have functional properties similar to stage models. In work on reading models, for example, tachistoscopic experiments on letter or word recognition and on the speed of making categorical semantic judgments, are used to infer basic stages of the reading process-a process that is optimistically alleged to be the same for all. The discovery of processing stages is, in itself, not sufficient proof that these operative functions cannot be changed by suitable environmental pressures such as task demands or learning. The uniformity hypothesis is rarely questioned.

Whether these hypotheses are adequately tested or not, information-processing research has aimed at discovering fixed psychological functions that are common to all readers. By contrast, work on mathemagenic activities has focused on how environmental pressures can alter the transformation of information that takes place during study. In part, this emphasis rests on the belief that any complex human activity is flexible, adaptive, and determined by the diverse experiential histories of individuals. In part, it is motivated by the desire to account for failure, for lack of persistence, and to deal with changeable purpose. Furthermore, practical theories about the instructional uses of any media such as text should deal not only with models of possible reading processes but also with instructional intervention that can modify these processes.

It must also be recalled, particularly with respect to text, that its structure is not an unchangeable characteristic of language and human thought. Text structure is determined by the psychology of writers, by changeable custom, by aesthetics, and by current methods for the manufacture of text. For this reason, text structure and organization may prove to be a fickle subject for studies. To be sure, text structured in customary ways has a lasting place among the artifacts of our civilization and thus is a proper subject for study. But current written instructional forms may change, as may any other technical or cultural artifact. Written communication is now entering a new, electronic era, and new forms are likely to evolve at an increasing pace. Structural features will change in order to capitalize on new electronic means. Writing forms are to an important degree determined by current means of production. Those whose research focuses on into traditional text structure may find that text forms in practical services have been greatly altered by electronic presentation media.

Another difference between the two approaches to the study of learning processes is that the cognitivists are usually too optimistic about their ability to analyze covert mental processes. Information-processing models have usually been fairly sanguine about how much detail about studying can be revealed by current experimental methods (see 5.4.1). Mathemagenic research, on the other hand, has followed a somewhat more conservative line. The resulting conceptual models try to anchor functions on the level of observation and seek to live within their empirical income, even if this limits the internal complexity of models.

Footnotes:

1. Introspection provides everyone with a front-row seat on mental processes, and this has led some cognitivist researchers to propose protocols of inspection as data for the analysis of learning processes. Thanks to the articulate advocacy by Simon and his coworkers (e.g., Ericsson & Simon, 1980), protocol analysis is currently a widely practiced form of inquiry into strategic learning processes. The shortcomings of this method are legion. Perhaps the most serious of these is that the analysis of protocols is highly selective informants. For these reasons, this technique can be of only limited heuristic value in the analysis of learning-related processes.
2. The term mathemagenic hypothesis is not mine; it has appeared frequently in the literature.
3. It is difficult to characterize the currently popular constructivist's position (van Glaserfeld, 1987) on the enumerability of content but it must, at least in practical domains, devolve to the pragmatics of constructed representations. In this respect, the constructivist's view on content may be closer to the mathemagenics position.