AECT Handbook of Research

Table of Contents

30. Control of Mathemagenic Activities
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  Introduction
30.1 Origins
30.2 Cognitive Models of Learning Processes
30.3 Some History
30.4 Characteristics of Mathemagenic Activity
30.5 Induction, Modification, and Maintenance
30.6 Interventions
30.7 Dispositional Social Influences
30.8 Learning In Schools and Other Instructive Settings
30.9 Macrotheory of Instruction
30.10 Research issues And the Role Of Mathemagenic Activities In New Instructional Models
30.11 Mathemagenic Activities And Developments In Instructional Technology
30.12 Summing Up
  References
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30.8 Learning in Schools and Other Instructive Settings

30.8.1 Study Skills Training

Training in study skills has long been on the educational scene (e.g., Deese, 1957; Robinson, 1970), usually on an individual basis. The study skills targeted in these courses involve actions that might be termed mathemagenic under many circumstances. The following section offers a critical perspective on study skills training and contrasts study skills training with shaping and support of mathemagenic activities.

Failure to meet academic standards is sometimes due to inadequate teaching or inadequate teaching materials. Another very important contributor to low achievement is insufficient or ineffective learning or study activities. Many students don't do enough homework or remember little of what they have studied. Students pay poor attention in class or gain little from instructional episodes from which other students have profited. Some of these failures have been ascribed to low abilities. But hardly anyone doubts that the exercise of appropriate learning activities can improve academic results. For this reason, many educators feel that training in study or learning skills will solve the achievement problems. They reason that part of the difficulty is that students do not know how to study and need to be taught. In the past, institutional efforts were usually fairly perfunctory. In recent years, however, stimulated by concern about low academic achievements, many schools have adopted systematic instruction in study skills. These training courses tended to be guided by the rationalistic conception of learning processes that are endemic among cognitivists.

Strong claims have been made for the educational efficacy of these courses, although evaluation studies provide mixed results (see Nicholson, 1988).

We see the inadequate study activities problem, instead, as a matter of the instructional management of Mathemagenic activities. There are three major differences between this view and the study skills approach to bolstering academic achievement. The first centers on the relative importance of the knowledge about how to study versus the disposition to use this knowledge. Mathemagenic research has emphasized the second concern. The second difference has to do with the general applicability of learning strategies to instructional situations. Much mathemagenic research points to content and form-specific improvements in the effectiveness of learning processes (including Rothkopf & Bisbicos, 1967; Duchastel, 1979; Glover, Plake & Roberts, 1981; Mayer, 1980; Reynolds & Anderson, 1982; Reynolds, Standiford & Anderson, 1979; Sagerman & Mayer, 1987). The third substantial difference between these two points of view is the degree of faith they place on intention during learning.

30.8.2 Knowledge versus Disposition

What is the nature of the skills that have been proposed for inclusion in formal learning-skill training programs? They are not like typing or serving a tennis ball, so automatic that highly proficient performers can barely describe what they do? Nor are they like folding a parachute or describing Wellington's maneuvers at the Battle of Waterloo. Neither are they like algebra or calculus, ready to be used whenever the situation demands it except for the erosions of forgetting.

No, they are more like the many skills for which the critical characteristic is not only knowing but also in translating knowledge into action. They are much more like good manners. Many of the folks in the subway who are staring at the elderly pregnant woman with the broken leg know they should offer her their seat. Yet sometimes such women stand all the way to the hospital.

Study skills are like dietary information that diabetics can describe in fastidious detail but neglect at the dinner table. They are like knowing how to protect the roses in your garden from aphids but failing to do so. They are like knowing about calories while wishing to be thin and continuing to eat too well.

Study skills training is like information about birth control. General educational programs produce results, but a substantial number of unwanted conceptions persist that are not due to deficiencies of method, or lack of knowledge or skill, but simply from failure to act in an appropriate way. Driving safety, industrial accident prevention, village sanitation-all of these involve skills from the same category as those trained in study and learning skills programs.

The concern of teachers with learning activities in Practical settings is not only whether students know how to study effectively but also whether they are willing or

disposed to do so. The relative importance of these two components is an interesting question for debate, analysis, and experiment. But it is fair to conclude that the disposition to translate learning skill into action is very important. This clearly has been one of the focuses of research on mathemagenic actions.

30.8.3 Learning Strategies and Educational Styles

Gross learning strategies that are taught tend to have three general components: (1) selection, (2) mnemonic mooring, and (3) integration (Cook & Mayer, 1983; Dansereau et al., 1979; Jones et al., 1984; Weinstein, 1978). Mayer (1987) has made similar distinctions, calling them selection, internal and external connection. Mayer's and other careful studies have shown that learning maneuvers, executed in any one of a number of variations, can produce gains in academic achievement and in retention. There is little evidence, however, that these learning strategies are universal, portable tools that can help students in any learning task whatsoever.

Learning strategies are neither content independent nor context-free. As most are taught today, their value to the learner depends on subject matter and educational goals. They depend on the structure and form of instructional information. Perhaps most. important, their value depends on the intellectual outlook and style favored by academics and educationists who manage the schools. The latter is, of course, important if the aim of learning strategy training is to foster academic success. But such training will not necessarily be useful in preparation for life and for the world of work. Clearly, a successful experimental demonstration in a particular setting is not a sufficient reason for a school to adopt a training program for a particular set of learning skills. The most important question is whether the targeted learning skills are really useful to the student.

The argument can be made that what certain learning (and some reasoning) strategies accomplish is to reduce information into forms that are currently in vogue in the academic/educational community. Such strategies are of immediate advantage to the learner because academic success depends on approval by members of this community. But it is uncertain whether these learning strategies will be useful in the long term, in the world of work or in more open, less-structured learning settings. To put it in blunter language, such learning strategy training teaches students to extract what their teachers want to hear and to put it into an approved form. And what teachers want to hear and the forms that are approved may change from time to time or from circumstance to circumstance. It depends on educational fashions. The notion of the main idea of a passage, for example, smacks of educationists' cant. It also carries with it the tacit assumption that the main aim of reading is reproduction of information in a testlike setting. There may be more to education than this. The developer of learning skill training must make sure that what is taught is sufficiently flexible to avoid fashionable educational traps. Learning strategies training should be determined by the information needs of the learner in the contemporary world and not necessarily by current pedagogic fashion!

One important difference between study strategy training and the conception of mathemagenic behavior is that the first tends to be oriented to general goals-towards receipt theories of understanding-while the latter is pragmatic and always oriented to a very specific educational purpose. Interest in practical exploration in learning strategies was at least partially stimulated by experimental work in learning laboratories, and by attendant theoretical conceptions. But the condition that makes learning skill training viable as an academic tool is uniformity of expectations about academic outcomes, the routine application of certain teaching methods, and the nature of currently used instructional media.

30.8.4 Selecting Learning Strategies and the Strategy of Selection

As indicated before, selection is an important component of learning skill. Selection includes two distinct but related components: (a) the choice of strategies appropriate for particular conditions and tasks, and (b) the choice from the instructional content of appropriate elements to which particular learning strategies may be applied. Selection is a critical component of learning activities because learning maneuvers and mnemonic devices, no matter how skillfully executed, are ineffective if they are inappropriately applied or if applied to inappropriate content elements. Inappropriate applications may result from mismatches between learning goals and the nominal purposes of a study maneuver. The nominal aim of the study maneuver may not be the most efficient method for achieving the actual learning goal, even when the nominal aim of the study maneuver appears to match the actual goal.

Selecting learning strategies according to nominal descriptions of their purposes is not necessarily efficient because incidental consequences of processes are sometimes more powerful than intentional, systematic approaches. Everyone wants the learner to acquire intelligent flexibility in the choice of learning maneuvers. Almost every learning skill-training program teaches that different learning goals require different learning activities. But broad identification of learning goals may not be sufficient for adapting the most efficient strategies. For example, if the actual study goal is to remember the exact sequence of events in a descriptive passage, it may be more efficient to try to remember the exact wording of the event description. These phenomena were very neatly demonstrated by the classical (and now apparently largely forgotten) study of Postman and Senders (1946). They asked subjects to read a Chekov short story under one of six goal-setting directions, e.g., general comprehension, or to remember the sequence of events, the details of wording, etc. Recall was tested using items appropriate to each goal. While some directions facilitated performance on relevant items, others produced reliable improvements in unrelated items, improvements that were in some cases substantially larger than those produced by directions relevant to the test questions. The Postman and Senders' experiment (1946) proved quite neatly that the nominal character of learning goals is not necessarily a good predictor of what the learner will achieve with the study activities that are induced by these descriptions of learning goals.

The second important selection activity does not involve choice of strategy but rather choice of appropriate content elements. Skill in content choices is probably the most difficult of all learning strategies to train, because it is so closely tied to the semantics of teaching materials and the pragmatics of the instructional tasks. Much learning material, and in particular text, is intended for many uses. Consequently, ordering of content elements with respect to centrality or importance does not depend on the material alone but also on instructional purpose or demand. An encyclopedia article, for example, is not like a blueplate special that can simply be analyzed into meat, accompanying vegetable, and decorative garnishes. In practical settings, cut-and-dried selection formulas will very likely flounder on the rocky complexities of human knowledge. It is interesting to speculate that much of the progressive gain in incidental learning that results from adjunct postquestions is probably due to the focusing of selection by inductive processes.

Two conclusions may be drawn about selection. The first is that the relationship between actual learning goals and the nominal intent of the learning maneuvers we teach can be surprisingly devious. Postman and Senders' (1946) work suggests that effective intentional control of learning activities can benefit from a little sophistication about the incidental consequences of learning activities. The second point is that when teachers have very specific instructional purposes but use general, multiuse materials, the materials themselves cannot be sufficient guides about what is important information.

 


Updated August 3, 2001
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