|This text was taken from P.A.Wozniak, Economics of learning, Doctoral Dissertation, University of Economics, Wroclaw, 1995|
Repetition spacing in learning was in the center of my research over the last ten years (for review see: Wozniak 1990). In this chapter I would like to familiarize the reader with the concept of the optimum spacing of repetitions that will frequently be referred to throughout the dissertation.
There has been a great deal of research on how different spacing of repetitions in time affects the strength of memory and how the resulting findings could be applied in the practice of effective learning. It has been predicted, and to a large degree confirmed, that by changing the spacing of repetitions, a substantial gain in the effectiveness of learning might be obtained (e.g., Bjork, 1979; Glenberg, 1979; Glenberg 1980; Clifford, 1981; Dempster, 1987; Bahrick, 1987).
A major breakthrough in the study of optimum spacing of repetitions came with the discovery of the spacing effect which has been found under a wide range of conditions, and which refers to the fact that sparsely spaced repetition produce a better performance in memory tests than do densely spaced repetitions (Melton, 1967; Hintzman, 1974; Crowder, 1976; Cuddy, 1982).
However, studies reporting a robust spacing effect in classroom conditions are the exception rather than the rule (Dempster, 1987). This follows directly from the fact that the spacing effect is subject to certain boundary conditions which limit its universal applicability. It has been found that with increasing spacing, the performance in memory tests improves only to a certain point after which it gradually decreases (Peterson, 1963; Hintzman, 1973; Glenberg, 1977; Glenberg, 1980; Toppino, 1985). The most convincing interpretation of this fact is that as the spacing increases, the initial memory trace becomes less and less accessible. Despite the reduced accessibility, in distributed spacing, the repetition produces an increased memory effect.
However, after the spacing reaches some critical point, the memory trace becomes completely inaccessible, and the processing of the to-be-remembered item is similar to the one that takes place at initial presentation (Underwood, 1961; Melton, 1970; Rose, 1984). In other words, in spaced repetition, a trade-off between the spacing effect and forgetting must be taken into consideration. As Bahrick pointly noticed, the optimum inter-repetition interval is likely to be the longest interval that avoids retrieval failures, and that finding optimum intervals will yield major contributions of memory research to education (Bahrick, 1987).
Though some theoretical models suggest that the strength of memory should increase gradually with successive repetitions (Atkinson, 1968; Bernbach, 1971), the major shortcoming of most of the research that has been done on the effects of inter-repetition intervals on the performance in memory tasks was application of equally spaced repetition schedules (e.g., Hintzman, 1973; Bellezza, 1975; Jensen, 1981; Bahrick, 1987; Greene, 1989). Another shortcoming that makes it hard to collect data concerning optimum spacing of repetitions is the fact that most of the available studies considered inter-repetition intervals on the order of seconds, minutes and hours. Spacing repetitions in periods longer than one week has been very scarcely studied (Glenberg, 1980).
A major exception to the rule was the report by Bahrick, who studied the effects of spacing in an experiment spanning 14 months, and who measured the resulting knowledge retention in a follow-up study after the period of 8 years (Bahrick, 1987). The third shortcoming often found in the research on spacing was the lack of consideration for the difficulty of particular items, i.e., the same repetition schedules were used for both easy and difficult items. The report by Atkinson (1972), though spanning the period of one week only, was a major exception here. Finally, the fourth limitation of the research on spacing was a small number of to-be-remembered items that were considered in the process of learning. For example, the report by Bahrick (1987) concerned the retention of 50 English-Spanish word pairs.
Let us have a closer look at theoretical implications of the spacing effect, and how they might be used to guide the research on optimum spacing of repetitions. There have been a number of theoretical explanations put forward to account for the spacing effect (see Hintzman 1974, Greene 1989 for a review).
They could be grouped into the following three categories:
There has been a number of contradictory reports, many of them invalidating the importance of encoding variability for the spacing effect (Bellezza,1975; Johnston, 1976; Bird, 1978; Postman, 1983). The encoding variability theories postulate that increased spacing facilitates memory by increasing the number of possible retrieval cues for repeated items. We believe, that the contradictory results of experiments on encoding variability come from the wrong interpretation of the impact of the contextual variability on the effectiveness of learning. Let's consider an example in which a subject is supposed to learn to recognize mammals by responding to the definition a warm-blooded vertebrate which produces milk. If in the repeated exposure, the subject encounters the definition a four-legged animal which produces milk, the strength of memory is likely to be increased not because of establishing two separate retrieval routes, but by strengthening the already established single path which emphasizes the intersection of defined characteristics; namely, the ability of mammals to produce milk (cf. Bellezza, 1975). If the new definition was a four-legged animal which is covered by hair, the effect of the variable context might be opposite because of the students confusion about what a mammal indeed is (is it milk producing, covered with hair, or both); hence, the possible discrepancies in studies on encoding-variability. Though the encoding variability may play a part in the spacing effect, it is certainly not sufficient to account for it (Greene, 1989).
Similarly, there has been a body of evidence, that though voluntary deficit in processing accorded an item may weaken memories in a massed presentation, elimination of the voluntary aspect of the deficit failed to suppress the spacing effect (Underwood, 1969; Hintzman, 1975a; Shaughnessy, 1976; Jensen, 1981).
By far most attractive, in my view, are the theories which take into account involuntary processes, and which predict that there exists a widespread, underlying, biological mechanism which weakens formation of memories in the period directly following the last repetition (Bjork, 1970; Hintzman, 1973; Hintzman, 1975b).
This mechanism may have a molecular nature, and may be beyond our control as far as its implications for learning are concerned. An interesting support for this view comes from the strength theory (Hinrichs, 1970), which concludes that temporal judgments are not based on temporal information stored in memory, but on the strength of memory traces. In other words we can judge the moment in which a repetition took place not because we store a temporal tag in memory, but because of the correlation between the lapse of time and decline in memory traces. Opponents of the strength theory argue that it doesn't explain why items subject to the primacy effect are not misjudged as more recent.
Let us have a look at the possible advantages of the involuntary habituation of memory from the evolutionary standpoint. The obvious value of forgetting is to prevent the nervous system from running out of the memory storage. The benefit coming from strengthening memories by means of repetition is that only most frequently encountered tasks are remembered. If we consider the fact that in real life a twice-encountered task is more probable to be encountered again than a once-encountered task, which is more probable to be encountered than a never-met task, we can conclude that the optimum action of the memory system should result in multiplying the period of the retrievability of a memory trace each time a task is encountered. In other words, the progressive spacing of repetitions stands the greatest chance to be validated on evolutionary grounds. The possible value of the post-repetition habituation of memories comes from the fact that a substantial increase in memory strength at each exposition does not seem to be advantageous for survivability. It would result in unnecessary waste of the storage for lifelong memories produced for massed phenomena which are transitory. In other words, the habituation of memories that follows a repetition seems to ensure that the brain maximizes the average probability of reencountering the remembered tasks, i.e. it maximizes the usefulness of memories