Optimal allocation of instructional effort to interrelated learning strands

The problem of allocating instructional effort to two interrelated blocks of learning material is studied. In many learning environments, the amount of material that has been mastered in one area of study affects the learning rate in another distinct but related area—for example, the curriculum subjects of mathematics and engineering. A model is developed that describes this phenomenon, and the Pontryagin Maximum Principle of control theory is applied to determine optimal instructional policies based on the model. The nature of this optimal solution is to allocate instructional effort so that the learner follows a maximal average learning rate “turnpike” path until near the end of the study period and then concentrates on only one strand. This strategy, when applied to a more realistic stochastic model, defines a closed-loop feedback controller that determines daily instructional allocation based on the best current estimate of how much the student has learned. This estimate is calculated by a multistage linear filter based on the Kalman filtering technique.     

Visibility of an afterimage alone and in the presence of,one or two additional afterimages

The total time for which a circular afterimage is visible has been found to be increased by the presence of one or two additional afterimages. This increased’ visibility, which has been called “facilitation, ” is greater the nearer the afterimages are to one another, being optimum at .25 deg and declining to zero at 2.0 deg separation.     

Verification of algebra step problems: A chronometric study of human problem solving

A class of simple problem solving tasks requiring fast accurate solutions is introduced. In an experiment subjects memorized a mapping rule represented by lists of words labeled by cue words and made true/false decisions about conjunctions of propositions of the form “Y is in the list labeled by X”, written “X → Y”. Response times are analyzed using a “stage modeling” technique where problem solving algorithms are composed using a small set of psychological operations that have real time characteristics specified parametrically. The theoretical analysis shows that response time performance is adequately described in terms of the sequential application of elementary psychological operations. Unexpectedly, it was found that the proposition “X → YandX → Z” was verified as quickly as the apparently simpler “X → Y”. A case is presented for the modeling technique as applied to memory and problem solving tasks in terms of theoretical parsimony, statistical simplicity, and flexibility in investigative empirical research. Suggestions are made as to possible theoretical relations among fast problem solving, more complex and slower problem solving, and research in fundamental memory processes.     

Parallel processing of position and form information in young children

Young children and adults were compared in their processing of position and form information when only one type of information was processed and when both types of information were processed. For adults, position information in both the single and combined tasks showed a linear increase in report accuracy with increasing duration. For children, this linear increase was found only in the single task, at longer durations, resulting in a loss of parity across tasks for position information among children. No loss of parity was found for form information for either age group. The children’s loss of parity in processing position information when combined with form information replicates their previously demonstrated inability to process multiple-form arrays using a parallel independent strategy.     

The effect of size,retinal locus,and orientation on the visibility of a single afterimage

Unitary and fragmentary visibilities of the afterimage of a small rectangular bar were measured at three retinal loci. Unitary visibility was higher for fovea] than for parafoveal viewing, whereas fragmentation was greater the longer the bar. A model for estimating the size of receptors has been applied and gives the mean size of a “functional unit” to be 1.5 deg in the fovea and 3–4 deg parafoveally. Unitary visibility has been shown to be higher for vertical and horizontal bars than for obliquely oriented bars. Explanations for this result have been suggested in terms of the distribution, size, and selectivity of cortical orientation selective units.     

Enhancement of visual perception under conditions of short-term exposure to sensory isolation: a comparison of procedures for altering vigilance

An experiment was conducted to determine the pre- and posttest performance of subjects on a signal-detection task for the following three experimental conditions: sensory isolation, sensory alertness, and sensory relaxation. All subjects were assessed on 36 pretest and 36 posttest trials. Each block of 36 trials consisted of 12 "strong signals," 12 "weak signals," and 12 "no signals." Exposure durations for each experimental condition lasted for one hour. Analyses showed significant improvements in hits from the pretest trials to the posttest trials on the "strong" and "weak signals" for the sensory isolation condition. Moreover, on the posttest "weak signal" trials, subjects in the sensory isolation condition scored a significantly greater number of hits than did those in the sensory alertness or sensory relaxation conditions. It was concluded that sensory isolation produces perceptual enhancement, as measured by a signal-detection task.     

Influence of marihuana on storage and retrieval processe in memory

Following presentation and immediate free recall testing of 10 20-word lists, 48 Ss were divided into two groups, one of which received an oral dose of marihuana extract calibrated to 20 mg of Δ¹-THC and one of which received placebo. One hour later, all Ss were administered delayed recall, recognition, and order tests on the first set of words. Presentation of another set of 10 lists followed, and there were immediate recall and delayed recall, recognition, and order tests on these words. Performance of drug and placebo Ss did not differ significantly for any of the first delayed tests. However, the performance of drug Ss was poorer than that of placebo Ss on immediate recall, delayed recall, and delayed recognition of the second set of lists. We concluded that retrieval of information relevant to the occurrence or nonocurrence of an event was not affected by marihuana intoxication. Storage difficulties probably account for memory deficits due to the drug, and these difficulties appear to occur in the process of transferring information from short-term to long-term memory.     

Effects of short-term memory contents on short-and long-term memory searches

The Ss memorized a long-term set (LT set) of 20 words before participating in a recognition memory test. On each trial Ss were given a new short-term set (ST set) of from one to four words or one to four digits. The Ss gave a positive response to a test item that was a member of either the ST or the LT set and gave a negative response to a test item not in either set; both words and digits were used as test stimuli. The results indicated that reaction time (RT) to positive test items from the ST set was an increasing function 0f the size of the ST set; the same was also true for negative responses to test digits when the ST set was composed of digits. RT to other test stimuli, however, did not depend on ST set size. These results are consistent with the view that Ss access long-term memory (LTM) and short-term memory (STM) simultaneously rather than sequentially. The results also showed that Ss responded more quickly to test items from the LT set when the ST set contained digits than when it contained words. Negative test items that were words, however, were rejected more slowly when the ST set contained digits than when it contained words. These results suggest that the search of LTM was affected by the contents of STM.     

Response latency in visual search with redundancy in the visual display

Two experiments were run to investigate the effects of redundant display items upon response latency in a visual search task. In the first study, Ss searched five-letter displays for a predesignated critical letter. Both critical and noncritical letters could be repeated in the displays. Mean response latency decreased markedly with increasing redundancy in the critical letter and was affected to a lesser extent by redundancy in the noncritical letters. In the second study, Ss were required to detect the presence of redundant letters in displays of from two to five letters, first with no information as to what letter might be repeated, then with knowledge of which letter would be repeated if the display contained a redundant letter. Response latencies in the former case were much slower than in the latter. The implications of these findings for current views of visual information processing were discussed.