Reducing Perceptions of Time Required to Complete Math Assignments by Adding Problems to Assignments: A Synthesis of the Additive Interspersal Research

Results from nine experiments were analyzed to evaluate the relationship between relative problem completion rates (RPCR) and judgments of time involving mathematics assignments. For each experiment, control assignments contained only target mathematics computation or word problems. Matched experimental assignments contained similar target problems with additional, briefer problems interspersed after every third target problem. After working on each assignment for the same amount of time, students selected the assignment that they judged would require the least or most amount of time to complete. Regression analysis revealed a significant linear relationship between RPCR (i.e., PCR on experimental assignments/PCR on control assignments) and time perceptions (r=.97). As RPCR increased, the percentage of students judging the experimental assignments as being less time consuming increased proportionally. Discussion focuses on application of time perception theories to educational settings.     

REPEATED ACQUISITION OF BEHAVIORAL CHAINS: RESPONSE SEQUENCES OR CONDITIONAL DISCRIMINATIONS?

The purpose of this study was to determine whether pigeons learn a sequence of positional responses or a series of conditional discriminations under a repeated-acquisition-of-behavioral-chains procedure. Three pigeons were trained under a repeated-acquisition procedure in which three different key colors served as stimuli correlated with the three steps in a chain. The order of presentation of the three stimuli was altered during the latter part of each test session after acquisition had occurred. If the pigeons had acquired a response sequence, the pattern of responding should remain the same as in the initial portion of the test session. However, if the pigeons had acquired a conditional discrimination, the response pattern should change in accordance with the changed order of the key colors. Although the results of this study do not rule out the possibility that the subjects acquired, to some degree, a response sequence, the results suggest that the behavior of pigeons under a repeated-acquisition-of-behavioral-chains procedure is controlled primarily by conditional discriminative stimuli.     

Choice between single and multiple delayed reinforcers.

Pigeons chose between alternatives that differed in the number of reinforcers and in the delay to each reinforcer. A peck on a red key produced the same consequences on every trial within a condition, but between conditions the number of reinforcers varied from one to three and the reinforcer delays varied between 5 s and 30 s. A peck on a green key produced a delay of adjustable duration and then a single reinforcer. The green-key delay was increased or decreased many times per session, depending on a subject's previous choices, which permitted estimation of an indifference point, or a delay at which a subject chose each alternative about equally often. The indifference points decreased systematically with more red-key reinforcers and with shorter red-key delays. The results did not support the suggestion of Moore (1979) that multiple delayed reinforcers have no effect on preference unless they are closely grouped. The results were well described in quantitative detail by a simple model stating that each of a series of reinforcers increases preference, but that a reinforcer's effect is inversely related to its delay. The success of this model, which considers only delay of reinforcement, suggested that the overall rate of reinforcement for each alternative had no effect on choice between those alternatives.     

Maximizing present value: A model to explain why moderate response rates obtain on variable-interval schedules

In Phases 1 and 3, two Japanese monkeys responded on a multiple variable-ratio 80 variable-interval X schedule, where the value of X was adjusted to ensure equal between-schedule reinforcement rates. Components strictly alternated following the delivery of a food pellet, and each session ended following 50 components. Phase 2 differed from the others only in that the 50 pellets previously earned during the session were delivered together at session's end. Variable-ratio response rates did not decrease across phases, but variable-interval response rates decreased substantially during the Phase 2 procedure. This rate decrease was attributed to the food-at-session's-end manipulation removing the greater immediacy of reinforcement provided by short interresponse times relative to long interresponse times. Without this time preference for short interresponse times, the variable-interval interresponse-time reinforcement feedback function largely controlled response emission, dictating a response-rate reduction. This result was explained in terms of the economic notion of “maximizing present value.”     

Color preference in pigeons: stimulus intensity and reinforcement contingency effects in the avoidance of blue stimuli.

In a procedure intended to determine color preference in pigeons (which partially replicated Catania, Owens, & von Lossberg, 1983), two keys were illuminated by different colors drawn from a set of amber, red, green, or blue stimuli; this was followed by the presentation of grain when either of the two colors was pecked. The grain was illuminated alternately across trials with the colors presented on the keys. In Experiment 1 the intensity of the color stimuli used was not equalized, whereas in Experiment 2 the intensity of the colors was equalized. The low preference for blue found in Experiment 1, as measured by differential key pecking, was not found in Experiment 2. The discriminability of the intensity-equalized colors was confirmed in Experiment 2a, in which equal-intensity color discrimination problems were presented. In Experiment 3, as in Catania et al. (1983), a response-independent reinforcement schedule was used, but with intensity-equalized colors. In contrast to Experiment 2, very low preference for blue was found here and in Experiment 4, which used a within-subject procedure. These findings suggest that pigeon color preference may be a function of intensity, but all controlling variables have not as yet been identified.     

A molecular analysis of choice on concurrent-chains schedules.

Six pigeons responded on concurrent-chains schedules with either independent or interdependent equal variable-interval schedules in the initial links and unequal variable-interval schedules, always in a 2:1 ratio, in the terminal links. Relative response rates in the initial links increased across conditions as initial-link duration was shortened and decreased across conditions as terminal-link duration was shortened, replicating previous findings. Responses in the initial links were recorded in 5-s bins, and local or molecular relative response rates were calculated in order to ascertain how relative response rate varied as a function of time since the onset of the initial links. Two distinct molecular patterns were found. With interdependent initial links, relative response rates for the preferred key were elevated for the first 10 or 20 s of the initial links and then declined to an asymptotic value. With independent initial links, a negative recency effect was found similar to that reported by Killeen (1970). These two molecular patterns were related to the different momentary reinforcement probabilities resulting from independent and interdependent scheduling.     

Punishment of autoshaped key-peck responses of pigeons

The effects of different voltages of response-dependent and response-independent electric shock on the frequency of key-peck responses engendered by an autoshaping procedure were studied. In Experiments I and II, each response produced a brief electric shock, and response frequency generally decreased more with higher-voltage shock. Preshock frequencies of responding were generally recovered across successive sessions of relatively low-voltage shock delivery but not at higher shock voltages. The effects of response-dependent and response-independent shock were compared in Experiment III by using a yoked-control procedure in which each pigeon received each type of shock delivery at different times. Response-dependent shock generally produced greater decreases in response frequency. In the final experiment, one response-independent shock per autoshaping trial was scheduled. The number of autoshaped responses per trial was related to shock voltages. These results suggest that response-dependent and response-independent electric shock effectively decrease frequency of autoshaped responses.     

A new procedure for detection of crossing DIF

The purpose of this paper is to present a hypothesis testing and estimation procedure, Crossing SIBTEST, for detecting crossing DIF. Crossing DIF exists when the difference in the probabilities of a correct answer for the two examinee groups changes signs as ability level is varied. In item response theory terms, crossing DIF is indicated by two crossing item characteristic curves. Our new procedure, denoted as Crossing SIBTEST, first estimates the matching subtest score at which crossing occurs using least squares regression analysis. A Crossing SIBTEST statistic then is used to test the hypothesis of crossing DIF. The performance of Crossing SIBTEST is evaluated in this study.This research was partially supported by a grant from the Law School Admission Council and by National Science Foundation Mathematics Grant NSF-DMS-94-04327. The research reported here is collaborative in every respect and the order of authorship is alphabetical. The authors thank Jeff Douglas and Louis Roussos for their useful comments and discussions.     

内隐记忆的证明逻辑与加工分离说（PDP）的修正模型

讨论了内隐记忆的证明逻辑和内隐与外显测验中的意识和无意识影响问题。间接证明内隐记忆的逻辑应用在功能分离实验中。它的前提假设是记忆测验都是＂纯净＂的。直接证明逻辑应用在匹配比较实验中。它认为测验中的意识和无意识影响是并存的,Ｊａｃｏｂｙ等人近期提出的加工分离说（ＰＤＰ）在匹配比较法的基础上,将测验中的意识和无意识影响进行了分离,并借用经典测验理论的公式计算这两种影响。作者认为,按照概率论关于两个随机独立事件之和与积的运算法则,必须把包含测验（ｉｎｃｌｕｓｉｏｎｔｅｓｔ）的公式修正为Ｉｎｃｌｕｓｉｏｎ＝Ｒ（１－ａ）＋Ａ（１－Ｒ）。修正过的ＰＤＰ由四个方程组成。它不仅考虑了原ＰＤＰ忽视的外显条件下的无意识缺失（１－ａ）,而且可以更加确切地估计回忆概率（Ｒ）。这在数学理论上已找到了证据。     

Choice in the time-left procedure and in concurrent chains with a time-left terminal link.

In two experiments, rats chose between a standard fixed-duration food-associated stimulus and a stimulus whose duration was the time remaining to reinforcement in an elapsing comparison interval. In Experiment 1, 4 rats responded in a time-left procedure wherein a single initial-link variable-interval schedule set up two potential terminal links simultaneously. As time elapsed in the initial-link schedule, the choice was between a standard fixed-interval 30-s terminal link and a time-left terminal link whose programmed interval requirement equaled 90 s minus the elapsed time in the initial link. Rats generally responded more on the lever with the shortest programmed terminal-link duration, but the temporal parameters of the procedure were found to vary with response distributions. Contrary to previous reports, therefore, time-left data were well predicted by choice models that make no assumptions about animal timing. In Experiment 2, 8 rats responded on a concurrent-chains schedule with independent variable-interval initial links and a time-left terminal link in one of the choice schedules. On the time-left lever, the programmed terminal-link delay equaled 90 s minus the elapsed time in the time-left initial link. On the standard lever, terminal-link responses were reinforced according to a variable-interval schedule whose average value varied over four conditions. Relative time-left initial-link responses increased in the elapsing time-left initial-link schedule as the time-left terminal link became shorter relative to the standard terminal link. Scalar expectancy theory failed to predict the resultant data, but a modified version of the delay-reduction model made good predictions. An analysis of the elaboration of scalar expectancy theory for variable delays demonstrated that the model is poorly formulated for arithmetically distributed delays.