A procedural theory of eye movements in doing arithmetic

A procedural theory of eye movement that accounts for main features of the stochastic behavior of eye-fixation durations and direction of movement of saccades in the process of solving arithmetic exercises of addition and subtraction is presented. The best-fitting distribution of fixation durations with a relatively simple theoretical justification consists of a mixture of an exponential distribution and the convolution of two exponential distributions. The eye movements themselves were found to approximate a random walk that fits rather closely in both adult and juvenile subjects the motion postulated by the normative algorithm ordinarily taught in schools. Certain structural features of addition and subtraction exercises, such as the number of columns, the presence or absence of a carry or a borrow, are well known to affect their difficulty. In this study, regressions on such structural variables were found to account for only a relatively small part of the variation in eye-fixation durations.     

Behavioral thresholds for tones during infancy

An adaptive up-down tracking procedure was used in combination with a visually reinforced head turn response to examine auditory sensitivity for 500, 2000, and 8000-Hz tone bursts in infants 6 to 18 months of age. Six- and 10-month-old infants were tested with headphone presentation of stimuli, while 10-, 14, and 18-month-olds were tested in sound field. Infant threshold estimates for both headphone and sound field were within 15 dB of adult comparisons for all frequencies and age groups. Six-month-olds were significantly less sensitive to the 8000-Hz tone than to either of the lower frequency stimuli, but older infants demonstrated approximately equal sensitivity for all three frequencies tested.     

Speaker bias in children's evaluation of the external consistency of statements

The hypothesis of this study is that an assumption of speaker credibility affects children's judgments of the external consistency of statements. In two experiments, first and third grade children (6 and 8 years of age, respectively) and college adults were read short paragraphs containing contradictory information from a contextual source and a speaker. The contextual source was described as either authoritative or nonauthoritative and discredited. The speaker was either an adult or child. Thus the contextual source was either more or less reliable than the speaker. Subjects were asked to affirm or contradict the speaker's statement, and to choose either the source or the speaker as most believable. The results showed that adult responses varied with the contextual source alone, while the responses of the first graders varied primarily with the speaker's age. The responses of the third graders varied with both factors. The results suggest young children can assess the external consistency of statements but frequently do not because of their assumptions about speakers and other performance factors.     

The development of derived stimulus relations through training in arbitrary-matching sequences

Five-year-old children were taught three-stage sequences of arbitrary matching: A-C, B-C, A-D; A-C, B-D, B-C; or A-C, A-D, B-C. Each stage refers to a sample-comparison relation between stimuli. Unreinforced test probes revealed untrained arbitrary matches (B-D, A-D, and B-D, respectively), derivable by substitution of stimuli with a common sample or comparison function. Additional probes revealed further untrained sample-comparison relations derivable by substitution and identity, including the commuted relations D-B, D-A, and D-B, respectively. These processes may have relevance to conceptual and verbal behavior.     

Reaction times of younger and older men and temporal contingencies of reinforcement

Influences of extended training and temporal contingencies on reaction time were studied in relation to developmental differences. Older and younger men were trained on a chained schedule in which completion of a variable interval produced a terminal link in which reaction time was measured. The reaction-time procedure involved a conditional discrimination with matching to sample in one component and oddity matching in the other. During baseline training, no time limit was placed on the response to the discrimination choice stimuli. Subsequently, increasingly severe time limits were imposed over a series of sessions. Older and younger men showed increased speeds (decreased reaction times) when temporal contingencies were imposed, and these changes were maintained during post-training baseline sessions when there was unlimited time in which to respond. The younger men generally responded faster than the older ones, and age differences were not appreciably reduced during the course of the experiment. The results indicated the feasibility of studying reaction time in human subjects using operant procedures analogous to those developed for the study of nonverbal organisms.     

A more powerful method for testing for agreement between a judge and a known standard

We assume that a judge's task is to categorize each ofN subjects into one ofr known classes. The design of primary interest is employed if the judge is presented withs groups, each containingr subjects, such that each group of sizer consists of exactly one subject of each of ther types. The probability distribution for the total number of correct choices is developed and used to test the null hypothesis that the judge is guessing in favor of the alternative that he or she is operating at a better than chance level. The power of the procedure is shown to be superior to two other procedures which appear in the literature.The authors are grateful for the suggestions of the referees and for computer funding provided by the Northeast Regional Data Center at the University of Florida.     

What is educational theory and how to make it?

An analysis is provided detailing the conditions for the appropriate theoretical study of the object of educational science: pedagogy.     

CONDITIONAL DISCRIMINATION VS. MATCHING TO SAMPLE: AN EXPANSION OF THE TESTING PARADIGM

A subject's performance under a conditional-discrimination procedure defines conditional relations between stimuli: “If A1, then B1; if A2, then B2.” The procedure may also generate matching to sample. If so, the stimuli will be related not only by conditionality, but by equivalence: A1 and B1 will become equivalent members of one stimulus class, A2 and B2 of another. One paradigm for testing whether a conditional-discrimination procedure has generated equivalence relations uses three sets of stimuli, A, B, and C, three stimuli per set. Subjects learn to select Set-B and Set-C comparisons conditionally upon Set-A samples. Having been explicitly taught six sample-comparison relations, A1B1, A1C1, A2B2, A2C2, A3B3, and A3C3, subjects prove immediately capable of matching the B- and C-stimuli; six new relations emerge (B1C1, B2C2, B3C3, C1B1, C2B2, C3B3). The 12 stimulus relations, six taught and six emergent, define the existence of three three-member stimulus classes, A1B1C1, A2B2C2, and A3B3C3. This paradigm was expanded by introducing three more stimuli (Set D), and teaching eight children not only the AB and AC relations but DC relations also—selecting Set-C comparisons conditionally upon Set-D samples. Six of the children proved immediately capable of matching the B- and D-stimuli to each other. By selecting appropriate Set-B comparisons conditionally upon Set-D samples, and Set-D comparisons conditionally upon Set-B samples, they demonstrated the existence of three four-member stimulus classes, A1B1C1D1, A2B2C2D2, and A3B3C3D3. These larger classes were confirmed by the subjects' success with the prerequisite lower-level conditional relations; they were also able to select Set-D comparisons conditionally upon samples from Sets A and C, and to do the BC and CB matching that defined the original three-member classes. Adding the three DC relations therefore generated 12 more, three each in BD, DB, AD, and CD. Enlarging each class by one member brought about a disproportionate increase in the number of emergent relations. Ancillary oral naming tests suggested that the subject's application of the same name to each stimulus was neither necessary nor sufficient to establish classes of equivalent stimuli.     

The influence of positive and negative reinforcement on selective attention in the rat

In Experiments 1 and 2 rats were trained under two multiple schedules of reinforcement. In one, bar pressing during a tone-light compound stimulus was reinforced under a variable-interval food reinforcement schedule. In the other multiple schedule, bar pressing avoided grid shock on a free-operant schedule. In both multiple schedules, a discrimination was maintained by an extinction schedule that was operative during the absence of the tone-light compound. In Experiments 1 and 2 the intensity of the tone-light compound was manipulated over three levels. Subsequent extinction tests revealed that light was attended to, almost exclusively of the tone, when food reinforcement had maintained bar pressing. On the other hand, the tone gained considerable attentional control under the shock avoidance schedule. This stimulus-reinforcer interaction was maintained for all three levels of the compound intensity. In Experiment 3 it was investigated whether this interaction was associative by presenting shock during the absence of the tone-light compound when food reinforcement maintained responding, and food during the absence of the compound when shock avoidance maintained responding. Since both food and shock were presented during a single session for both schedules, nonassociative effects of the reinforcing stimuli were equivalent across the schedules. Nevertheless, the stimulus-reinforcer interaction was maintained, indicating that the interaction was an associative effect.