On Herrnstein's equation and related forms

In 1970, Herrnstein proposed a simple equation to describe the relation between response and reinforcement rates on interval schedules. Its empirical basis is firm, but its theoretical foundation is still uncertain. Two approaches to the derivation of Herrnstein's equation are discussed. It can be derived as the equilibrium solution to a process model equivalent to familiar linear-operator learning models. Modifications of this approach yield competing power-function formulations. The equation can also be derived from the assumption that response strength is proportional to reinforcement rate, given that there is a ceiling on response rate. The proportional relation can, in turn, be derived from a threshold assumption equivalent to Shimp's “momentary maximizing”. This derivation implies that the two parameters of Herrnstein's equation should be correlated, and may explain its special utility in application to internal schedules.     

Precriterion stationarity in markovian learning models

Two forms of stationarity prior to criterion in absorbing Markov chains are examined. Both forms require that the probability of a particular response on a particular trial before absorption be independent of trial number. The stronger of these forms holds that this is true independent of starting state; the weaker, only for a specified set of starting probabilities. Simple, necessary and sufficient conditions for both forms are developed and applied to several examples.The author would like to thank Charles Lewis for his help in developing this article, and Peter Polson of the University of Colorado and an anonymous referee for several fruitful suggestions made in reviews of earlier versions.     

The stages of acquisition in stimulus fading

Pigeons were exposed to a stimulus fading procedure in which control of responding was transferred from red and black stimuli to lines of different angular orientation. After superimposing one line on the red stimulus and the other line on the black stimulus, the intensity of the lines was gradually increased and that of the red stimulus was gradually reduced. Probes consisting of red and line stimuli presented separately were used during the course of fading to assess control exerted by each element of the compound. As the lines were faded in, they did not acquire control of responding. As red was faded out, control of responding was acquired first by the lower intensity red stimuli in combination with the line stimulus, and finally by the angular orientation of the lines. Probes also determined the point at which the line stimuli, presented alone, would maintain a high degree of stimulus control. The results demonstrated that new stimuli in fading acquire dimensional control of responding in two sequential stages. Acquisition of stimulus control in fading was explained in terms of attenuation of stimulus blocking.     

Acquiring verbal reference: The interplay of cognitive,linguistic, and general learning capacities

Verbal reference is the ability to use language to communicate about objects, events, or ideas, even if they are not witnessed directly, such as past events or faraway places. It rests on a three-way link between words, their referents, and mental representations of those referents. A foundational human capacity, verbal reference extends the communicative power of language beyond the here-and-now, enabling access to language-mediated learning and thus fueling cognitive development. In the current review, we consider how and when verbal reference develops. The existing literature suggests that verbal reference emerges around infants’ first birthdays and becomes increasingly robust by their second. In discussing the powerful developmental advantages of acquiring verbal reference we propose that this achievement requires a dynamic interplay among infants’ cognitive and language development, fueled by general learning capacities. We close by describing new research directions, aimed at advancing our understanding of how verbal reference emerges.     

Tapping into the interplay of lexical and number knowledge using fast mapping: A longitudinal eye-tracking study with two-year-olds

Language skills and mathematical competencies are argued to influence each other during development. While a relation between the development of vocabulary size and mathematical skills is already documented in the literature, this study further examines how children’s ability to map a novel word to an unknown object as well as their ability to retain this word from memory may be related to their knowledge of number words. Twenty-five children were tested longitudinally (at 30 and at 36 months of age) using an eye-tracking-based fast mapping task, the Give-a-Number task, and standardized measures of vocabulary. The results reveal that children’s ability to create and retain a mental representation of a novel word was related to number knowledge at 30 months, but not at 36 months while vocabulary size correlated with number knowledge only at 36 months. These results show that even specific mapping processes are initially related to the acquisition of number words and they speak for a parallelism between the development of lexical and number-concept knowledge despite their semantic and syntactic differences.     

The Persistence of Priming: Exploring Long-lasting Syntactic Priming Effects in Children and Adults

The implicit learning account of syntactic priming proposes that the same mechanism underlies syntactic priming and language development, providing a link between a child and adult language processing. The present experiment tested predictions of this account by comparing the persistence of syntactic priming effects in children and adults. Four-year-olds and adults first described transitive events after hearing transitive primes, constituting an exposure phase that established priming effects for passives. The persistence of this priming effect was measured in a test phase as participants described further transitive events but no longer heard primes. Their production of passives was compared to a baseline group who described the same pictures without any exposure to primes. Neither immediate nor long-term priming effects differed between children and adults but both children and adults showed significant immediate and persistent effects of the priming when the test phase occurred immediately after the exposure phase and when a short delay separated the exposure and test phase. The implications of these results for an implicit learning account of syntactic priming are discussed.     

Priming productive study strategies with preparatory quizzes in an engineering course

One approach to encourage productive study strategies is to incorporate preparatory quizzes (or pre‐quizzes) in which students are required to submit answers to questions before the underlying material is covered in class. In the present study, students took an introductory mechanical engineering class that either included pre‐quizzes (treatment group) or did not (control group). Students in the treatment group visited the online textbook more often and earlier in advance of deadlines, indicating better management of their study time—behaviors that have been shown to be productive study strategies. They also performed better in the course, indicating that techniques intended to prime productive study strategies can pay off. Finally, measures of productive learning strategies correlated with measures of course performance for both groups. These findings support the pretesting principle, which holds that students study more effectively and learn better when they take practice tests before a lesson.