How to learn the natural numbers: inductive inference and the acquisition of number concepts

Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap: How not to learn the natural numbers. Cognition, 101, B51-B60.] argue that such an inductive inference is consistent with a representational system that clearly does not express the natural numbers and that possession of the natural numbers requires further principles that make the inductive inference superfluous. We argue that their critique is unsuccessful. Provided that children have access to a suitable initial system of representation, the sort of inductive inference that Rips et al. call into question can in fact facilitate the acquisition of larger integer concepts without the addition of any further principles.     

Inflexibility of experts--reality or myth? Quantifying the Einstellung effect in chess masters

How does the knowledge of experts affect their behaviour in situations that require unusual methods of dealing? One possibility, loosely originating in research on creativity and skill acquisition, is that an increase in expertise can lead to inflexibility of thought due to automation of procedures. Yet another possibility, based on expertise research, is that experts' knowledge leads to flexibility of thought. We tested these two possibilities in a series of experiments using the Einstellung (set) effect paradigm. Chess players tried to solve problems that had both a familiar but non-optimal solution and a better but less familiar one. The more familiar solution induced the Einstellung (set) effect even in experts, preventing them from finding the optimal solution. The presence of the non-optimal solution reduced experts' problem solving ability was reduced to about that of players three standard deviations lower in skill level by the presence of the non-optimal solution. Inflexibility of thought induced by prior knowledge (i.e., the blocking effect of the familiar solution) was shown by experts but the more expert they were, the less prone they were to the effect. Inflexibility of experts is both reality and myth. But the greater the level of expertise, the more of a myth it becomes.     

Can infants be "taught" to attend to a new physical variable in an event category? The case of height in covering events

As they observe or produce events, infants identify variables that help them predict outcomes in each category of events. How do infants identify a new variable? An explanation-based learning (EBL) account suggests three essential steps: (1) observing contrastive outcomes relevant to the variable; (2) discovering the conditions associated with these outcomes; and (3) generating an explanation for the condition-outcome regularity discovered. In Experiments 1-3, 9-month-old infants watched events designed to "teach" them the variable height in covering events. After watching these events, designed in accord with the EBL account, the infants detected a height violation in a covering event, three months earlier than they ordinarily would have. In Experiments 4-6, the "teaching" events were modified to remove one of the EBL steps, and the infants no longer detected the height violation. The present findings thus support the EBL account and help specify the processes by which infants acquire their physical knowledge.     

Rapid acquisition of preference in concurrent chains: effects of d-amphetamine on sensitivity to reinforcement delay

The purpose of this study was to examine effects of d-amphetamine on choice controlled by reinforcement delay. Eight pigeons responded under a concurrent-chains procedure in which one terminal-link schedule was always fixed-interval 8 s, and the other terminal-link schedule changed from session to session between fixed-interval 4 s and fixed-interval 16 s according to a 31-step pseudorandom binary sequence. After sufficient exposure to these contingencies (at least once through the pseudorandom binary sequence), the pigeons acquired a preference for the shorter reinforcement delay within each session. Estimates of the sensitivity to reinforcement immediacy were similar to those obtained in previous studies. For all pigeons, at least one dose of d-amphetamine attenuated preference and, hence, decreased estimates of sensitivity to reinforcement immediacy; in most cases, this effect occurred without a change in overall response rates. In many cases, the reduced sensitivity to reinforcement delay produced by d-amphetamine resulted primarily from a decrease in the asymptotic level of preference achieved within the session; in some cases, d-amphetamine produced complete indifference. These findings suggest that a reduction in the sensitivity to reinforcement delay may be an important behavioral mechanism of the effects of psychomotor stimulants.     

Intergenerational influence and ontogenetic development in the emergence of spatial grammar in Nicaraguan Sign Language

The recent emergence of a new sign language among deaf children and adolescents in Nicaragua provides an opportunity to study how grammatical features of a language arise and spread, and how new language environments are constructed. The grammatical regularities that underlie language use reside largely outside the domain of explicit awareness. Nevertheless, knowledge of these regularities must be transmitted from one generation to the next to survive as part of the language. During this transmission, language form and use is shaped by both the characteristics of ontogenetic development within individual users and by historical changes in patterns of interaction between users. To capture this process, the present study follows the emergence of spatial modulations in Nicaraguan Sign Language (NSL). A comprehension task examining interpretations of spatially modulated verbs reveals that new form-function mappings arise among children who functionally differentiate previously equivalent forms. The new mappings are then acquired by their age peers (who are also children), and by subsequent generations of children who learn the language, but not by adult contemporaries. As a result, language emergence is characterized by a convergence on form within each age cohort, and a mismatch in form from one age cohort to the cohort that follows. In this way, each age cohort, in sequence, transforms the language environment for the next, enabling each new cohort of learners to develop further than its predecessors.     

An Examination of the Effects of Repeated Readings with Secondary Students

Reading is a fundamental skill for success in school and as an adult. However, many children and adults experience difficulties reading. Previous research has demonstrated that repeated readings is an effective intervention for increasing both fluency and comprehension for elementary age readers of all skill levels. However, the impact of repeated readings on fluency and comprehension has not been examined with secondary students with reading deficits. The purpose of this study was to examine the effectiveness of repeated readings for increasing four secondary student's fluency on passages at their instructional level, at the ninth grade level, and on generalization passages from their school curriculum. Furthermore, the effects on comprehension were also explored. A comparison group of average readers served as an estimate for how fluently secondary students read. The results of this study demonstrated that fluency improvements were achieved for all of the participants with just ten additional hours of practice. Effects on comprehension were not as clear. Limitations and future directions for research are discussed.     

Fluent Reading as the Improvement of Stimulus Control: Additive Effects of Performance-Based Interventions to Repeated Reading on Students' Reading and Error Rates

The impact of adding performance-based interventions to a skill-based intervention on oral reading fluency was examined with 3 elementary students identified as having difficulty with reading. Two performance-based interventions were combined with the skill-based intervention Repeated Reading (RR) to create the three instructional packages investigated. The packages included Repeated Readings (RR), Repeated Readings with Performance Feedback (RR/FB), and Repeated Readings with Performance Feedback and Contingent Reward (RR/FB/REW). Results suggested that Repeated Reading (RR) alone led to the greatest increase in reading fluency for participants with the highest reading rates and lowest error rates at baseline. In contrast, the participant who exhibited the lowest reading rate and highest error rate benefited the most when Repeated Readings was offered in conjunction with Performance Feedback (RR/FB) or Performance Feedback plus Contingent Reward (RR/FB/RW). Implications for blending skill- and performance-based interventions to develop stimulus control over fluent reading and future research directions are discussed.     

Deviations from Prescribed Prompting Procedures: Implications for Treatment Integrity

The acquisition of new skills may be hindered when teaching procedures vary from previously validated approaches or contain errors. In the present study, we compared the acquisition and maintenance of response chains taught using a perfectly implemented system of least prompts and a multiple verbal prompts procedure (i.e., addition of multiple verbal prompts and failure to follow through with more intrusive prompts). Four children, aged 6–9, participated in the study. An adapted alternating treatments design was used to compare the effectiveness and efficiency of learning during the system of least prompts and the alternative system of least prompts. Results were consistent with those obtained in previous studies in that the perfectly implemented and alternative prompting procedures were effective in teaching new skills for all participants. However, the perfectly implemented treatment required fewer trials to mastery for 4 of the 5 evaluations. Response chains taught under the multiple verbal prompts condition had poorer maintenance for 2 of the 5 evaluations. The results of the current study suggest that deviations from empirically identified teaching procedures may reduce the speed with which new skills are acquired.     

A Bayesian framework for word segmentation: Exploring the effects of context

Since the experiments of Saffran et al. [Saffran, J., Aslin, R., & Newport, E. (1996). Statistical learning in 8-month-old infants. Science, 274, 1926-1928], there has been a great deal of interest in the question of how statistical regularities in the speech stream might be used by infants to begin to identify individual words. In this work, we use computational modeling to explore the effects of different assumptions the learner might make regarding the nature of words - in particular, how these assumptions affect the kinds of words that are segmented from a corpus of transcribed child-directed speech. We develop several models within a Bayesian ideal observer framework, and use them to examine the consequences of assuming either that words are independent units, or units that help to predict other units. We show through empirical and theoretical results that the assumption of independence causes the learner to undersegment the corpus, with many two- and three-word sequences (e.g. what’s that, do you, in the house) misidentified as individual words. In contrast, when the learner assumes that words are predictive, the resulting segmentation is far more accurate. These results indicate that taking context into account is important for a statistical word segmentation strategy to be successful, and raise the possibility that even young infants may be able to exploit more subtle statistical patterns than have usually been considered.     

Finding one's meaning: a test of the relation between quantifiers and integers in language development

We explored children’s early interpretation of numerals and linguistic number marking, in order to test the hypothesis (e.g., Carey (2004). Bootstrapping and the origin of concepts. Daedalus, 59-68) that children’s initial distinction between one and other numerals (i.e., two, three, etc.) is bootstrapped from a prior distinction between singular and plural nouns. Previous studies have presented evidence that in languages without singular-plural morphology, like Japanese and Chinese, children acquire the meaning of the word one later than in singular-plural languages like English and Russian. In two experiments, we sought to corroborate this relation between grammatical number and integer acquisition within English. We found a significant correlation between children’s comprehension of numerals and a large set of natural language quantifiers and determiners, even when controlling for effects due to age. However, we also found that 2-year-old children, who are just acquiring singular-plural morphology and the word one, fail to assign an exact interpretation to singular noun phrases (e.g., a banana), despite interpreting one as exact. For example, in a Truth-Value Judgment task, most children judged that a banana was consistent with a set of two objects, despite rejecting sets of two for the numeral one. Also, children who gave exactly one object for singular nouns did not have a better comprehension of numerals relative to children who did not give exactly one. Thus, we conclude that the correlation between quantifier comprehension and numeral comprehension in children of this age is not attributable to the singular-plural distinction facilitating the acquisition of the word one. We argue that quantifiers play a more general role in highlighting the semantic function of numerals, and that children distinguish between numerals and other quantifiers from the beginning, assigning exact interpretations only to numerals.