The enigma of number: why children find the meanings of even small number words hard to learn and how we can help them do better

Less is not always more: Rich and meaningful counting books lead to greater gains in number understanding than sparse counting books

Children vary widely in their number knowledge by the time they enter kindergarten, and this variation is related to their future academic success. Although talk about number predicts children's early understanding of foundational number concepts, we know little about whether interventions can increase this talk nor about the types of number talk that are most beneficial to children's number understanding. The current project examines whether embedding number talk in goal-based stories leads to more robust number learning than providing the same numeric input outside of this context. Parent-child dyads (N = 71; child age = 3 years) were randomly assigned within their preintervention cardinal number understanding levels to one of three conditions: rich counting books (narrative and pictures involving a number goal), sparse counting books (text and pictures that provide opportunities to count and label the same cardinalities as in the rich condition but with no narrative), or nonnumerical control books that involve labeling colors of objects. Children's number knowledge was measured at pretest and at 2 and 4 weeks into the intervention. Findings showed that children randomized to rich counting book condition showed significantly greater cardinal number knowledge and counting skill by the final testing session compared to children in the sparse counting book condition and the color control book condition, which did not significantly differ from each other. Results have implications for the types of number talk that most effectively support children's number learning in the home environment and for the design of interventions. (PsycInfo Database Record (c) 2025 APA, all rights reserved).

The influence of language on the formation of number concepts: Evidence from preschool children who are bilingual in English and Arabic

We asked whether grammatical number marking has specific influence on the formation of early number concepts. In particular, does comprehension of dual case marking support young children's understanding of cardinality? We assessed number knowledge in 77 3-year-old Arabic-English bilingual children using the Give-a-Number task in both languages. Given recent concerns around the administration and scoring of the Give-a-Number task, we used two complementary approaches: one based on conceptual levels and the other based on overall test scores. We also tested comprehension of dual case marking in Arabic and number sequence knowledge in both languages. Regression analyses showed that dual case comprehension exerts a strong influence on cardinality tested in Arabic independent of age, general language skills, and number sequence knowledge. No such influence was found for cardinality tested in English, indicating a language-specific effect. Further analyses tested for transfer of cardinality knowledge between languages. These revealed, in addition to the findings outlined above, a powerful cross-linguistic transfer effect. Our findings are consistent with a model in which the direct effect of dual case marking is language specific, but concepts, once acquired, may be represented abstractly and transferred between languages.

Individual differences in working memory predict the efficacy of experimenter-manipulated gestures in first-grade children

Why is instructional gesture ineffective in some contexts? And what is it about learners that predicts whether they will learn from gestures? This between-subjects linear measurement training study compares gesture instruction to two controls-operant action and transient action-in a diverse sample of first-grade students (N = 174, Mage = 7.01 years; Nfemale = 84; Nmale = 90, 10% Latinx-identified; 70% White; 6% Black; 6% Asian; 18% multiple racial categories, Mincome = $59,750, SDincome ≈ $25,000; data collected 03/16-03/19). Results show that instructor-manipulated gestures may be less effective than demonstrative actions in part because they are iterative and do not leave a lasting trace. Verbal working memory, but not spatial, positively predicted an ability to learn from gesture and transient action in children with the lowest context knowledge.

Overturning Children's Misconceptions about Ruler Measurement: The Power of Disconfirming Evidence

Children have persistent difficulty with foundational measurement concepts, which may be linked to the instruction they receive. Here, we focus on testing various ways to support their understanding that rulers comprise spatial interval units. We examined whether evidence-based learning tools-disconfirming evidence and/or structural alignment-enhance their understanding of ruler units. Disconfirming evidence, in this context, involves having children count the spatial interval units under an object that is not aligned with the origin of a ruler. Structural alignment, in this context, involves highlighting what a ruler unit is by overlaying plastic unit chips on top of ruler units when an object is aligned with the origin of a ruler. In three experiments employing a pre-test/training/post-test design, a total of 120 second graders were randomly assigned to one of six training conditions (two training conditions per experiment). The training conditions included different evidence-based learning principles or "business-as-usual" instruction (control), with equal allocation to each (N = 20 for each condition). In each experiment, children who did not perform above chance level on the pre-test were selected to continue with training, which resulted in a total of 88 students for the analysis of improvement. The children showed significant improvement in training conditions that included disconfirming evidence, but not in the structural alignment or control conditions. However, an exploratory analysis suggests that improvement occurred more rapidly and was retained better when structural alignment was combined with disconfirming evidence compared to disconfirming evidence alone.

The Effects of Linear Order in Category Learning: Some Replications of Ramscar et al. (2010) and Their Implications for Replicating Training Studies

Ramscar, Yarlett, Dye, Denny, and Thorpe (2010) showed how, consistent with the predictions of error-driven learning models, the order in which stimuli are presented in training can affect category learning. Specifically, learners exposed to artificial language input where objects preceded their labels learned the discriminating features of categories better than learners exposed to input where labels preceded objects. We sought to replicate this finding in two online experiments employing the same tests used originally: A four pictures test (match a label to one of four pictures) and a four labels test (match a picture to one of four labels). In our study, only findings from the four pictures test were consistent with the original result. Additionally, the effect sizes observed were smaller, and participants over-generalized high-frequency category labels more than in the original study. We suggest that although Ramscar, Yarlett, Dye, Denny, and Thorpe (2010) feature-label order predictions were derived from error-driven learning, they failed to consider that this mechanism also predicts that performance in any training paradigm must inevitably be influenced by participant prior experience. We consider our findings in light of these factors, and discuss implications for the generalizability and replication of training studies.

The Keys to the Future? An Examination of Statistical Versus Discriminative Accounts of Serial Pattern Learning

Sequence learning is fundamental to a wide range of cognitive functions. Explaining how sequences-and the relations between the elements they comprise-are learned is a fundamental challenge to cognitive science. However, although hundreds of articles addressing this question are published each year, the actual learning mechanisms involved in the learning of sequences are rarely investigated. We present three experiments that seek to examine these mechanisms during a typing task. Experiments 1 and 2 tested learning during typing single letters on each trial. Experiment 3 tested for "chunking" of these letters into "words." The results of these experiments were used to examine the mechanisms that could best account for them, with a focus on two particular proposals: statistical transitional probability learning and discriminative error-driven learning. Experiments 1 and 2 showed that error-driven learning was a better predictor of response latencies than either n-gram frequencies or transitional probabilities. No evidence for chunking was found in Experiment 3, probably due to interspersing visual cues with the motor response. In addition, learning occurred across a greater distance in Experiment 1 than Experiment 2, suggesting that the greater predictability that comes with increased structure leads to greater learnability. These results shed new light on the mechanism responsible for sequence learning. Despite the widely held assumption that transitional probability learning is essential to this process, the present results suggest instead that the sequences are learned through a process of discriminative learning, involving prediction and feedback from prediction error.

An exploration of error-driven learning in simple two-layer networks from a discriminative learning perspective

Error-driven learning algorithms, which iteratively adjust expectations based on prediction error, are the basis for a vast array of computational models in the brain and cognitive sciences that often differ widely in their precise form and application: they range from simple models in psychology and cybernetics to current complex deep learning models dominating discussions in machine learning and artificial intelligence. However, despite the ubiquity of this mechanism, detailed analyses of its basic workings uninfluenced by existing theories or specific research goals are rare in the literature. To address this, we present an exposition of error-driven learning - focusing on its simplest form for clarity - and relate this to the historical development of error-driven learning models in the cognitive sciences. Although historically error-driven models have been thought of as associative, such that learning is thought to combine preexisting elemental representations, our analysis will highlight the discriminative nature of learning in these models and the implications of this for the way how learning is conceptualized. We complement our theoretical introduction to error-driven learning with a practical guide to the application of simple error-driven learning models in which we discuss a number of example simulations, that are also presented in detail in an accompanying tutorial.

Toward a unified account of nonsymbolic and symbolic representations of number: Insights from a combined psychophysical-computational approach

There is an ongoing, vibrant debate about whether numerical information in both nonsymbolic and symbolic notations would be supported by different neurocognitive systems or rather by a common preverbal approximate number system, which is ratio dependent and follows Weber's law. Here, we propose that the similarities between nonsymbolic and symbolic number processing can be explained based on the principle of efficient coding. To probe this hypothesis we employed a new empirical approach, by predicting the behavioural performance in number comparison tasks with symbolic (i.e., number words) and nonsymbolic (i.e., arrays of dots) information not only from numerical ratio, but for the first time also from natural language data. That is, we used data extracted from vector-space models that are informative about the distributional pattern of number-words usage in natural language. Results showed that linguistic estimates predicted the behavioural performance in both symbolic and nonsymbolic tasks. However, and critically, our results also showed a task-dependent dissociation: linguistic data better predicted the performance in the symbolic task, whereas real numerical ratio better predicted the performance in the nonsymbolic task. These findings indicate that efficient coding of environmental regularities is an explanatory principle of human behavior in tasks involving numerical information. They also suggest that the ability to discriminate a stimulus from similar ones varies as a function of the specific statistical structure of the considered learning environment.

How children learn to communicate discriminatively

How do children learn to communicate, and what do they learn? Traditionally, most theories have taken an associative, compositional approach to these questions, supposing children acquire an inventory of form-meaning associations, and procedures for composing / decomposing them; into / from messages in production and comprehension. This paper presents an alternative account of human communication and its acquisition based on the systematic, discriminative approach embodied in psychological and computational models of learning, and formally described by communication theory. It describes how discriminative learning theory offers an alternative perspective on the way that systems of semantic cues are conditioned onto communicative codes, while information theory provides a very different view of the nature of the codes themselves. It shows how the distributional properties of languages satisfy the communicative requirements described in information theory, enabling language learners to align their expectations despite the vastly different levels of experience among language users, and to master communication systems far more abstract than linguistic intuitions traditionally assume. Topics reviewed include morphological development, the acquisition of verb argument structures, and the functions of linguistic systems that have proven to be stumbling blocks for compositional theories: grammatical gender and personal names.

Prediction and error in early infant speech learning: A speech acquisition model

In the last two decades, statistical clustering models have emerged as a dominant model of how infants learn the sounds of their language. However, recent empirical and computational evidence suggests that purely statistical clustering methods may not be sufficient to explain speech sound acquisition. To model early development of speech perception, the present study used a two-layer network trained with Rescorla-Wagner learning equations, an implementation of discriminative, error-driven learning. The model contained no a priori linguistic units, such as phonemes or phonetic features. Instead, expectations about the upcoming acoustic speech signal were learned from the surrounding speech signal, with spectral components extracted from an audio recording of child-directed speech as both inputs and outputs of the model. To evaluate model performance, we simulated infant responses in the high-amplitude sucking paradigm using vowel and fricative pairs and continua. The simulations were able to discriminate vowel and consonant pairs and predicted the infant speech perception data. The model also showed the greatest amount of discrimination in the expected spectral frequencies. These results suggest that discriminative error-driven learning may provide a viable approach to modelling early infant speech sound acquisition.

Simulating the Acquisition of Verb Inflection in Typically Developing Children and Children With Developmental Language Disorder in English and Spanish

Children with developmental language disorder (DLD) have significant deficits in language ability that cannot be attributed to neurological damage, hearing impairment, or intellectual disability. The symptoms displayed by children with DLD differ across languages. In English, DLD is often marked by severe difficulties acquiring verb inflection. Such difficulties are less apparent in languages with rich verb morphology like Spanish and Italian. Here we show how these differential profiles can be understood in terms of an interaction between properties of the input language, and the child's ability to learn predictive relations between linguistic elements that are separated within a sentence. We apply a simple associative learning model to sequential English and Spanish stimuli and show how the model's ability to associate cues occurring earlier in time with later outcomes affects the acquisition of verb inflection in English more than in Spanish. We relate this to the high frequency of the English bare form (which acts as a default) and the English process of question formation, which means that (unlike in Spanish) bare forms frequently occur in third-person singular contexts. Finally, we hypothesize that the pro-drop nature of Spanish makes it easier to associate person and number cues with the verb inflection than in English. Since the factors that conspire to make English verb inflection particularly challenging for learners with weak sequential learning abilities are much reduced or absent in Spanish, this provides an explanation for why learning Spanish verb inflection is relatively unaffected in children with DLD.

Causal Effects of Parent Number Talk on Preschoolers' Number Knowledge

Individual differences in children's number knowledge arise early and are associated with variation in parents' number talk. However, there exists little experimental evidence of a causal link between parent number talk and children's number knowledge. Parent number talk was manipulated by creating picture books which parents were asked to read with their children every day for 4 weeks. N = 100 two- to four-year olds and their parents were randomly assigned to read either Small Number (1-3), Large Number (4-6), or Control (non-numerical) books. Small Number books were particularly effective in promoting number knowledge relative to the Control books. However, children who began the study further along in their number development also benefited from reading the Large Number Books with their parents.

Order Matters! Influences of Linear Order on Linguistic Category Learning

Linguistic category learning has been shown to be highly sensitive to linear order, and depending on the task, differentially sensitive to the information provided by preceding category markers (premarkers, e.g., gendered articles) or succeeding category markers (postmarkers, e.g., gendered suffixes). Given that numerous systems for marking grammatical categories exist in natural languages, it follows that a better understanding of these findings can shed light on the factors underlying this diversity. In two discriminative learning simulations and an artificial language learning experiment, we identify two factors that modulate linear order effects in linguistic category learning: category structure and the level of abstraction in a category hierarchy. Regarding category structure, we find that postmarking brings an advantage for learning category diagnostic stimulus dimensions, an effect not present when categories are non-confusable. Regarding levels of abstraction, we find that premarking of super-ordinate categories (e.g., noun class) facilitates learning of subordinate categories (e.g., nouns). We present detailed simulations using a plausible candidate mechanism for the observed effects, along with a comprehensive analysis of linear order effects within an expectation-based account of learning. Our findings indicate that linguistic category learning is differentially guided by pre- and postmarking, and that the influence of each is modulated by the specific characteristics of a given category system.

Of mice and men: Speech sound acquisition as discriminative learning from prediction error, not just statistical tracking

Despite burgeoning evidence that listeners are highly sensitive to statistical distributions of speech cues, the mechanism underlying learning may not be purely statistical tracking. Decades of research in animal learning suggest that learning results from prediction and prediction error. Two artificial language learning experiments test two predictions that distinguish error-driven from purely statistical models; namely, cue competition - specifically, Kamin's (1968) 'blocking' effect (Experiment 1) - and the predictive structure of learning events (Experiment 2). In Experiment 1, prior knowledge of an informative cue blocked learning of a second cue. This finding may help explain second language learners' difficulty in acquiring native-level perception of non-native speech cues. In Experiment 2, learning was better with a discriminative (cue-outcome) order compared to a non-discriminative (outcome-cue) order. Experiment 2 suggests that learning speech cues, including reversing effects of blocking, depends on (un)learning from prediction error and depends on the temporal order of auditory cues versus semantic outcomes. Together, these results show that (a) existing knowledge of acoustic cues can block later learning of new cues, and (b) speech sound acquisition depends on the predictive structure of learning events. When feedback from prediction error is available, this drives learners to ignore salient non-discriminative cues and effectively learn to use target cue dimensions. These findings may have considerable implications for the field of speech acquisition.

Conceptualizing syntactic categories as semantic categories: Unifying part-of-speech identification and semantics using co-occurrence vector averaging

Co-occurrence models have been of considerable interest to psychologists because they are built on very simple functionality. This is particularly clear in the case of prediction models, such as the continuous skip-gram model introduced in Mikolov, Chen, Corrado, and Dean (2013), because these models depend on functionality closely related to the simple Rescorla-Wagner model of discriminant learning in nonhuman animals (Rescorla & Wagner, 1972), which has a rich history within psychology as a model of many animal learning processes. We replicate and extend earlier work showing that it is possible to extract accurate information about syntactic category and morphological family membership directly from patterns of word co-occurrence, and provide evidence from four experiments showing that this information predicts human reaction times and accuracy for class membership decisions.

Number gestures predict learning of number words

When asked to explain their solutions to a problem, children often gesture and, at times, these gestures convey information that is different from the information conveyed in speech. Children who produce these gesture-speech "mismatches" on a particular task have been found to profit from instruction on that task. We have recently found that some children produce gesture-speech mismatches when identifying numbers at the cusp of their knowledge, for example, a child incorrectly labels a set of two objects with the word "three" and simultaneously holds up two fingers. These mismatches differ from previously studied mismatches (where the information conveyed in gesture has the potential to be integrated with the information conveyed in speech) in that the gestured response contradicts the spoken response. Here, we ask whether these contradictory number mismatches predict which learners will profit from number-word instruction. We used the Give-a-Number task to measure number knowledge in 47 children (Mage  = 4.1 years, SD = 0.58), and used the What's on this Card task to assess whether children produced gesture-speech mismatches above their knower level. Children who were early in their number learning trajectories ("one-knowers" and "two-knowers") were then randomly assigned, within knower level, to one of two training conditions: a Counting condition in which children practiced counting objects; or an Enriched Number Talk condition containing counting, labeling set sizes, spatial alignment of neighboring sets, and comparison of these sets. Controlling for counting ability, we found that children were more likely to learn the meaning of new number words in the Enriched Number Talk condition than in the Counting condition, but only if they had produced gesture-speech mismatches at pretest. The findings suggest that numerical gesture-speech mismatches are a reliable signal that a child is ready to profit from rich number instruction and provide evidence, for the first time, that cardinal number gestures have a role to play in number-learning.

The nature of the association between number line and mathematical performance: An international twin study

BACKGROUND

The number line task assesses the ability to estimate numerical magnitudes. People vary greatly in this ability, and this variability has been previously associated with mathematical skills. However, the sources of individual differences in number line estimation and its association with mathematics are not fully understood.

AIMS

This large-scale genetically sensitive study uses a twin design to estimate the magnitude of the effects of genes and environments on: (1) individual variation in number line estimation and (2) the covariation of number line estimation with mathematics.

SAMPLES

We used over 3,000 8- to 16-year-old twins from the United States, Canada, the United Kingdom, and Russia, and a sample of 1,456 8- to 18-year-old singleton Russian students.

METHODS

Twins were assessed on: (1) estimation of numerical magnitudes using a number line task and (2) two mathematics components: fluency and problem-solving.

RESULTS

Results suggest that environments largely drive individual differences in number line estimation. Both genes and environments contribute to different extents to the number line estimation and mathematics correlation, depending on the sample and mathematics component.

CONCLUSIONS

Taken together, the results suggest that in more heterogeneous school settings, environments may be more important in driving variation in number line estimation and its association with mathematics, whereas in more homogeneous school settings, genetic effects drive the covariation between number line estimation and mathematics. These results are discussed in the light of development and educational settings.

Cognitive and linguistic biases in morphology learning

Morphology is the study of the relationship between form and meaning. The study of morphology involves understanding the rules and processes that underlie word formation, including the use and productivity of affixes, and the systems that create novel word forms. The present review explores these processes by examining the cognitive components that contribute to typological regularities among morphological systems across the world's language. The review will focus on research in morpheme segmentation, the suffixing preference, acquisition of morphophonology, and acquiring morphological categories and inflectional paradigms. The review will highlight research in a range of areas of linguistics, from child language acquisition, to computational modeling, to adult language learning experiments. In order to best understand the cognitive biases that shape morphological learning, a broad, interdisciplinary approach must be taken. This article is categorized under: Linguistics > Linguistic Theory Linguistics > Language Acquisition Psychology > Language.

Do analog number representations underlie the meanings of young children's verbal numerals?

Children learn to count, and even learn the cardinal meanings of the first three or four verbal numerals ("one" through "three" or "four"), before they master the numerical significance of counting. If so, it follows that the cardinal meanings of those first few numerals cannot be derived, initially, from their place in the count list and the counting routine. What non-verbal representations, then, support the cardinal meanings of verbal numerals before children have mastered how counting does so? Four experiments addressed the commonly adopted assumption that in the earliest period of learning the meanings of number words, children map verbal numerals to regions of the analog number system (ANS), a system of representation with numerical content that is widely attested in animals and in human infants. Experiment 1 confirmed that children who know what "three" means, but who do not yet know what "four" means, and do not yet know how counting represents number, can be easily taught the meaning of "four," if they are trained to indicate sets of four when they are paired with a series of sets that contrast numerically with four. If children learn "four" by mapping the word to an ANS representation of sets of four, and if such ANS value-to-word mappings underlie the meanings of other known numerals early in development, then analogous teaching should enable young children to establish a ANS value-to-word mapping for between "ten" and sets of 10 as specified by the ANS. Furthermore, the ease of learning should be a function of the ratio of the number of individuals in the comparison set to 10. Three further experiments tested these hypotheses by attempting to teach young Cardinal Principle-knowers the meaning of the word "ten," under the same training conditions "three-"knowers are easily taught the meaning of "four". The children learned which picture in each training pair had "ten." However, test trials with novel animals and spatial configurations showed that they had failed to learn what set sizes should be labeled "ten", even when, after training, they were asked to indicate a set of 10 vs. a set of 20 or 30 (well within the ratio sensitivity of the ANS even early in infancy). Furthermore, there was no effect of ratio on success during test trials. These data provide new evidence that ANS value-to-word mappings do not underlie the meanings of number words early in development. We discuss what other non-verbal representations might do so, and discuss other ways the ANS may support learning how counting represents number.

Discrimination in lexical decision

In this study we present a novel set of discrimination-based indicators of language processing derived from Naive Discriminative Learning (ndl) theory. We compare the effectiveness of these new measures with classical lexical-distributional measures-in particular, frequency counts and form similarity measures-to predict lexical decision latencies when a complete morphological segmentation of masked primes is or is not possible. Data derive from a re-analysis of a large subset of decision latencies from the English Lexicon Project, as well as from the results of two new masked priming studies. Results demonstrate the superiority of discrimination-based predictors over lexical-distributional predictors alone, across both the simple and primed lexical decision tasks. Comparable priming after masked corner and cornea type primes, across two experiments, fails to support early obligatory segmentation into morphemes as predicted by the morpho-orthographic account of reading. Results fit well with ndl theory, which, in conformity with Word and Paradigm theory, rejects the morpheme as a relevant unit of analysis. Furthermore, results indicate that readers with greater spelling proficiency and larger vocabularies make better use of orthographic priors and handle lexical competition more efficiently.

Early Literacy and Numeracy Skills in Bilingual Minority Children: Toward a Relative Independence of Linguistic and Numerical Processing

Many studies have suggested that the concept of "number" is relatively independent from linguistic skills, although an increasing number of studies suggest that language abilities may play a pivotal role in the development of arithmetic skills. The condition of bilingualism can offer a unique perspective into the role of linguistic competence in numerical development. The present study was aimed at evaluating the relationship between language skills and early numeracy through a multilevel investigation in monolingual and bilingual minority children attending preschool. The sample included 156 preschool children. Of these, 77 were bilingual minority children (mean age = 58.27 ± 5.90), and 79 were monolinguals (mean age = 58.45 ± 6.03). The study focused on three levels of analysis: group differences in language and number skills, concurrent linguistic predictors of early numeracy and, finally, profile analysis of linguistic skills in children with impaired vs. adequate numeracy skills. The results showed that, apart from the expected differences in linguistic measures, bilinguals differed from monolinguals in numerical skills with a verbal component, such as semantic knowledge of digits, but they did not differ in a pure non-verbal component such as quantity comparison. The multigroup structural equation model indicated that letter knowledge was a significant predictor of the verbal component of numeracy for both groups. Phonological awareness was a significant predictor of numeracy skills only in the monolingual group. Profile analysis showed that children with a selective weakness in the non-verbal component of numeracy had fully adequate verbal skills. Results from the present study suggest that only some specific components of language competence predict numerical processing, although linguistic proficiency may not be a prerequisite for developing adequate early numeracy skills.

Regularization of languages by adults and children: A mathematical framework

The fascinating ability of humans to modify the linguistic input and "create" a language has been widely discussed. In the work of Newport and colleagues, it has been demonstrated that both children and adults have some ability to process inconsistent linguistic input and "improve" it by making it more consistent. In Hudson Kam and Newport (2009), artificial miniature language acquisition from an inconsistent source was studied. It was shown that (i) children are better at language regularization than adults and that (ii) adults can also regularize, depending on the structure of the input. In this paper we create a learning algorithm of the reinforcement-learning type, which exhibits patterns reported in Hudson Kam and Newport (2009) and suggests a way to explain them. It turns out that in order to capture the differences between children's and adults' learning patterns, we need to introduce a certain asymmetry in the learning algorithm. Namely, we have to assume that the reaction of the learners differs depending on whether or not the source's input coincides with the learner's internal hypothesis. We interpret this result in the context of a different reaction of children and adults to implicit, expectation-based evidence, positive or negative. We propose that a possible mechanism that contributes to the children's ability to regularize an inconsistent input is related to their heightened sensitivity to positive evidence rather than the (implicit) negative evidence. In our model, regularization comes naturally as a consequence of a stronger reaction of the children to evidence supporting their preferred hypothesis. In adults, their ability to adequately process implicit negative evidence prevents them from regularizing the inconsistent input, resulting in a weaker degree of regularization.

A cognitively grounded measure of pronunciation distance

In this study we develop pronunciation distances based on naive discriminative learning (NDL). Measures of pronunciation distance are used in several subfields of linguistics, including psycholinguistics, dialectology and typology. In contrast to the commonly used Levenshtein algorithm, NDL is grounded in cognitive theory of competitive reinforcement learning and is able to generate asymmetrical pronunciation distances. In a first study, we validated the NDL-based pronunciation distances by comparing them to a large set of native-likeness ratings given by native American English speakers when presented with accented English speech. In a second study, the NDL-based pronunciation distances were validated on the basis of perceptual dialect distances of Norwegian speakers. Results indicated that the NDL-based pronunciation distances matched perceptual distances reasonably well with correlations ranging between 0.7 and 0.8. While the correlations were comparable to those obtained using the Levenshtein distance, the NDL-based approach is more flexible as it is also able to incorporate acoustic information other than sound segments.

Sidestepping the combinatorial explosion: an explanation of n-gram frequency effects based on naive discriminative learning

Arnon and Snider ((2010). More than words: Frequency effects for multi-word phrases. Journal of memory and language, 62, 67-82) documented frequency effects for compositional four-grams independently of the frequencies of lower-order n-grams. They argue that comprehenders apparently store frequency information about multi-word units. We show that n-gram frequency effects can emerge in a parameter-free computational model driven by naive discriminative learning, trained on a sample of 300,000 four-word phrases from the British National Corpus. The discriminative learning model is a full decomposition model, associating orthographic input features straightforwardly with meanings. The model does not make use of separate representations for derived or inflected words, nor for compounds, nor for phrases. Nevertheless, frequency effects are correctly predicted for all these linguistic units. Naive discriminative learning provides the simplest and most economical explanation for frequency effects in language processing, obviating the need to posit counters in the head for, and the existence of, hundreds of millions of n-gram representations.

Dual routes to cognitive flexibility: learning and response-conflict resolution in the dimensional change card sort task

Cognitive control, the ability to align our actions with goals or context, is largely absent in children under four. How then are preschoolers able to tailor their behavior to best match the situation? Learning may provide an alternative route to context-sensitive responding. This study investigated this hypothesis in the Dimensional Change Card Sort (DCCS), a classic test of cognitive control that most under-fours fail. A training intervention based on learning theoretic principles proved highly effective: Three-year-olds who learned about DCCS rules and game contexts in a card-labeling task, subsequently transferred this knowledge to sorting in the DCCS, passing at more than 3 times the rate of controls (N = 47). This surprising finding reveals much about the nature of the developing mind.

Granularity and the acquisition of grammatical gender: how order-of-acquisition affects what gets learned

Why do adult language learners typically fail to acquire second languages with native proficiency? Does prior linguistic experience influence the size of the "units" adults attend to in learning, and if so, how does this influence what gets learned? Here, we examine these questions in relation to grammatical gender, which adult learners almost invariably struggle to master. We present a model of learning that predicts that exposure to smaller units (such as nouns) before exposure to larger linguistic units (such as sentences) can critically impair learning about predictive relations between units: such as that between a noun and its article. This prediction is then confirmed by a study of adult participants learning grammatical gender in an artificial language. Adults learned both nouns and their articles better when they were first heard nouns used in context with their articles prior to hearing the nouns individually, compared with learners who first heard the nouns in isolation, prior to hearing them used in context. In the light of these results, we discuss the role gender appears to play in language, the importance of meaning in artificial grammar learning, and the implications of this work for the structure of L2-training.