Mathematical difficulties as decoupling of expectation and developmental trajectories

Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science

Nature/nurture and the origin of individual differences in mathematics:evidence from infant and behavioural genetics studies

In this chapter, we discuss empirical evidence addressing the nature-nurture debate from two different perspectives: infant studies and behavioural genetics. Current evidence suggests that there are two cognitive systems for encoding numerical information, and perhaps core systems for geometry. However, questions remain about whether these systems are both present at birth and hence the degree of determinism and the mechanisms by which they connect to later mathematics are still far from established. Behavioural genetics studies offer a valuable way to assess the origin of individual differences in mathematical cognition and to discriminate between genetic and environmental contributions. We thus review relevant evidence on core quantitative knowledge, mathematical abilities and cross-domain relations from twin studies. We conclude by suggesting that while there is convincing evidence of nature’s general and specific role in mathematics, it is clear that environment plays a fundamental role too. The real question for the future is not whether mathematics has a natural core but how to optimise the interaction between nature and nurture so that differential domain-specific and domain-general predispositions can meet an ideal environment to blossom into competent mathematics

What children learn from adults’ utterances:an ephemeral lexical boost and persistent syntactic priming in adult–child dialogue

We show that children’s syntactic production is immediately affected by individual experiences of structures and verb–structure pairings within a dialogue, but that these effects have different timecourses. In a picture-matching game, three- to four-year-olds were more likely to describe a transitive action using a passive immediately after hearing the experimenter produce a passive than an active (abstract priming), and this tendency was stronger when the verb was repeated (lexical boost). The lexical boost disappeared after two intervening utterances, but the abstract priming effect persisted. This pattern did not differ significantly from control adults. Children also showed a cumulative priming effect. Our results suggest that whereas the same mechanism may underlie children’s immediate syntactic priming and long-term syntactic learning, different mechanisms underlie the lexical boost versus long-term learning of verb–structure links. They also suggest broad continuity of syntactic processing in production between this age group and adults

The relationship between numerical mapping abilities, maths achievement, and socio-economic status in 4- and 5-year-old children

Background: Early numeracy skills are associated with academic and life-long outcomes. Children from low-income backgrounds typically have poorer maths outcomes, and their learning can already be disadvantaged before they begin formal schooling. Understanding the relationship between the skills that support the acquisition of early maths skills could scaffold maths learning and improve life chances. Aims: The present study aimed to examine how the ability of children from different SES backgrounds to map between symbolic (Arabic numerals) and non-symbolic (dot arrays) at two difficulty ratios related to their math performance. Sample: Participants were 398 children in their first year of formal schooling (Mean age = 60 months), and 75% were from low SES backgrounds. Method: The children completed symbolic to non-symbolic and non-symbolic to symbolic mapping tasks at two difficulty ratios (1:2; 2:3) plus standardized maths tasks. Results: The results showed that all the children performed better for symbolic to non-symbolic mapping and when the ratio was 1:2. Mapping task performance was significantly related to maths task achievement, but low-SES children showed significantly lower performance on all tasks. Conclusion: The results suggest that mapping tasks could be a useful way to identify children at risk of low maths attainment.</p

Do you know what I know? The impact of participant role in children's referential communication

For successful language use, interlocutors must be able to accurately assess their shared knowledge (“common ground”). Such knowledge can be accumulated through linguistic and non-linguistic context, but the same context can be associated with different patterns of knowledge, depending on the interlocutor’s participant role (Wilkes-Gibbs and Clark, 1992). Although there is substantial evidence that children’s ability to model partners’ knowledge develops gradually, most such evidence focuses on non-linguistic context. We investigated the extent to which 8- to 10-year-old children can assess common ground developed through prior linguistic context, and whether this is sensitive to variations in participant role. Children repeatedly described tangram figures to another child, and then described the same figures to a third child who had been a side-participant, an overhearer, or absent during the initial conversation. Children showed evidence of partner modeling, producing shorter referential expressions with repeated mention to the same partner. Moreover, they demonstrated sensitivity to differences in common ground with the third child based on participant role on some but not all measures (e.g., description length, but not definiteness). Our results suggest that by ten, children make distinctions about common ground accumulated through prior linguistic context but do not yet consistently deploy this knowledge in an adult-like way

Interference in the shared-Stroop task:a comparison of self- and other-monitoring

Co-actors represent and integrate each other's actions, even when they need not monitor one another. However, monitoring is important for successful interactions, particularly those involving language, and monitoring others' utterances probably relies on similar mechanisms as monitoring one's own. We investigated the effect of monitoring on the integration of self- and other-generated utterances in the shared-Stroop task. In a solo version of the Stroop task (with a single participant responding to all stimuli; Experiment 1), participants named the ink colour of mismatching colour words (incongruent stimuli) more slowly than matching colour words (congruent). In the shared-Stroop task, one participant named the ink colour of words in one colour (e.g. red), while ignoring stimuli in the other colour (e.g. green); the other participant either named the other ink colour or did not respond. Crucially, participants either provided feedback about the correctness of their partner's response (Experiment 3) or did not (Experiment 2). Interference was greater when both participants responded than when they did not, but only when their partners provided feedback. We argue that feedback increased interference because monitoring one's partner enhanced representations of the partner's target utterance, which in turn interfered with self-monitoring of the participant's own utterance

Exploring effects of response biases in affect induction procedures

This study examined whether self-reports or ratings of experienced affect, often used as manipulation checks on the efficacy of affect induction procedures (AIPs), reflect genuine changes in affective states rather than response biases arising from demand characteristics or social desirability effects. In a between-participants design, participants were exposed to positive, negative and neutral images with valence-congruent music or sound to induce happy, sad and neutral mood. Half of the participants had to actively appraise each image whereas the other half viewed images passively. We hypothesised that if ratings of affective valence are subject to response biases then they should reflect the target mood in the same way for active appraisal and passive exposure as participants encountered the same affective stimuli in both conditions. We also tested whether the AIP resulted in mood-congruent changes in facial expressions analysed by FaceReader to see whether behavioural indicators corroborate the self-reports. The results showed that while participants’ ratings reflected the induced target valence, the difference between positive and negative AIP was significantly attenuated in the active appraisal condition, suggesting that self-reports of mood experienced after the AIP are not entirely a reflection of response biases. However, there were no effects of the AIP on FaceReader valence scores, in line with theories questioning the existence of cross-culturally and inter-individually universal behavioural indicators of affective states. Efficacy of AIPs is therefore best checked using self-reports

Lexically-specific syntactic restrictions in second-language speakers

In two structural priming experiments, we investigated the representations of lexically-specific syntactic restrictions of English verbs for highly proficient and immersed second language (L2) speakers of English. We considered the interplay of two possible mechanisms: generalization from the first language (L1) and statistical learning within the L2 (both of abstract structure and of lexically-specific information). In both experiments, L2 speakers with either Germanic or Romance languages as L1 were primed to produce dispreferred double-object structures involving non-alternating dative verbs. Priming occurred from ungrammatical double-object primes involving different non-alternating verbs (Experiment 1) and from grammatical primes involving alternating verbs (Experiment 2), supporting abstract statistical learning within the L2. However, we found no differences between L1-Germanic speakers (who have the double object structure in their L1) and L1-Romance speakers (who do not), inconsistent with the prediction for between-group differences of the L1-generalization account. Additionally, L2 speakers in Experiment 2 showed a lexical boost: There was stronger priming after (dispreferred) non-alternating same-verb double object primes than after (grammatical) alternating different-verb primes. Such lexically-driven persistence was also shown by L1 English speakers (Ivanova et al., 2012a) and may underlie statistical learning of lexically-dependent structural regularities. We conclude that lexically-specific syntactic restrictions in highly proficient and immersed L2 speakers are shaped by statistical learning (both abstract and lexically-specific) within the L2, but not by generalization from the L1

Put you in the problem:effects of self-pronouns on mathematical problem solving

Self-cues such as personal pronouns are known to elicit processing biases, such as attention capture and prioritisation in working memory. This may impact the performance of tasks that have a high attentional load like mathematical problem-solving. Here, we compared the speed and accuracy with which children solved numerical problems that included either the self-cue “you,” or a different character name. First, we piloted a self-referencing manipulation with N = 52, 7 to 11 year-olds, testing performance on addition and subtraction problems that had either a single referent (“You”/“Sam”) or more than one referent. We took into account operation and positioning of the pronoun and also measured performance on attention and working memory tasks. We found a robust accuracy advantage for problems that included “you,” regardless of how many characters were included. The accuracy advantage for problems with a self-pronoun was not statistically associated with individual differences in attention or working memory. In our main study (9 to 11 year-olds, N = 144), we manipulated problem difficulty by creating consistently and inconsistently worded addition and subtraction problems. We found significantly higher speed and accuracy for problems that included “you.” However, this effect varied by task difficulty, with the self-pronoun effect being strongest in the most difficult inconsistently worded, subtraction problems. The advantage of problems with a self-pronoun was not associated with individual differences in working memory. These findings suggest that self-cues like the pronoun “you” can be usefully applied in numerical processing tasks, an effect that may be attributable to the effects of self-cues on attention.</p

Is young children’s passive syntax semantically constrained? Evidence from syntactic priming

a b s t r a c t Previous research suggests that English-speaking children comprehend agent-patient verb passives earlier than experiencer-theme verb passive