Substitution and sameness: two components of a relational conception of the equals sign

A sophisticated and flexible understanding of the equals sign (=) is important for arithmetic competence and for learning further mathematics, particularly algebra. Research has identified two common conceptions held by children: the equals sign as an operator and the equals sign as signaling the same value on both sides of the equation. We argue here that, in addition to these two conceptions, the notion of substitution is also an important part of a sophisticated understanding of mathematical equivalence. We provide evidence from a cross-cultural study in which English and Chinese children were asked to rate the "cleverness" of operational, sameness, and substitutive definitions of the equals sign. A principal components analysis revealed that the substitutive items were distinct from the sameness items. Furthermore, Chinese children rated the substitutive items as 'sort of clever' or 'very clever', whereas English children rated them as not so clever, suggesting that the notion of substitution develops differently across the two countries. Implications for developmental models of children's understanding of equivalence are discussed.     

Reduced ADHD symptoms in adults with ADHD after structured skills training group: results from a randomized controlled trial

Objective

Feasibility, acceptability, and efficacy of a Dialectical Behavioral Therapy (DBT) -based method developed in Germany were evaluated in a Swedish outpatient psychiatric context.

Method

Fifty-one adults with ADHD on stable medical treatment or on no medication were randomized to the DBT-based skills training (n = 26) or a parallel loosely structured discussion group (n = 25). Self-rating scales were administered before randomization and after the treatment.

Results

Feasibility and participant satisfaction were good in both groups while skills training was perceived as more logical and effective for ADHD-related problems. The analyses of the individuals who completed the treatment and remained stable with regard to medication (n = 19 in skills training; n = 18 in control group) showed a significant reduction in ADHD symptoms in the skills training group, but not in the control group. No reduction of comorbidity was observed in any of the groups.

Conclusions

The treatment was feasible in an outpatient psychiatric context, well tolerated, and significantly reduced ADHD symptoms in on-treatment individuals who remained stable regarding medication status.     

The role of immigrant acculturation preferences and generational status in determining majority intergroup attitudes

Two experiments (Ns = 220, 135) investigated the role of first and second generation immigrants' desire for Culture Maintenance and Intercultural Contact in affecting majority members' intergroup attitudes (2 × 2 × 2 design). Participants were presented with fictitious interviews through which immigrants' acculturation preferences and generational status were manipulated. Immigrants' desire for contact strongly affected host members' attitudes: those who were perceived to want contact elicited more favourable intergroup attitudes than those who did not. Desire for contact also moderated the relationship between immigrants' desire for culture maintenance and attitudes towards them: culture maintenance only stimulated favourable attitudes if the immigrant also expressed desire for contact. Immigrants' generational status and their desire for Culture Maintenance were found to interact, such that less favourable attitudes were shown towards second generation immigrants refusing their heritage culture. Psychological processes mediating these effects were investigated, finding evidence for symbolic threat, appreciation for multiculturalism and metastereotypes. Overall, the results suggest that both immigrants' generational status and acculturation attitudes should be taken into account when studying intergroup attitudes of dominant groups and in planning interventions for the improvement of intercultural relations.     

Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties

This study examined numerical magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively. In total, 20 children with MLD, 21 children with LA, and 41 regular achievers completed a numerical magnitude comparison task and an approximate addition task, which were presented in a symbolic and a nonsymbolic (dot arrays) format. Children with MLD and LA were impaired on tasks that involved the access of numerical magnitude information from symbolic representations, with the LA children showing a less severe performance pattern than children with MLD. They showed no deficits in accessing magnitude from underlying nonsymbolic magnitude representations. Our findings indicate that this performance pattern occurs in children from first grade onward and generalizes beyond numerical magnitude comparison tasks. These findings shed light on the types of intervention that may help children who struggle with learning mathematics.     

Personal narratives about states of suffering and wellbeing: Children's conceptualization in terms of physical and psychological domain

The aim was to investigate how children conceptualize personal events of positive and negative valences pertaining to the physical and psychological domains. Five‐ to 9‐year‐olds narrated events referring to suffering states (Study 1, n = 112) and to suffering and wellbeing states (Study 2, n = 118). Analysis of the narratives revealed differences between the two states, with higher focus on events pertaining to a physical domain for suffering and to psychological domain for wellbeing; however, older children were more oriented toward psychological than physical events for both valences. Children showed higher tendency to produce causes compared to consequences, with younger children finding it difficult to introduce physical causes. Psychological suffering narratives revealed a richer psychological lexicon and more instances of domain coexistence. Asymmetry in the representation of different state valences and domains indicates multifaceted and developing conceptualization. Copyright © 2010 John Wiley & Sons, Ltd.     

Working memory skills and educational attainment: evidence from national curriculum assessments at 7 and 14 years of age

The relationship between working memory skills and performance on national curriculum assessments in English, mathematics and science was explored in groups of children aged 7 and 14 years. At 7 years, children's levels of attainment in both English and mathematics were significantly associated with working memory scores, and in particular with performance on complex span tasks. At 14 years, strong links persisted between the complex working memory test scores and attainments levels in both mathematics and science, although ability in the English assessments showed no strong association with working memory skill. The results suggest that the intellectual operations required in the curriculum areas of mathematics and science are constrained by the general capacity of working memory across the childhood years. However, whereas success in the acquisition in literacy (tapped by the English assessments at the youngest age) was also linked with working memory capacity, achievements in the higher‐level skills of comprehension and analysis of English literature assessed at 14 years were independent of working memory capacity. Copyright © 2003 John Wiley & Sons, Ltd.     

Delay and Inhibition as Early Predictors of ADHD Symptoms in Third Grade

We used data from a large, longitudinal study of children in the community, the NICHD Study of Early Child Care and Youth Development, to examine how well earlier measures of delay capacity, inhibitory control, planning, and attention predicted symptoms of attention deficit hyperactivity disorder (ADHD) assessed in third grade. Children with elevated symptoms of both inattention and hyperactivity-impulsivity (n = 57) and with inattentive symptoms only (n = 80) were identified via mother and teacher reports using the “or” rule, as were children without significant symptoms (n = 790). Multinomial logistic regression analyses indicated that poorer performance on earlier measures of resistance to temptation, delay of gratification, response inhibition, attention, and planning obtained from 36 months to 1st grade predicted membership in the two symptom groups relative to the comparison group in 3rd grade, albeit with somewhat different patterns of predictors. Controls for 36 month school readiness and externalizing symptoms indicated that these results were generally robust and not an artifact of initial cognitive or behavioral differences. Implications for developmental models of ADHD are discussed.

Type of stimulus mediates the relationship between working-memory performance and type of precocity

The relationship between type of stimulus (numeric and verbal) and type of precocity (mathematical and verbal) was examined in tasks designed to tap three aspects of working memory: encoding, capacity, and manipulation of information. The tasks included semantic categorization, odd-even categorization, recall of five-item lists after semantic categorization, and recall of items in a continuous paired-associates task. Correlations between task performance and the mathematical and verbal portions of the Scholastic Aptitude Test (SAT-M and SAT-V) were computed for gifted youth. There were no sex differences in the performance measures or in the pattern of correlations between performance and SAT scores. The analysis revealed positive relationships between SAT-M scores and numeric categorization latency, recall in the continuous paired-associate task with words and digits, and recall of digit lists. SAT-V scores were related only to word recall in the continuous paired-associate task and recall of word lists. In the working-memory tasks used, mathematical precocity is more strongly related to performance than is verbal precocity. The relationship is especially strong with numeric stimuli, even when the numeric stimuli are simply items to be remembered. The relationship between type of stimulus and type of precocity suggests underlying differences between verbally and mathematically precocious youth in how different types of stimuli are represented in memory.