Patterning counts: Individual differences in children's calculation are uniquely predicted by sequence patterning.

Many studies have examined the cognitive determinants of children's calculation, yet the specific contribution of children's patterning abilities to calculation remains relatively unexplored. This study investigated whether children's ability to complete sequence patterns (i.e., add the missing element into 2-4-?-8) uniquely predicted individual differences in calculation and whether these associations differed depending on the type of stimuli in these sequence patterns (i.e., number, letter, time, or rotation). Participants were 65 children in first and second grade (Mage = 7.40 years, SD = 0.44). All children completed four tasks of sequence patterning: number, letter, time, and rotation. Calculation was measured via addition and subtraction tasks. We also measured cognitive determinants of individual differences in calculation-namely symbolic number comparison, motor processing speed, visuospatial working memory, and nonverbal IQ-to verify whether patterning predicted calculation when controlling for these additional measures. We observed significant relationships between the patterning dimensions and calculation, except for the rotation dimension. Follow-up regressions, controlling for the aforementioned cognitive determinants of calculation, revealed that the number and time dimensions were strong predictors of calculation, whereas the evidence for the letter dimension was only anecdotal and the evidence for the rotation dimension was nonexistent, suggesting some degree of specificity of different types of sequence patterning in predicting calculation. Symbolic magnitude processing remained a powerful unique correlate of calculation performance. These findings add to our understanding of individual differences in calculation ability, such that sequence patterning could begin to be considered as one of the cognitive skills underlying calculation ability in young children.

The structure of the notation system in adults' number line estimation: An eye-tracking study.

Research on rational numbers suggests that adults experience more difficulties in understanding the numerical magnitude of rational than natural numbers. Within rational numbers, the numerical magnitude of fractions has been found to be more difficult to understand than that of decimals. Using a number line estimation (NLE) task, the current study investigated two sources of difficulty in adults' numerical magnitude understanding: number type (natural vs rational) and structure of the notation system (place-value-based vs non-place-value-based). This within-subjects design led to four conditions: natural numbers (natural/place-value-based), decimals (rational/place-value-based), fractions (rational/non-place-value-based), and separated fractions (natural/non-place-value-based). In addition to percentage absolute error (PAE) and response times, we collected eye-tracking data. Results showed that participants estimated natural and place-value-based notations more accurately than rational and non-place-value-based notations, respectively. Participants were also slower to respond to fractions compared with the three other notations. Consistent with the response time data, eye-tracking data showed that participants spent more time encoding fractions and re-visited them more often than the other notations. Moreover, in general, participants spent more time positioning non-place-value-based than place-value-based notations on the number line. Overall, the present study contends that when both sources of difficulty are present in a notation (i.e., both rational and non-place-value-based), adults understand its numerical magnitude less well than when there is only one source of difficulty present (i.e., either rational or non-place-value-based). When no sources of difficulty are present in a notation (i.e., both natural and place-value-based), adults have the strongest understanding of its numerical magnitude.

Comparing Alliance in Two Cognitive-Behavioural Therapies for Adolescents With ADHD Using a Randomized Controlled Trial.

Alliance is defined as the client-therapist bond and their ability to collaborate on therapeutic activities. Treatment for adolescents with ADHD is rarely studied in terms of alliance. In this study, two cognitive-behavioral treatments (CBT; one structured treatment aimed at planning skills and one less-structured solution-focused treatment, both delivered in the style of Motivational Interviewing) were compared with regard to alliance and alliance-outcome association. The influence of therapist competence on this alliance-outcome association was also evaluated. The alliance between 69 adolescents diagnosed with ADHD and their therapists was measured early in treatment, using the Therapy Process Observational Coding System for Child Psychotherapy-Alliance scale. Observer-rated therapist competence was measured using the Motivational Interviewing Treatment Integrity scale (version 3.1.1.). Outcome variables were the adolescents' reduction in planning problems and ADHD symptoms. The alliance, and, more specifically, collaboration on therapeutic activities, was significantly higher for the more structured CBT (p = .04; moderate effect size). Alliance was not related to outcome in the more structured CBT, while the alliance was positively related to the reduction in planning problems in the less structured CBT. Finally, alliance was a significant mediator between therapist competence and treatment outcome for the less-structured CBT. The clarity and structure of CBT may help facilitate alliance formation for adolescents with ADHD who often have difficulty implementing structure themselves. Therapists may need to invest more in alliance formation in less structured CBT as the alliance affects outcome. Moreover, enhancing therapist competence in less structured CBT may help improve outcomes in less structured CBT, as therapist competence may impact outcome through alliance.