Priming effects of arithmetic signs in 10- to 15-year-old children

In this research, 10- to 12- and 13- to 15-year-old children were presented with very simple addition and multiplication problems involving operands from 1 to 4. Critically, the arithmetic sign was presented before the operands in half of the trials, whereas it was presented at the same time as the operands in the other half. Our results indicate that presenting the ‘x’ sign before the operands of a multiplication problem does not speed up the solving process, irrespective of the age of children. In contrast, presenting the ‘+’ sign before the operands of an addition problem facilitates the solving process, but only in 13 to 15-year-old children. Such priming effects of the arithmetic sign have been previously interpreted as the result of a pre-activation of an automated counting procedure, which can be applied as soon as the operands are presented. Therefore, our results echo previous conclusions of the literature that simple additions but not multiplications can be solved by fast counting procedures. More importantly, we show here that these procedures are possibly convoked automatically by children after the age of 13 years. At a more theoretical level, our results do not support the theory that simple additions are solved through retrieval of the answers from long-term memory by experts. Rather, the development of expertise for mental addition would consist in an acceleration of procedures until automatization.     

The use of procedural knowledge in simple addition and subtraction problems

In a first experiment, adults were asked to solve one-digit additions, subtractions and multiplications. When the sign appeared 150 ms before the operands, addition and subtraction were solved faster than when the sign and the operands appeared simultaneously on screen. This priming effect was not observed for multiplication problems. A second experiment replicates these results on addition and multiplication and, moreover, shows that the priming effect in addition is observed for all problems, including very small ones such as 4+3. In fact, the only problems that were not primed by the addition sign were tie problems, which confirms that they have a special status in memory. Taken together, these results suggest that abstract procedures are pre-activated by the addition and subtraction signs and that these procedures are consequently used by adults to solve the problems. No such procedures would be pre-activated for multiplication, which are then most probably solved by retrieval of the result from memory. Moreover, while obviously two different strategies were used by individuals in order to solve addition and multiplication, solution times were similar when the problems were presented in their whole. These results, which question most of the conclusions of the current literature, support Anderson's model (1982) and Baroody's assumptions (1983) on the existence of compacted procedures that could be as fast as retrievals.     

Interactive effects of numerical surface form and operand parity in cognitive arithmetic

In Experiment 1, adults (n = 48) performed simple addition, multiplication, and parity (i.e., odd-even) comparisons on pairs of Arabic digits or English number words. For addition and comparison, but not multiplication, response time increased with the number of odd operands. For addition, but not comparison, this parity effect was greater for words than for digits. In Experiment 2, adults (n = 50) solved simple addition problems in digit and word format and reported their strategies (i.e., retrieval or procedures). Procedural strategies were used more for odd than even addends and much more for word than digit problems. The results indicate that problem encoding and answer retrieval processes for cognitive arithmetic are interactive rather than strictly additive stages.     

A microgenetic study of simple division

How simple division strategies develop over a short period of time was examined with a microgenetic study. Grade 5 students (mean age = 10 years, 3 months) solved simple division problems in 8 weekly sessions. Performance improved with faster and more accurate responses across the study. Consistent with R. S. Siegler's (1996) overlapping waves model, strategies varied in their use. Direct retrieval increased, retrieval of multiplication facts remained steady, and addition facts, derived facts, and special tricks marginally decreased. Consistent with previous research, multiplication fact retrieval was the most common strategy, although it was slower and more error prone than direct retrieval. Strategy variability within and across individuals was striking across all of the sessions and underscores Siegler's (1996) assertion that development is in a constant transitional state. (PsycINFO Database Record (c) 2008 APA, all rights reserved).     

Interacting neighbors: A connectionist model of retrieval in single-digit multiplication

For most adults, retrieval is the most common way to solve a single-digit multiplication problem (Campbell & Xue, 2001). Many theories have been proposed to describe the underlying mechanism of arithmetical fact retrieval. Testing their validity hinges on evaluating how well they account for the basic findings in mental arithmetic. The most important findings are the problem size effect (small multiplication problems are easier than larger ones; cf. 3 x 2 and 7 x 8), the five effect (problems with 5 are easier than can be accounted for by their size), and the tie effect (problems with identical operands are easier than other problems; cf. 8 x 8 and 8 x 7). We show that all existing theories have difficulties in accounting for one or more of these phenomena A new theory is presented that avoids these difficulties. The basic assumption is that candidate answers to a particular problem are in cooperative/competitive interactions and these interactions favor small, five, and tie problems. The theory is implemented as a connectionist model, and simulation data are described that are in good accord with empirical data.     

Capacity and contextual constraints on product activation: Evidence from task-irrelevant fact retrieval

Three experiments tested the limiting conditions of multiplication facts retrieval in a number-matching task (LeFevre, Bisanz, & Mrkonjic, 1988). By presenting two digits as cue and by requiring participants to decide whether a subsequent numerical target had been present in the pair, we found interference when the target coincided with the product of the cue digits. This was evidence for obligatory activation of multiplication facts. Also, we showed that multiplication facts retrieval occurred even in the absence of any arithmetic context (i.e., a multiplication sign between the cue digits) and did not require processing resources (i.e., the process met the capacity criterion of automaticity; Jonides, 1981), whereas manipulation of the spatial relation between the two operands (cue digits) negatively affected retrieval. The present work appears to be unique in the context of previous similar studies on mental calculation, which invariably adopted an arithmetic task as the primary demand. We identify this difference as the reason for the failure of all previous studies in revealing independence of multiplication facts from attentional resources. Furthermore, we suggest the application of a contextual definition of automaticity to this kind of retrieval, given the fact that it might depend both on association strength and on contextual setting variables.     

Neural correlates of autobiographical memory retrieval in children and adults

Autobiographical memory (AM) is a critically important form of memory for life events that undergoes substantial developmental changes from childhood to adulthood. Relatively little is known regarding the functional neural correlates of AM retrieval in children as assessed with fMRI, and how they may differ from adults. We investigated this question with 14 children ages 8–11 years and 14 adults ages 19–30 years, contrasting AM retrieval with semantic memory (SM) retrieval. During scanning, participants were cued by verbal prompts to retrieve previously selected recent AMs or to verify semantic properties of words. As predicted, both groups showed AM retrieval-related increased activation in regions implicated in prior studies, including bilateral hippocampus, and prefrontal, posterior cingulate, and parietal cortices. Adults showed greater activation in the hippocampal/parahippocampal region as well as prefrontal and parietal cortex, relative to children; age-related differences were most prominent in the first 8?sec versus the second 8?sec of AM retrieval and when AM retrieval was contrasted with semantic retrieval. This study is the first to characterise similarities and differences during AM retrieval in children and adults using fMRI.     

Rote memory and arithmetic fact processing

The goal of the study was to examine the part played by skill in memorizing arbitrary sequences in the efficiency with which normal young adults perform simple arithmetic fact problems. The first experiment showed a clear independent role for sequence memory in all arithmetic fact processing, but a lesser role for semantic retrieval. This result was particularly true for large-answer multiplication problems and subtraction and division problems with large first operands. In a second experiment, which included a visuomotor processing control task, sequence memory predicted processing of all arithmetic problems apart from small additions independently of semantic retrieval, with the most robust independent contribution being to large-answer multiplication problems. The results, which are compatible with Dehaene and colleagues' triple-code model, suggest that rote learning may be a successful way for some people to process arithmetic facts efficiently.     

Word fluency performance and strategies in children with cochlear implants: age‐dependent effects?

Löfkvist, U., Almkvist, O., Lyxell, B. & Tallberg, I.‐M. (2012). Word fluency performance and strategies in children with cochlear implants: age‐dependent effects? Scandinavian Journal of Psychology 53, 467–474. Word fluency was examined in 73 Swedish children aged 6–9 years divided into two age groups, 6–7 and 8–9 years; 34 deaf children with cochlear implants (CI) (15 girls/19 boys) and 39 age‐matched children with normal hearing (NH) (20 girls/19 boys). One purpose was to compare the ability to retrieve words in two different word fluency tasks; one phonemically based (FAS letter fluency) and one semantically based (animal fluency). A second purpose was to examine retrieval strategies in the two tasks by conducting an analysis of clustering and switching of word sequences. In general we found that age was an important factor for word fluency ability, in both the CI and the NH groups. It was also demonstrated that children with CI aged 8–9 years retrieved significantly fewer words and used less efficient strategies in the retrieval process, especially on the phonemically based task compared to children with NH of the same ages, whereas children 6–7 years performed similarly in both groups regarding number of retrieved words and use of strategies. The results are discussed with respect to factors such as age differences in performance for children with CI, especially for the phonemically based task.     

Adults' strategies for simple addition and multiplication: verbal self-reports and the operand recognition paradigm

Accurate measurement of cognitive strategies is important in diverse areas of psychological research. Strategy self-reports are a common measure, but C. Thevenot, M. Fanget, and M. Fayol (2007) proposed a more objective method to distinguish different strategies in the context of mental arithmetic. In their operand recognition paradigm, speed of recognition memory for problem operands after solving a problem indexes strategy (e.g., direct memory retrieval vs. a procedural strategy). Here, in 2 experiments, operand recognition time was the same following simple addition or multiplication, but, consistent with a wide variety of previous research, strategy reports indicated much greater use of procedures (e.g., counting) for addition than multiplication. Operation, problem size (e.g., 2 + 3 vs. 8 + 9), and operand format (digits vs. words) had interactive effects on reported procedure use that were not reflected in recognition performance. Regression analyses suggested that recognition time was influenced at least as much by the relative difficulty of the preceding problem as by the strategy used. The findings indicate that the operand recognition paradigm is not a reliable substitute for strategy reports and highlight the potential impact of difficulty-related carryover effects in sequential cognitive tasks.     

Testing a model of pain appraisal and coping in children with chronic abdominal pain.

This prospective study of children with recurrent abdominal pain (N=133; ages 8--15 years) used path analysis to examine relations among dispositional pain beliefs and coping styles, cognitions and behavior related to a specific pain episode, and short- and long-term outcomes. Children believing they could not reduce or accept pain appraised their episode-specific coping ability as low and reported passive coping behavior. Dispositional passive coping had direct effects on both episode-specific passive coping and long-term symptoms and disability. Accommodative coping (acceptance and self-encouragement) was associated with reduced episode-specific distress, which itself predicted reduced depressive symptoms 3 months later. Results suggest that coping-skill interventions for children with chronic pain should target reductions in passive coping and consider the potential benefits of accommodative coping strategies.     

Longitudinal Intellectual Assessment of Children With HIV Infection

The objective of this paper was to describe the intellectual development of 39 children with HIV infection. The children received serial evaluations over a 10-year period. Thirty-nine children were assessed with age-appropriate intellectual measures at regular intervals as part of their treatment in the HIV Program of a children's hospital. Children showed an 24-point drop in mean Bayley Mental scores over the first 2 years of life. McCarthy scores remained in the low average range from ages 3–5 years. IQ scores were stable by age 6 in the low average range, and unchanged through age 12. Significant changes in memory, vocabulary, and performance subtests were noted. Children with HIV infection demonstrated a significant decline in mental functioning over the first 2 years of life, fell into the low average range by age 3, and remained in the low average range, with subtle changes in some areas.     

Temperament Variation in Sensitivity to Parenting: Predicting Changes in Depression and Anxiety

Temperament was examined as a moderator of maternal parenting behaviors, including warmth, negativity, autonomy granting, and guidance. Observations of parenting and questionnaire measures of temperament and adjustment were obtained from a community sample (N = 214; ages 8–12). Trajectories of depression and anxiety were assessed across 3 years. The pattern of parenting as a predictor of internalizing symptoms depended on temperament. Maternal negativity predicted increases in depression for children low in fear. Effortful control moderated sensitivity to maternal negativity, autonomy granting, and guidance. Children low in effortful control reported more symptoms in the presence of negative or poor-fitting parenting. The results support differential responding, but also suggest that temperament may render children vulnerable for the development of problems regardless of parenting.     

Effects of a structured behavior modification treatment program on locus of control in behaviorally disturbed children

The effect of a 10-day behavior modification treatment program on locus of control was investigated. The subjects were children (N = 130; 6 to 12 years old) with severe behavioral disorders who were predominantly from low socioeconomic backgrounds, from broken homes, and socially deprived. Pre- and post-testing was done with the Nowicki-Strickland Preschool and Primary Internal-External Control Scale (Nowicki & Duke, 1974) and the Nowicki-Strickland Locus of Control Scale for Children (Nowicki & Strickland, 1973). Children between the ages of 10 and 12 responded to therapy with a significant increase in internality, but younger children did not.     

Early developmental trajectories of number knowledge and math achievement from 4 to 10 years: Low-persistent profile and early-life predictors

Little is known about the development of number knowledge (NK) and the antecedents of low-persistent NK profiles in early childhood. We documented the developmental trajectories of NK across the transition from preschool to elementary school, their predictive validity with respect to later math achievement, and the child and family early-life factors associated with low NK profiles. Children's NK was assessed four times at regular intervals between the ages 4 and 7 years in a large, representative population-based sample. Developmental trajectories of NK were established for 1597 children. These children were also assessed with respect to several features of their family environment at 5, 17, and 29 months, as well as their cognitive skills at age 41 months. Analyses revealed a best-fitting 4-trajectory model, characterized by Low-Increasing (10% of the children), Moderate-Increasing (39%), Moderate-Fast Increasing (32%) and High-Increasing (19%) groups. Children of these trajectory groups differed significantly with respect to math achievement at ages 8 and 10 years, with the Low-Increasing group persistently scoring lower than the other groups throughout these years. Children of Low-Increasing NK group were from household of lower income and father with low educational background, poorer early cognitive development, and more importantly, reduced visual-spatial skills and memory-span. Children displaying reduced cognitive abilities and impoverished living conditions early in life are at greater risk of low NK throughout late preschool and school entry, with ensuing difficulties in math achievement. They deserve early preventive attention to help alleviate later mathematic difficulties.     

Verbal fluency in children with ADHD: Strategy using and temporal properties

Verbal fluency tasks are commonly used in cognitive and developmental neuropsychology in assessing executive functions, language skills as well as divergent thinking. Twenty-two typically developing children and 22 children with ADHD between the ages of 8 and12 years were examined using verbal fluency tasks, prepotent response inhibition, and working memory tests. The clinical group showed impaired inhibitory and spatial working memory processes. We used different qualitative analyses of verbal fluency tasks to explore the lexical and executive strategies (word clustering and switching), and the temporal properties of the responses. Children with ADHD had a leeway in applying relevant lexical or executive strategies related to difficulties in strategy using. The reduced efficiency of children with ADHD in semantic fluency task is based on suboptimal shifting between word clusters and is related to the lack of ability of producing new clusters of items. The group difference appeared at the level of accessing and/or activating common words; however, the executive process of searching the lexicon extensively is intact.     

Sensitivity to general and specific numerical features in typical achievers and children with mathematics learning disability

We examined the development of sensitivity to general and specific numerical features in typical achievers and in 6th and 8th graders with mathematics learning disability (MLD), using two effects in mental multiplication: operand-relatedness (i.e., difficulty in avoiding errors that are related to the operands via a shared multiplication row) and decade-consistency (i.e., difficulty in avoiding errors that are operand related and also share a decade with the true result). Responses to decade-consistent products were quick but erroneous. In line with the processing sequence in adults, children first became sensitive to the general numerical feature of operand-relatedness (typical achievers—from 3rd grade; children with MLD in 8th grade) and only later to the specific feature of decade-consistency (typical achievers—from 4th grade, but only from 6th grade in a mature pattern). Implications of the numerical sensitivity in children with MLD are discussed.     

Predictors and outcomes of joint trajectories of callous-unemotional traits and conduct problems in childhood

Callous-unemotional (CU) traits are associated with antisocial and delinquent behaviors in children and represent a potential risk factor for adult psychopathy. However, there is a paucity of longitudinal research that explores the development of these traits, their longitudinal association with conduct problems (CP), and their psychosocial predictors and outcomes. Using a large sample of children followed longitudinally from the Twins Early Development Study (N=9,578), we described the joint developmental trajectories of CU traits and CP during childhood (between ages 7 and 12) and examined the child- and family-level predictors (4 years old) and concomitant outcomes (12 years old) associated with the trajectories. The developmental trajectories were characterized with teachers' ratings of CU traits and CP from ages 7 to 12. Using general growth mixture modeling, we identified four trajectories of CU traits (stable high, increasing, decreasing, and stable low) and two trajectories of CP (high and low). Compared with the children who followed a low trajectory of CU traits and CP, those who followed a high trajectory of CU traits and CP had more negative child- and family-level predictors at 4 years (including CP, hyperactivity, negative parental discipline, and chaos in the home). Children with high or increasing levels of CU traits and concomitant high levels of CP presented the most negative outcomes at 12 years (including hyperactivity, peer problems, emotional problems, and negative parental feelings). Children with high CU traits and concomitant high levels of CP in childhood should be prioritized for targeted intervention.     

Bidirectional links in the network of multiplication facts

In three experiments, we tested the hypothesis that activation of multiplication operand nodes (e.g., 3 and 8) can occur through presentation of their product (e.g., 24). In Experiments 1 and 2 we found activation of the operands when the product was presented as a cue in a number-matching task. In Experiment 3, activation also occurred in a parity-matching task, where the product (24) was not relevant to the parity matching on its operands (3 and 8). We concluded that bidirectional links exist among the operands and their product for multiplication problems and these links can be activated in a purely stimulus-driven manner. We suggest this may constitute the basis for the solution of simple divisions by mediation through the complementary multiplication facts.