French preschool and primary teachers' attitude towards finger counting.

Teachers' beliefs and attitudes are known to guide the type of activities they implement in their classrooms. A traditional conception that finger counting is merely a back-up when children fail to use more sophisticated and efficient strategies could therefore prevent teachers from encouraging children's use of fingers in arithmetic tasks. However, the potential benefit of finger counting for young learners has been recently documented and setting aside its practice within classrooms may hinder children's mathematical skill development. It is therefore important to establish whether there is a discrepancy between teacher's beliefs regarding finger counting and the latest discoveries in this field of research. To this aim, we interrogated 413 teachers from preschool to Grade 5. We found that, despite being generally positive towards finger counting, teachers think that finger counting is typical of children who present math difficulties or lack of confidence, even during the first years of learning. These results are discussed considering what is known and what remains to be determined in the current scientific literature.

Neural evidence for procedural automatization during cognitive development: Intraparietal response to changes in very-small addition problem-size increases with age.

Cognitive development is often thought to depend on qualitative changes in problem-solving strategies, with early developing algorithmic procedures (e.g., counting when adding numbers) considered being replaced by retrieval of associations (e.g., between operands and answers of addition problems) in adults. However, algorithmic procedures might also become automatized with practice. In a large cross-sectional fMRI study from age 8 to adulthood (n = 128), we evaluate this hypothesis by measuring neural changes associated with age-related reductions in a behavioral hallmark of mental addition, the problem-size effect (an increase in solving time as problem sum increases). We found that age-related decreases in problem-size effect were paralleled by age-related increases of activity in a region of the intraparietal sulcus that already supported the problem-size effect in 8- to 9-year-olds, at an age the effect is at least partly due to explicit counting. This developmental effect, which was also observed in the basal ganglia and prefrontal cortex, was restricted to problems with operands ≤ 4. These findings are consistent with a model positing that very-small arithmetic problems-and not larger problems-might rely on an automatization of counting procedures rather than a shift towards retrieval, and suggest a neural automatization of procedural knowledge during cognitive development.

The development of simple addition problem solving in children: Reliance on automatized counting or memory retrieval depends on both expertise and problem size.

In an experiment, 98 children aged 8 to 9, 10 to 12, and 13 to 15 years solved addition problems with a sum up to 10. In another experiment, the same children solved the same calculations within a sign priming paradigm where half the additions were displayed with the "+" sign 150 ms before the addends. Therefore, size effects and priming effects could be considered conjointly within the same populations. Our analyses revealed that small problems, constructed with addends from 1 to 4, presented a linear increase of solution times as a function of problem sums (i.e., size effect) in all age groups. However, an operator priming effect (i.e., facilitation of the solving process with the anticipated presentation of the "+" sign) was observed only in the group of oldest children. These results support the idea that children use a counting procedure that becomes automatized (as revealed by the priming effect) around 13 years of age. For larger problems and whatever the age group, no size or priming effects were observed, suggesting that the answers to these problems were already retrieved from memory at 8 to 9 years of age. For this specific category of large problems, negative slopes in solution times demonstrate that retrieval starts from the largest problems during development. These results are discussed in light of a horse race model in which procedures can win over retrieval.

The Evolution of Finger Counting between Kindergarten and Grade 2.

In this longitudinal study, we aimed at determining whether children who efficiently use finger counting are more likely to develop internalized arithmetic strategies than children who are less efficient. More precisely, we analyzed the behavior of 24 kindergarteners aged between 5 and 6 years who used their fingers to solve addition problems, and we were interested in determining the evolution of their finger counting strategies towards mental strategies after 2 years (Grade 2). Our results show that kindergarteners who were the most proficient in calculating on fingers were the more likely to have abandoned this strategy in Grade 2. This shows that the use of efficient finger counting strategies early during development optimizes the shift to mental strategies later on during school years. Moreover, children who still use their fingers to solve additions in Grade 2 present lower working memory capacities than children who had already abandoned this strategy.

Socio-Emotional Competencies and School Performance in Adolescence: What Role for School Adjustment?

There is growing evidence in the literature of positive relationships between socio-emotional competencies and school performance. Several hypotheses have been used to explain how these variables may be related to school performance. In this paper, we explored the role of various school adjustment variables in the relationship between interpersonal socio-emotional competencies and school grades, using a weighted network approach. This network approach allowed us to analyze the structure of interrelations between each variable, pointing to both central and mediatory school and socio-emotional variables within the network. Self-reported data from around 3,400 French vocational high school students were examined. This data included a set of interpersonal socio-emotional competencies (cognitive and affective empathy, socio-emotional behaviors and collective orientation), school adjustment measures (adaptation to the institution, school anxiety, self-regulation at school, and self-perceived competence at school) as well as grades in mathematics and French language. The results showed that self-regulation at school weighted the most strongly on the whole network, and was the most important mediatory pathway. More specifically, self-regulation mediated the relationships between interpersonal socio-emotional competencies and school grades.

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.

Strategic Variations in Fitts' Task: Comparison of Healthy Older Adults and Cognitively Impaired Patients.

The present study aimed at investigating how healthy older adults (HOA) and cognitively impaired patients (CIP) differ in a discrete Fitts' aiming task. Four levels of task difficulty were used, resulting from the simultaneous manipulation of the size of the target and its distance from home position. We found that movement times (MTs) followed Fitts' law in both HOA and CIP, with the latter being significantly slower and more affected by increased task difficulty. Moreover, correlation analyses suggest that lower information processing speed (IPS) and deficits in executive functions (EFs) are associated with decline of sensorimotor performance in Fitts' task. Analyses of strategic variations showed that HOA and CIP differed in strategy repertoire (which strategies they used), strategy distribution (i.e., how often they used each available strategy), and strategy execution (i.e., how quick they were with each available strategy). These findings further our understanding of how strategic variations used in a sensorimotor task are affected by cognitive impairment in older adults.

Sensori-motor strategic variations and sequential effects in young and older adults performing a Fitts' task.

The present study aimed at investigating age-related changes in strategic variations and sequential effects in discrete Fitts' aiming task. Three sequential effects were investigated, namely trial sequential difficulty effects (TSDE), strategy sequential difficulty effects (SSDE), and strategy repetition effects (SRE). After generalizing previously observed aging effects on strategic variations, our results showed that movement times were longer when performed after harder ID level than when following easier ID level (TSDE). We also observed SSDE, such that is movement times were longer when participants executed a strategy of intermediate difficulty (i.e., the progressive-deceleration strategy) after having used a more difficult strategy (i.e., the undershoot strategy) on the previous trial than after an easier strategy (i.e., the one-shot strategy). These sequential difficulty effects related to both difficulty and strategy were similar in young and older adults. In addition, we found that across two successive trials, participants tended to repeat the one-shot strategy the most often and the undershoot strategy the least often, with repetition rates of the progressive-deceleration strategy being in-between (SRE). Finally, age-related differences in strategy repetition effects varied with strategies (e.g., they were largest for the one-shot strategy). These findings have important implications for deciphering processes responsible for sequential effects in sensori-motor tasks as well as in cognitive tasks in general, and for our understanding of processes underlying sensori-motor performance in young and older adults.

Older and younger adults' strategies in sensorimotor tasks: insights from Fitts' pointing task.

We investigated how young and older adults differ in sensorimotor tasks. Two groups of participants (young and older adults) performed discrete Fitts' tasks in which 4 levels of difficulty (ID) were used, resulting from either the manipulation of the size of the target (ID(W)) or of the distance between home and target positions (ID(D)). Kinematic analysis allowed distinguishing 4 different types of strategies used to reach the target, on the basis of the existence and the nature of submovements. Results showed that the repertoire of strategies was significantly smaller in older than in young participants. In addition, the frequency of use of the different strategies varied with participants' age. Specifically, the most frequent strategies used by older participants included submovements, while those used by young participants did not include submovements. The differences observed between young and older adults were independent of whether ID was manipulated via target size or movement distance. Finally, age-related differences in strategy performance were found. These results have important implications for furthering our understanding of aging effects in sensorimotor tasks. They also illustrate the usefulness of a strategy approach in a domain where it had never been formally used before.

The time course of strategy sequential difficulty effects: an ERP study in arithmetic.

Uittenhove and Lemaire (Exp Psychol 59(5):295-301, 2012) found that we are slower when executing a strategy following a difficult strategy than when executing the same strategy following an easier strategy (i.e., strategy sequential difficulty effects). Uittenhove and Lemaire suggested that difficult strategies temporarily reduce available executive capacities, interfering with the next strategy execution. In this study, we used ERP to determine the time course of these effects. In a computational estimation task, we found greater cerebral activities during strategy execution following a more difficult compared to an easier strategy. Interestingly, greater cerebral activities were most apparent immediately after the encoding of the problem and not during encoding or in later stages of processing. This suggests that strategy sequential difficulty effects interfere most with the retrieval of procedures in contrast to execution of these procedures. We discuss implications of these findings for further understanding of execution of cognitive strategies.