Development of numerical cognition among Brazilian school-aged children

The Numerical Cognition is influenced by biological, cognitive, educational, and cultural factors and entails the following systems: Number Sense (NS) represents the innate ability to recognize, compare, add, and subtract small quantities, without the need of counting; Number Production (NP) which includes reading, writing and counting numbers or objects; Number Comprehension (NC), i.e., the understanding the nature of the numerical symbols and their number, and the calculation (CA). The aims of the present study were to: i) assess theoretical constructs (NS, NC, NP and CA) in children from public schools from 1 st -to 6 th - grades; and ii) investigate their relationship with schooling and working memory. The sample included 162 children, both genders, of 7-to 12-years-old that studied in public school from 1 st -to 6 th -grades, which participated in the normative study of Zareki-R (Battery of neuropsychological tests for number processing and calculation in children, Revised; von Aster & Dellatolas, 2006). Children of 1 st and 2 nd grades demonstrated an inferior global score in NC, NP and CA. There were no genderrelated differences. The results indicated that the contribution of NS domain in Zareki-R performance is low in comparison to the other three domains, which are dependent on school-related arithmetic skills.

Moving along the mental number line: Interactions between whole-body motion and numerical cognition

Active head turns to the left and right have recently been shown to influence numerical cognition by shifting attention along the mental number line. In the present study, we found that passive whole-body motion influences numerical cognition. In a random-number generation task (Experiment 1), leftward and downward displacement of participants facilitated small number generation, whereas rightward and upward displacement facilitated the generation of large numbers. Influences of leftward and rightward motion were also found for the processing of auditorily presented numbers in a magnitude-judgment task (Experiment 2). Additionally, we investigated the reverse effect of the number-space association (Experiment 3). Participants were displaced leftward or rightward and asked to detect motion direction as fast as possible while small or large numbers were auditorily presented. When motion detection was difficult, leftward motion was detected faster when hearing small number and rightward motion when hearing large number. We provide new evidence that bottom-up vestibular activation is sufficient to interact with the higher-order spatial representation underlying numerical cognition. The results show that action planning or motor activity is not necessary to influence spatial attention. Moreover, our results suggest that self-motion perception and numerical cognition can mutually influence each other.

Number Processing and Calculation in Brazilian Children Aged 7-12 Years

Numerical cognition is based on two components - number processing and calculation. Its development is influenced by biological, cognitive, educational, and cultural factors. The objectives of the present study were to: i) assess number processing and calculation in Brazilian children aged 7-12 years from public schools using the Zareki-R (Battery of neuropsychological tests for number processing and calculation in children, Revised; von Aster & Dellatolas, 2006) in order to obtain normative data for Portuguese speakers; ii) identify how environment, age, and gender influences the development of these mathematical skills; iii) investigate the construct validity of the Zareki-R by the contrast with the Arithmetic subtest of WISC-III. The sample included 172 children, both genders, divided in two groups: urban (N= 119) and rural (N= 53) assessed by the Zareki-R. Rural children presented lower scores in one aspect of number processing; children aged 7-8 years demonstrated an inferior global score than older; boys presented a superior performance in both number processing and calculation. Construct validity of Zareki-R was demonstrated by high to moderate correlations with Arithmetic subtest of WISC-III. The Zareki-R therefore is a suitable instrument to assess the development of mathematical skills, which is influenced by factors such as environment, age, and gender.

O efeito do treino musical sobre a capacidade da memória operacional e da cognição numérica de crianças com discalculia do desenvolvimento

Pós-graduação em Psicologia do Desenvolvimento e Aprendizagem - FC

Treino musical como proposta para a estimulação da cognição numérica em crianças de idade escolar

Pós-graduação em Psicologia do Desenvolvimento e Aprendizagem - FC

Desempenho de crianças com deficiência auditiva e implante coclear em tarefas de seleção de e de nomeação de figuras

The aim of this study was to investigate the development of specific domains of Numerical Cognition (Number Sense – NS, Number Comprehension – NC, Number Production – NP, and Calculation – CA) in Brazilian children with Specific Learning Disorders. The study included 72 children (36 boys), from 9-to 10-years-old, enrolled in 4th and 5th years of elementary school of public schools at countryside of Sao Paulo State, Brazil. They were divided into three groups: control (CT, N = 42), Developmental Dyslexia (DL, N = 11) and Developmental Dyscalculia combined with dyslexia (DDc, N = 19). All participants had intellectual level within the normal range, however, children from the last two groups had Learning Disorders classified by School Achievement Test - TDE (Stein, 1994) and DDc children received necessarily classification as 'inferior' in Arithmetic Test of TDE. The children did not differ in NS. DL and DDc children showed slight deficits in NC. However, DDc children had moderate in NP and mild to moderate deficits in CA, which indicates a more generalized impairment in Numerical Cognition. Furthermore, DDc children showed discrepancy in Numerical Cognition performance when compared to the other groups. Thus, children with Learning Disorders showed different performances in Numerical Cognition, although both groups had preserved SN, DDc children showed higher deficits and discrepancy in relation DL and typically developing children.

Does the acute cerebellitis play a role in the neurocognitive profile of a child after its onset?

This study aimed to present the neuropsychological assessment of MC, a seven-year-old girl, who was diagnosed with acute viral cerebellitis. The protocol included cognitive tests, stress and mood scales, behavioral observation, and interviews with family and school. In the neuropsychological assessment, difficulties in crystallized skills, especially in language and numerical cognition domains, were observed. The results of the neuropsychological assessment were discussed to detail her neurocognitive profile and verify to what extent her impairment could be attributed to the acute viral cerebellitis.

Cognição Numérica de crianças pré-escolares brasileiras pela ZAREKI-K

The Numerical Cognition is infl uenced by biological, cognitive, educational and cultural factors. It consists of a primary system, called Number Sense that would be innate and universal, also of secondary systems: the Calculation, implied to perform mathematical operations by means of symbols or words and Number Processing, which is divided into two components, Number Comprehension, related with the understanding of numerical symbols and Number Production, which includes reading, writing and coun-ting numbers. However, studies that show the development of these functions in children of preschool age are scarce. Therefore, aims of this study were to investigate numerical cognition in preschool Brazilian children to demonstrate the construct validity of the ZAREKI-K (A Neuropsychological Battery for the Assessment of Treatment of Numbers and Calculation for preschool children). The participants were 42 children of both genders, who attended public elementary schools; the children were evaluated by this battery and WISC-III. The results indicated signifi cant differences associated with age which children of 6 years had better scores on subtests related to Number Production, Calculation and Number Comprehension, as well moderate and high correlations between some subtests of both instruments, demonstrating the construct validity of the battery. In conclusion, preliminary normative data were obtained for ZAREKI-K. The analyses suggested that it is a promising tool for the assessment of numerical cognition in preschool children.Keywords: Mathematics, number, preschoolers, working memory, Developmental Dyscalculia.

There is more than "more is up": Hand and foot responses reverse the vertical association of number magnitudes

Recent research in cognitive sciences shows a growing interest in spatial-numerical associations. The horizontal SNARC (spatial-numerical association of response codes) effect is defined by faster left-sided responses to small numbers and faster right-sided responses to large numbers in a parity judgment task. In this study we investigated whether there is also a SNARC effect for upper and lower responses. The grounded cognition approach suggests that the universal experience of "more is up" serves as a robust frame of reference for vertical number representation. In line with this view, lower hand responses to small numbers were faster than to large numbers (Experiment 1). Interestingly, the vertical SNARC effect reversed when the lower responses were given by foot instead of the hand (Experiments 2, 3, and 4). We found faster upper (hand) responses to small numbers and faster lower (foot) responses to large numbers. Additional experiments showed that spatial factors cannot account for the reversal of the vertical SNARC effect (Experiments 4 and 5). Our results question the view of "more is up" as a robust frame of reference for spatial-numerical associations. We discuss our results within a hierarchical framework of numerical cognition and point to a possible link between effectors and number representation.

Decision-Making in the Primate Brain

Making decisions is fundamental to everything we do, yet it can be impaired in various disorders and conditions. While research into the neural basis of decision-making has flourished in recent years, many questions remain about how decisions are instantiated in the brain. Here we explored how primates make abstract decisions and decisions in social contexts, as well as one way to non-invasively modulate the brain circuits underlying decision-making. We used rhesus macaques as our model organism. First we probed numerical decision-making, a form of abstract decision-making. We demonstrated that monkeys are able to compare discrete ratios, choosing an array with a greater ratio of positive to negative stimuli, even when this array does not have a greater absolute number of positive stimuli. Monkeys’ performance in this task adhered to Weber’s law, indicating that monkeys—like humans—treat proportions as analog magnitudes. Next we showed that monkeys’ ordinal decisions are influenced by spatial associations; when trained to select the fourth stimulus from the bottom in a vertical array, they subsequently selected the fourth stimulus from the left—and not from the right—in a horizontal array. In other words, they begin enumerating from one side of space and not the other, mirroring the human tendency to associate numbers with space. These and other studies confirmed that monkeys’ numerical decision-making follows similar patterns to that of humans, making them a good model for investigations of the neurobiological basis of numerical decision-making.

We sought to develop a system for exploring the neuronal basis of the cognitive and behavioral effects observed following transcranial magnetic stimulation, a relatively new, non-invasive method of brain stimulation that may be used to treat clinical disorders. We completed a set of pilot studies applying offline low-frequency repetitive transcranial magnetic stimulation to the macaque posterior parietal cortex, which has been implicated in numerical processing, while subjects performed a numerical comparison and control color comparison task, and while electrophysiological activity was recorded from the stimulated region of cortex. We found tentative evidence in one paradigm that stimulation did selectively impair performance in the number task, causally implicating the posterior parietal cortex in numerical decisions. In another paradigm, however, we manipulated the subject’s reaching behavior but not her number or color comparison performance. We also found that stimulation produced variable changes in neuronal firing and local field potentials. Together these findings lay the groundwork for detailed investigations into how different parameters of transcranial magnetic stimulation can interact with cortical architecture to produce various cognitive and behavioral changes.

Finally, we explored how monkeys decide how to behave in competitive social interactions. In a zero-sum computer game in which two monkeys played as a shooter or a goalie during a hockey-like “penalty shot” scenario, we found that shooters developed complex movement trajectories so as to conceal their intentions from the goalies. Additionally, we found that neurons in the dorsolateral and dorsomedial prefrontal cortex played a role in generating this “deceptive” behavior. We conclude that these regions of prefrontal cortex form part of a circuit that guides decisions to make an individual less predictable to an opponent.

Essays on decision sciences: exploring cognition, information processing, and complexity

This thesis provides three original contributions to the field of Decision Sciences. The first contribution explores the field of heuristics and biases. New variations of the Cognitive Reflection Test (CRT--a test to measure "the ability or disposition to resist reporting the response that first comes to mind"), are provided. The original CRT (S. Frederick [2005] Journal of Economic Perspectives, v. 19:4, pp.24-42) has items in which the response is immediate--and erroneous. It is shown that by merely varying the numerical parameters of the problems, large deviations in response are found. Not only the final results are affected by the proposed variations, but so is processing fluency. It seems that numbers' magnitudes serve as a cue to activate system-2 type reasoning. The second contribution explores Managerial Algorithmics Theory (M. Moldoveanu [2009] Strategic Management Journal, v. 30, pp. 737-763); an ambitious research program that states that managers display cognitive choices with a "preference towards solving problems of low computational complexity". An empirical test of this hypothesis is conducted, with results showing that this premise is not supported. A number of problems are designed with the intent of testing the predictions from managerial algorithmics against the predictions of cognitive psychology. The results demonstrate (once again) that framing effects profoundly affect choice, and (an original insight) that managers are unable to distinguish computational complexity problem classes. The third contribution explores a new approach to a computationally complex problem in marketing: the shelf space allocation problem (M-H Yang [2001] European Journal of Operational Research, v. 131, pp.107--118). A new representation for a genetic algorithm is developed, and computational experiments demonstrate its feasibility as a practical solution method. These studies lie at the interface of psychology and economics (with bounded rationality and the heuristics and biases programme), psychology, strategy, and computational complexity, and heuristics for computationally hard problems in management science.

Pushing forward in embodied cognition: May we mouse the mathematical mind?

Freely available software has popularized “mousetracking” to study cognitive processing; this involves the on-line recording of cursor positions while participants move a computer mouse to indicate their choice. Movement trajectories of the cursor can then be reconstructed off-line to assess the efficiency of responding in time and across space. Here we focus on the process of selecting among alternative numerical responses. Several studies have recently measured the mathematical mind with cursor movements while people decided about number magnitude or parity, computed sums or differences, or simply located numbers on a number line. After some general methodological considerations about mouse tracking we discuss several conceptual concerns that become particularly evident when “mousing” the mathematical mind.

Joining forces - Combining cognition-targeted motor control training with group or individual pain physiology education: A successful treatment for chronic low back pain

Chronic unremittent low back pain (LBP) is characterised by cognitive barriers to treatment. Combining a motor control training approach with individualised education about pain physiology is effective in this group of patients. This randomized comparative trial (i) evaluates an approach to motor control acquisition and training that considers the complexities of the relationship between pain and motor output, and (ii) compares the efficacy and cost of individualized and group pain physiology education. After an "ongoing usual treatment" period, patients participated in a 4-week motor control and pain physiology education program. Patients received four one-hour individualized education sessions (IE) or one 4-hour group lecture (GE). Both groups reduced pain (numerical rating scale) and disability (Roland Morris Disability Questionnaire). IE showed bigger decreases, which were maintained at 12 months (P < 0.05 for all). The combined motor control and education approach is effective. Although group education imparts a lesser effect, it may be more cost-efficient. [ABSTRACT FROM AUTHOR]