Intuition and Visualization in Mathematical Problem Solving

In this article, I will discuss the relationship between mathematical intuition and mathematical visualization. I will argue that in order to investigate this relationship, it is necessary to consider mathematical activity as a complex phenomenon, which involves many different cognitive resources. I will focus on two kinds of danger in recurring to visualization and I will show that they are not a good reason to conclude that visualization is not reliable, if we consider its use in mathematical practice. Then, I will give an example of mathematical reasoning with a figure, and show that both visualization and intuition are involved. I claim that mathematical intuition depends on background knowledge and expertise, and that it allows to see the generality of the conclusions obtained by means of visualization.     

Age-related quantitative and qualitative changes in decision making ability

The "frontal aging hypothesis" predicts that brain senescence affects predominantly the prefrontal regions. Preliminary evidence has recently been gathered in favour of an age-related change in a typically frontal process, i.e. decision making, using the Iowa Gambling Task (IGT), but overall findings have been conflicting. Following the traditional scoring method, coupled with a qualitative analysis, in the present study we compared IGT performance of 40 young (mean age: 27.9+/-4.7) and 40 old (mean age: 65.4+/-8.6) healthy adults and of 18 patients affected by frontal lobe dementia of mild severity (mean age: 65.1+/-7.4, mean MMSE score: 24.1+/-3.9). Quantitative findings support the notion that decision making ability declines with age; moreover, it approximates the impairment observed in executive dysfunction due to neurodegeneration. Results of the qualitative analysis did not reach statistical significance for the motivational and learning decision making components considered, but approached significance for the attentional component for elderly versus young normals, suggesting a possible decrease in the ability to maintain sustained attention during complex and prolonged tasks as the putative deficit underlying impaired decision making in normal aging.     

Scaffolding the design of accessible eLearning content: a user-centered approach and cognitive perspective

There exist various guidelines for facilitating the design, preparation, and deployment of accessible eLearning applications and contents. However, such guidelines prevalently address accessibility in a rather technical sense, without giving sufficient consideration to the cognitive aspects and issues related to the use of eLearning materials by learners with disabilities. In this paper we describe how a user-centered design process was applied to develop a method and set of guidelines for didactical experts to scaffold their creation of accessible eLearning content, based on a more sound approach to accessibility. The paper also discusses possible design solutions for tools supporting eLearning content authors in the adoption and application of the proposed approach.     

Central ghrelin increases anxiety in the Open Field test and impairs retention memory in a passive avoidance task in neonatal chicks

Ghrelin (Grh) is an endogenous ligand for the growth hormone secretagogue receptor. Although Ghr stimulates feeding in rats, it inhibits feeding in neonatal chicks. However, little is known about other central behavioral effects of Ghr. Therefore, we investigated the Ghr effects, injected intracerebroventricularly, on anxiety and memory retention of neonatal chicks in an Open Field test and in a one-trial passive avoidance task, respectively. In the Open Field test, the administration of Ghr in a dose-dependent manner increased the latency to ambulate but decreased ambulation activity, indicating an anxiogenic effect. Furthermore, chicks trained on a passive avoidance task and injected with a dose of 30 pmol of Ghr immediately after training showed an impairment of memory retention. However, there were no significant effects on the number of pecks during the pretraining, training, retention and discrimination. In addition, different doses of Ghr produced an inhibition in food intake at different times after injection. Our results indicate that Ghr induces anxiogenesis in chicks. Moreover, we have shown for the first time that Ghr can decrease memory retention in a non-mammalian species, suggesting that Ghr may play an important role in the processes of memory retention in birds.     

Programmed to learn? The ontogeny of mirror neurons

Mirror neurons are increasingly recognized as a crucial substrate for many developmental processes, including imitation and social learning. Although there has been considerable progress in describing their function and localization in the primate and adult human brain, we still know little about their ontogeny. The idea that mirror neurons result from Hebbian learning while the child observes/hears his/her own actions has received remarkable empirical support in recent years. Here we add a new element to this proposal, by suggesting that the infant's perceptual‐motor system is optimized to provide the brain with the correct input for Hebbian learning, thus facilitating the association between the perception of actions and their corresponding motor programs. We review evidence that infants (1) have a marked visual preference for hands, (2) show cyclic movement patterns with a frequency that could be in the optimal range for enhanced Hebbian learning, and (3) show synchronized theta EEG (also known to favour synaptic Hebbian learning) in mirror cortical areas during self‐observation of grasping. These conditions, taken together, would allow mirror neurons for manual actions to develop quickly and reliably through experiential canalization. Our hypothesis provides a plausible pathway for the emergence of mirror neurons that integrates learning with genetic pre‐programming, suggesting new avenues for research on the link between synaptic processes and behaviour in ontogeny.     

Number development in young children

This paper presents new data on children's acquisition of counting skills. Three aspects of counting were studied: the formation of the cardinality rule that the last number named during counting denotes the number of objects in an array, the mastery of the counting procedure or the coordination of ordered number names and objects counted, and the growth of the knowledge that x + 1 is greater than x. A model was outlined which posits the hierarchic integration of six number skills to account for the growth of the knowledge that x + 1 is greater than x and the development of number conservation. The six skills are: the cardinality rule, the counting procedure, acquisition of more x's, judgments of relative numerosity, pattern recognition of small numbers, and one-to-one correspondences.     

Teaching children with autism spectrum disorder to tact auditory stimuli: A replication

It is important that tacts are controlled by stimuli across all senses but teaching tacts to children with autism spectrum disorder (ASD) is often limited to visual stimuli. This study replicated and extended a study on the effects of antecedent-stimulus presentations on the acquisition of auditory tacts. We used a concurrent multiple probe across sets design and an embedded adapted alternating treatments design to evaluate acquisition of auditory tacts when auditory stimuli were presented alone (i.e., isolated) or with corresponding pictures (i.e., compound-with-known and compound-with-unknown) with two school-aged boys with ASD. Both participants' responding met the mastery criterion no matter the stimulus presentation with at least one set, but one participant failed to acquire one set of stimuli in the isolated condition. The isolated condition was rarely the most efficient. We conducted post-training stimulus-control probes, and we observed disrupted stimulus control in the isolated condition for one participant. Implications for arranging auditory tacts instruction are discussed.     

The Practice of Mathematics: Cognitive Resources and Conceptual Content

Topoi - In the past 10 years, contemporary philosophy of mathematics has seen the development of a trend that conceives mathematics as first and foremost a human activity and in...     

Intellectual profiles and violent behavior in juvenile delinquents

Hemispheric laterality, measured by the Wechsler Verbal IQ-Performance IQ differential score, in a large group of delinquents (N = 101) was not associated with violent-nonviolent behavior. Delinquents were, however, likely to be relatively more impaired on verbal than on nonverbal intellectual capacities.