Challenging the Science Curriculum Paradigm: TeachingPrimary Children Atomic-Molecular Theory

Solutions to global issues demand the involvement of scientists, yet concern exists about retention rates in science as students pass through school into University. Young children are curious about science, yet are considered incapable of grappling with abstract and microscopic concepts such as atoms, sub-atomic particles, molecules and DNA. School curricula for primary (elementary) aged children reflect this by their limitation to examining only what phenomena are without providing any explanatory frameworks for how or why they occur. This research challenges the assumption that atomic-molecular theory is too difficult for young children, examining new ways of introducing atomic theory to 9 year olds and seeks to verify their efficacy in producing genuine learning in the participants. Early results in three cases in different schools indicate these novel methods fostered further interest in science, allowed diverse children to engage and learn aspects of atomic theory, and satisfied the children’s desire for intellectual challenge. Learning exceeded expectations as demonstrated in the post-interview findings. Learning was also remarkably robust, as demonstrated in two schools eight weeks after the intervention, and in one school, one year after their first exposure to ideas about atoms, elements and molecules

Effective connectivity reveals strategy differences in an expert calculator

Mathematical reasoning is a core component of cognition and the study of experts defines the upper limits of human cognitive abilities, which is why we are fascinated by peak performers, such as chess masters and mental calculators. Here, we investigated the neural bases of calendrical skills, i.e. the ability to rapidly identify the weekday of a particular date, in a gifted mental calculator who does not fall in the autistic spectrum, using functional MRI. Graph-based mapping of effective connectivity, but not univariate analysis, revealed distinct anatomical location of “cortical hubs” supporting the processing of well-practiced close dates and less-practiced remote dates: the former engaged predominantly occipital and medial temporal areas, whereas the latter were associated mainly with prefrontal, orbitofrontal and anterior cingulate connectivity. These results point to the effect of extensive practice on the development of expertise and long term working memory, and demonstrate the role of frontal networks in supporting performance on less practiced calculations, which incur additional processing demands. Through the example of calendrical skills, our results demonstrate that the ability to perform complex calculations is initially supported by extensive attentional and strategic resources, which, as expertise develops, are gradually replaced by access to long term working memory for familiar material

The Search for Invariance: Repeated Positive Testing Serves the Goals of Causal Learning

Positive testing is characteristic of exploratory behavior, yet it seems to be at odds with the aim of information seeking. After all, repeated demonstrations of one’s current hypothesis often produce the same evidence and fail to distinguish it from potential alternatives. Research on the development of scientific reasoning and adult rule learning have both documented and attempted to explain this behavior. The current chapter reviews this prior work and introduces a novel theoretical account—the Search for Invariance (SI) hypothesis—which suggests that producing multiple positive examples serves the goals of causal learning. This hypothesis draws on the interventionist framework of causal reasoning, which suggests that causal learners are concerned with the invariance of candidate hypotheses. In a probabilistic and interdependent causal world, our primary goal is to determine whether, and in what contexts, our causal hypotheses provide accurate foundations for inference and intervention—not to disconfirm their alternatives. By recognizing the central role of invariance in causal learning, the phenomenon of positive testing may be reinterpreted as a rational information-seeking strategy

Impact of High Mathematics Education on the Number Sense

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS

The benefit of symbols: monkeys show linear, human-like, accuracy when using symbols to represent scalar value

When humans and animals estimate numbers of items, their error rate is proportional to the number. To date, however, only humans show the capacity to represent large numbers symbolically, which endows them with increased precision, especially for large numbers, and with tools for manipulating numbers. This ability depends critically on our capacity to acquire and represent explicit symbols. Here we show that when rhesus monkeys are trained to use an explicit symbol system, they too show more precise, and linear, scaling than they do using a one-to-one corresponding numerosity representation. We also found that when taught two different types of representations for reward amount, the monkeys systematically undervalued the less precise representation. The results indicate that monkeys, like humans, can learn alternative mechanisms for representing a single value scale and that performance variability and relative value depend on the distinguishability of each representation

Whole number thinking, learning and development: neuro-cognitive, cognitive and developmental approaches

The participants of working group 2 presented a broad range of studies, 11 papers in total, related to whole number learning representing research groups from 11 countries as follows. Two large cross-sectional studies focused on developmental aspects of young children’s number learning provide a lens for re-examining ‘traditional’ features of number acquisition. van den Heuvel-Panhuizen (the Netherlands) presented a co-authored paper with Elia (Cyprus; Elia and van den Heuvel-Panhuizen 2015) on a cross-cultural study of kindergartners’ number competence focused on counting, additive and multiplicative thinking. Second, Milinković (2015) examined the development of young Serbian children’s initial understanding of representations of whole numbers and counting strategies in a large study of 3- to 7-year-olds. Children’s invented (formal) representations such as set representation and the number line were found to be limited in their recordings. In a South African study focused on early counting and addition, Roberts (2015) directs attention to the role of teachers by providing a framework to support teachers’ interpretation of young disadvantaged learners’ representations of number when engaging with whole number additive tasks. Some papers reflected the increasing role of neuroscientific concepts and methodologies utilised in research on WNA learning and development. Sinclair and Coles (2015) drew upon neuroscientific research to highlight the significant role of symbol-to-symbol connections and the use of fingers and touch counting exempli- fied by the TouchCounts iPad app. Gould (2015) reported aspects of a large Australian large study of children in the first years of schooling aimed at improving numeracy and literacy in disadvantaged communities. A case study exemplified how numerals were identified by relying on a mental number line by using location to retrieve number names. This raised the question addressed in the neuroscientific work of Dehaene and other papers focused on individual differences in how the brain processes numbers. The Italian PerContare1 project (Baccaglini-Frank 2015) built upon the collaboration between cognitive psychologists and mathematics educators, aimed at developing teaching strategies for preventing and addressing early low achievement in arithmetic. It takes an innovative approach to the development of number sense that is grounded upon a kinaesthetic and visual-spatial approach to part-whole relationships. Mulligan and Woolcott (2015) provided a discussion paper on the underlying nature of number. They presented a broader view of mathematics learning (including WNA) as linked to spatial interaction with the environment; the concept of connectivity across concepts and the development of underlying pattern and structural relationships are central to their approach

Spatial Intuition in Elementary Arithmetic: A Neurocomputational Account

Elementary arithmetic (e.g., addition, subtraction) in humans has been shown to exhibit spatial properties. Its exact nature has remained elusive, however. To address this issue, we combine two earlier models for parietal cortex: A model we recently proposed on number-space interactions and a modeling framework of parietal cortex that implements radial basis functions for performing spatial transformations. Together, they provide us with a framework in which elementary arithmetic is based on evolutionarily more basic spatial transformations, thus providing the first implemented instance of Dehaene and Cohen's recycling hypothesis

Children’s Internal Attributions of Anxiety-Related Physical Symptoms: Age-Related Patterns and the Role of Cognitive Development and Anxiety Sensitivity

The present study examined age-related patterns in children’s anxiety-related interpretations and internal attributions of physical symptoms. A large sample of 388 children aged between 4 and 13 years completed a vignette paradigm during which they had to explain the emotional response of the main character who experienced anxiety-related physical symptoms in a variety of daily situations. In addition, children completed measures of cognitive development and anxiety sensitivity. Results demonstrated that age, cognitive development, and anxiety sensitivity were all positively related to children’s ability to perceive physical symptoms as a signal of anxiety and making internal attributions. Further, while a substantial proportion of the younger children (i.e., <7 years) were able to make a valid anxiety-related interpretation of a physical symptom, very few were capable of making an internal attribution, which means that children of this age lack the developmental prerequisites for applying physical symptoms-based theories of childhood anxiety

Deconstructing Insight: EEG Correlates of Insightful Problem Solving

Background: Cognitive insight phenomenon lies at the core of numerous discoveries. Behavioral research indicates four salient features of insightful problem solving: (i) mental impasse, followed by (ii) restructuring of the problem representation, which leads to (iii) a deeper understanding of the problem, and finally culminates in (iv) an “Aha!” feeling of suddenness and obviousness of the solution. However, until now no efforts have been made to investigate the neural mechanisms of these constituent features of insight in a unified framework. Methodology/Principal Findings: In an electroencephalographic study using verbal remote associate problems, we identified neural correlates of these four features of insightful problem solving. Hints were provided for unsolved problems or after mental impasse. Subjective ratings of the restructuring process and the feeling of suddenness were obtained on trial-by-trial basis. A negative correlation was found between these two ratings indicating that sudden insightful solutions, where restructuring is a key feature, involve automatic, subconscious recombination of information. Electroencephalogram signals were analyzed in the space×time×frequency domain with a nonparametric cluster randomization test. First, we found strong gamma band responses at parieto-occipital regions which we interpreted as (i) an adjustment of selective attention (leading to a mental impasse or to a correct solution depending on the gamma band power level) and (ii) encoding and retrieval processes for the emergence of spontaneous new solutions. Secondly, we observed an increased upper alpha band response in right temporal regions (suggesting active suppression of weakly activated solution relevant information) for initially unsuccessful trials that after hint presentation led to a correct solution. Finally, for trials with high restructuring, decreased alpha power (suggesting greater cortical excitation) was observed in right prefrontal area. Conclusions/Significance: Our results provide a first account of cognitive insight by dissociating its constituent components and potential neural correlates