Number-space associations in synaesthesia are not influenced by finger-counting habits

In many cultures, one of the earliest representations of number to be learned is a finger-counting system. Although most children stop using their fingers to count as they grow more confident with number, traces of this system can still be seen in adulthood. For example, an individual's finger-counting habits appear to affect the ways in which numbers are implicitly associated with certain areas of space, as inferred from the spatial–numerical association of response codes (SNARC) effect. In this study, we questioned the finger-counting habits of 98 participants who make explicit, idiosyncratic associations between number and space, known as number-space synaesthesia. Unexpectedly, neither handedness nor finger-counting direction (left-to-right or right-to-left) was associated with the relative positions of 1 and 10 in an individual's number-space synaesthesia. This lack of association between finger-counting styles and number-space synaesthesia layout may result from habitual use of synaesthetic space rather than fingers when learning to count; we offer some testable hypotheses that could assess whether this is the case

Magnitude Representations and Counting Skills in Preschool Children

This is an Accepted Manuscript of an article published by Taylor & Francis Group in Mathematical Thinking and Learning on 7/05/2015, available online: http://www.tandfonline.com/10.1080/10986065.2015.1016811.When children learn to count, they map newly acquired symbolic representations of number onto preexisting nonsymbolic representations. The nature and timing of this mapping is currently unclear. Some researchers have suggested this mapping process helps children understand the cardinal principle of counting, while other evidence suggests that this mapping only occurs once children have cardinality understanding. One difficulty with the current literature is that studies have employed tasks that only indirectly assess children’s nonsymbolic-symbolic mappings. We introduce a task in which preschoolers made magnitude comparisons across representation formats (e.g., dot arrays vs. verbal number), allowing a direct assessment of mapping. We gave this task to 60 children aged 2;7 - 4;10, together with counting and Give-a-Number tasks. We found that some children could map between nonsymbolic quantities and the number words they understood the cardinal meaning of, even if they had yet to grasp the general cardinality principle of counting

International Consensus Statement on Allergy and Rhinology: Allergic Rhinitis

Background: Critical examination of the quality and validity of available allergic rhinitis (AR) literature is necessary to improve understanding and to appropriately translate this knowledge to clinical care of the AR patient. To evaluate the existing AR literature, international multidisciplinary experts with an interest in AR have produced the International Consensus statement on Allergy and Rhinology: Allergic Rhinitis (ICAR:AR). Methods: Using previously described methodology, specific topics were developed relating to AR. Each topic was assigned a literature review, evidence-based review (EBR), or evidence-based review with recommendations (EBRR) format as dictated by available evidence and purpose within the ICAR:AR document. Following iterative reviews of each topic, the ICAR:AR document was synthesized and reviewed by all authors for consensus. Results: The ICAR:AR document addresses over 100 individual topics related to AR, including diagnosis, pathophysiology, epidemiology, disease burden, risk factors for the development of AR, allergy testing modalities, treatment, and other conditions/comorbidities associated with AR. Conclusion: This critical review of the AR literature has identified several strengths; providers can be confident that treatment decisions are supported by rigorous studies. However, there are also substantial gaps in the AR literature. These knowledge gaps should be viewed as opportunities for improvement, as often the things that we teach and the medicine that we practice are not based on the best quality evidence. This document aims to highlight the strengths and weaknesses of the AR literature to identify areas for future AR research and improved understanding

Early numerical competencies in 5- and 6-year-old children with autism spectrum disorder

Research Findings: To date, studies comparing the mathematical abilities of children with autism spectrum disorder (ASD) and typically developing children are scarce, and results remain inconclusive. In general, studies on this topic focus on mathematical abilities learned from elementary school onward, with little attention for possible precursors at younger ages. The current exploratory study focused on the important developmental period of preschool age, investigating 5 early numerical competencies in 30 high-functioning children with ASD and 30 age-matched control children: verbal subitizing, counting, magnitude comparison, estimation, and arithmetic operations. Children were examined at 5 or 6 years of age, attending the 3rd and final year of preschool. Overall, rather similar early number processing was found in children with and without ASD, although marginally significant results indicated a weaker performance of children with ASD on verbal subitizing and conceptual counting. Practice or Policy: Given the pervasiveness and impact of ASD on other domains of functioning, it is important to know that no general deficits in early numerical competencies were found in this study. However, some downward trends in mathematics performance were identified in children with ASD, which can serve as the basis for additional research in this field

Abordagem aos números decimais e suas operações: a importância de uma “eficaz navegação” entre representações

Este artigo foca alguns aspectos e ideias de tarefas a serem exploradas com os alunos relativamente à multiplicação de números decimais, discutindo o conhecimento matemático para o ensino subjacente à preparação e à aplicação de tais tarefas. Discutem-se algumas representações dessa multiplicação e a importância de um rico e fundamentado conhecimento matemático para o ensino como promotor de um conhecimento matemático com significado, por parte dos alunos, por via de uma eficaz navegação entre representações. A escolha das representações pretende, aqui, tornar também evidente o motivo pelo qual, ao multiplicar dois números decimais, o número de casas decimais do produto é a soma dos factores. O texto tem por base um trabalho colaborativo desenvolvido ao longo dos últimos anos com professores do 1º ciclo do ensino básico (alunos com idade entre seis e nove anos), tendo como ponto de partida as discussões ocorridas ali, as reflexões subjacentes e as maiores dificuldades sentidas tanto pelos alunos, como pelos próprios professores. É de salientar que o facto de se abordarem conjuntamente representações dos números em decimais e fraccionários possibilita que os alunos se consciencializem de diferentes representações para um mesmo valor, o mesmo ocorrendo quando se utilizam diversas quantidades como unidades discretas, ou distintos tipos de unidades. Apenas se o professor for detentor de um sustentado conhecimento matemático para o ensino ele poderá recorrer a essas distintas representações de maneira construtiva e de modo a que tenham significado para os alunos

Field independence associates with mathematics and science performance in 5- to 10-year-olds after accounting for domain-general factors

Field independence describes the extent to which individuals are influenced by context when trying to identify embedded targets. It associates with cognitive functioning and is a predictor of academic achievement. However, little is known about the neural and cognitive underpinnings of field independence which lead to these associations. Here we investigated behavioural associations between two measures of field independence (Children’s Embedded Figures Test (CEFT) and Design Organisation Test (DOT)) and performance on mathematics (reasoning and written arithmetic) and science tests (reasoning and scientific inquiry) in 135 children aged 5-10 years. There were strong associations between field independence and mathematics and science, which were largely explained by individual differences in age, IQ, and verbal working memory. However, regression analyses indicated that after controlling for these variables, the CEFT explained additional variance on the mathematical reasoning and science tests, whereas the DOT predicted unique variance on the written arithmetic test

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

Structured feedback on students’ concept maps: the proverbial path to learning?

Good conceptual knowledge is an essential requirement for health professions students, in that they are required to apply concepts learned in the classroom to a variety of different contexts. However, the use of traditional methods of assessment limits the educator’s ability to correct students’ conceptual knowledge prior to altering the educational context. Concept mapping (CM) is an educational tool for evaluating conceptual knowledge, but little is known about its use in facilitating the development of richer knowledge frameworks. In addition, structured feedback has the potential to develop good conceptual knowledge. The purpose of this study was to use Kinchin’s criteria to assess the impact of structured feedback on the graphical complexity of CM’s by observing the development of richer knowledge frameworks. Fifty-eight physiotherapy students created CM’s targeting the integration of two knowledge domains within a case-based teaching paradigm. Each student received one round of structured feedback that addressed correction, reinforcement, forensic diagnosis, benchmarking, and longitudinal development on their CM’s prior to the final submission. The concept maps were categorized according to Kinchin’s criteria as either Spoke, Chain or Net representations, and then evaluated against defined traits of meaningful learning. The inter-rater reliability of categorizing CM’s was good. Pre-feedback CM’s were predominantly Chain structures (57%), with Net structures appearing least often. There was a significant reduction of the basic Spoke- structured CMs (P = 0.002) and a significant increase of Net-structured maps (P < 0.001) at the final evaluation (post-feedback). Changes in structural complexity of CMs appeared to be indicative of broader knowledge frameworks as assessed against the meaningful learning traits. Feedback on CM’s seemed to have contributed towards improving conceptual knowledge and correcting naive conceptions of related knowledge. Educators in medical education could therefore consider using CM’s to target individual student development