Intuitive and Informal Knowledge in Preschoolers’ Development of Probabilistic Thinking

Preschoolers develop a wide range of mathematical informal knowledge and intuitive thinking before they enter formal, goal-oriented education. In their everyday activities young children get engaged with situations that enhance them to develop skills, concepts, strategies, representations, attitudes, constructs and operations concerning a wide range of mathematical notions. Recently there is scientific interest in linking children’s informal and formal knowledge in order to provide them with opportunities to avoid biases aiming at formulating, perceiving, reflecting on and exercising probabilistic notions. The current study investigates preschoolers’ (N=90) intuitive understanding of the likelihood of events in a probabilistic task with spinners. Participants, at the age of 4 to 6, are tested on their predictions of the most probable outcome prior to and after an instructive session of reasoning. The probabilistic task, based on constructivist principles, includes methodological alterations concerning the sample space and the themes of the stimuli. Educational implications are further discussed under the general point of view that in order to link informal to formal mathematical learning in preschool classroom, the subject content and the cognitive capacity of children are important to match

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

Confidence and competence with mathematical procedures

Confidence assessment (CA), in which students state alongside each of their answers a confidence level expressing how certain they are, has been employed successfully within higher education. However, it has not been widely explored with school pupils. This study examined how school mathematics pupils (N = 345) in five different secondary schools in England responded to the use of a CA instrument designed to incentivise the eliciting of truthful confidence ratings in the topic of directed (positive and negative) numbers. Pupils readily understood the negative marking aspect of the CA process and their facility correlated with their mean confidence with r = .546, N = 336, p < .001, indicating that pupils were generally well calibrated. Pupils’ comments indicated that the vast majority were positive about the CA approach, despite its dramatic differences from more usual assessment practices in UK schools. Some pupils felt that CA promoted deeper thinking, increased their confidence and had a potential role to play in classroom formative assessment

Symbolic arithmetic knowledge without instruction

This article was published in the journal, Nature [© The Nature Publishing Group]. The definitive version is available at: http://dx.doi.org/10.1038/nature05850Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill. When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations and their performance suffers if this nonsymbolic system is impaired. Nonsymbolic number representations also allow adults, children, and even infants to add or subtract pairs of dot arrays and to compare the resulting sum or difference to a third array, provided that only approximate accuracy is required. Here we report that young children, who have mastered verbal counting and are on the threshold of arithmetic instruction, can build on their nonsymbolic number system to perform symbolic addition and subtraction. Children across a broad socio-economic spectrum solved symbolic problems involving approximate addition or subtraction of large numbers, both in a laboratory test and in a school setting. Aspects of symbolic arithmetic therefore lie within the reach of children who have learned no algorithms for manipulating numerical symbols. Our findings help to delimit the sources of children’s difficulties learning symbolic arithmetic, and they suggest ways to enhance children’s engagement with formal mathematics

EAACI position paper on occupational rhinitis

The present document is the result of a consensus reached by a panel of experts from European and non-European countries on Occupational Rhinitis (OR), a disease of emerging relevance which has received little attention in comparison to occupational asthma. The document covers the main items of OR including epidemiology, diagnosis, management, socio-economic impact, preventive strategies and medicolegal issues. An operational definition and classification of OR tailored on that of occupational asthma, as well as a diagnostic algorithm based on steps allowing for different levels of diagnostic evidence are proposed. The needs for future research are pointed out. Key messages are issued for each item

A comprehensive overview of radioguided surgery using gamma detection probe technology

The concept of radioguided surgery, which was first developed some 60 years ago, involves the use of a radiation detection probe system for the intraoperative detection of radionuclides. The use of gamma detection probe technology in radioguided surgery has tremendously expanded and has evolved into what is now considered an established discipline within the practice of surgery, revolutionizing the surgical management of many malignancies, including breast cancer, melanoma, and colorectal cancer, as well as the surgical management of parathyroid disease. The impact of radioguided surgery on the surgical management of cancer patients includes providing vital and real-time information to the surgeon regarding the location and extent of disease, as well as regarding the assessment of surgical resection margins. Additionally, it has allowed the surgeon to minimize the surgical invasiveness of many diagnostic and therapeutic procedures, while still maintaining maximum benefit to the cancer patient. In the current review, we have attempted to comprehensively evaluate the history, technical aspects, and clinical applications of radioguided surgery using gamma detection probe technology

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. </p

International Consensus Statement on Rhinology and Allergy: Rhinosinusitis

Background: The 5 years since the publication of the first International Consensus Statement on Allergy and Rhinology: Rhinosinusitis (ICAR‐RS) has witnessed foundational progress in our understanding and treatment of rhinologic disease. These advances are reflected within the more than 40 new topics covered within the ICAR‐RS‐2021 as well as updates to the original 140 topics. This executive summary consolidates the evidence‐based findings of the document. Methods: ICAR‐RS presents over 180 topics in the forms of evidence‐based reviews with recommendations (EBRRs), evidence‐based reviews, and literature reviews. The highest grade structured recommendations of the EBRR sections are summarized in this executive summary. Results: ICAR‐RS‐2021 covers 22 topics regarding the medical management of RS, which are grade A/B and are presented in the executive summary. Additionally, 4 topics regarding the surgical management of RS are grade A/B and are presented in the executive summary. Finally, a comprehensive evidence‐based management algorithm is provided. Conclusion: This ICAR‐RS‐2021 executive summary provides a compilation of the evidence‐based recommendations for medical and surgical treatment of the most common forms of RS

The development of arithmetic concepts and skills: Constructing adaptive expertise

This volume focuses on two related questions that are central to both the psychology of mathematical thinking and learning and to the improvement of mathematics education: What is the nature of arithmetic expertise? How can instruction best promote it? Contributors from a variety of specialities, including cognitive, developmental, educational, and neurological psychology; mathematics education; and special education offer theoretical perspectives and much needed empirical evidence about these issues. As reported in this volume, both theory and research indicate that the nature of arithmetic expertise and how to best promote it are far more complex than conventional wisdom and many scholars, past and present, have suggested. The results of psychological, educational, and clinical studies using a wide range of arithmetic tasks and populations (including "normally" and atypically developing children, non-injured and brain-injured adults, and savants) all point to the same conclusion: The heart of arithmetic fluency, in general, and the flexible and creative use of strategies, in particular, is what is termed "adaptive expertise" (meaningful or conceptually based knowledge). The construction of adaptive expertise in mathematics is, for the first time, examined across various arithmetic topics and age groups. This book will be an invaluable resource for researchers and graduate students interested in mathematical cognition and learning (including mathematics educators, developmental and educational psychologists, and neuropsychologists), educators (including teachers, curriculum supervisors, and school administrators), and others interested in improving arithmetic instruction (including officials in national and local education departments, the media, and parents)