Mastery of the counting principles in toddlers: A crucial step in the development of budding arithmetic abilities?

Counting abilities have been described as determinative precursors for a good development of later arithmetic abilities. Mastery of the stable order, the one–one-correspondence and the cardinality principles can be seen as essential features for the development of counting abilities. Mastery of the counting principles in kindergarten was assessed in a large group of children with a broad range of arithmetic abilities (N = 423). Not all children mastered the counting principles by the end of kindergarten. Mastery of the counting principles in kindergarten was predictive for arithmetic abilities one year later in first grade, especially for scores on arithmetic achievement tests. Children sharing a common educational background tend to have more similar scores on arithmetic tests, yet the importance of mastery of the essential counting principles in the prediction of later arithmetic achievement was the same for all classrooms.     

Preschoolers’ use of count information to judge relative quantity

We examined preschool children's use of count information in making quantity judgments. Study 1 involved 35 children 3–5 years old using a balance-scale task to judge relative quantity with or without count information provided. Study 2 replicated and extended the exploration as 54 children 3–4 years old judged relative quantity in multiple counting contexts. Children who were given count information successfully used count information in quantity evaluation when visual cues were not useful. Limited experience of counting skills, strategy choice, and limited processing capacity are each discussed as potential explanations. Implications for early childhood practice and teacher education, as well as directions for future research are explored.     

Subitizing or counting as possible screening variables for learning disabilities in mathematics education or learning?

This paper aims to highlight the significance of a particular aspect of magnitude processing, namely counting and subitizing or the rapid enumeration of small sets of items, for learning. Emphasis is laid on the historical roots and the conceptual framework as well as on studies on pre-verbal and school-age children. Evidence of the potential value of this research for the assessment of children at risk of mathematical learning disabilities, is presented. Inherent to its nature, subitizing relies on rapid, preverbal analogue magnitude comparisons being triggered. We will highlight the differences with counting, and the implications of shortcomings in counting and subitizing in children with mathematical learning disabilities for the automaticity of number magnitude processing. Furthermore we especially look in this paper at the varying assessment paradigms which are used in research with different age groups, something which has received insufficient attention in the past. Finally, we outline the challenges for future research on mathematical learning disabilities.     

Publication counting methods for a national research evaluation exercise

In this paper, we investigate the effects of using four methods of publication counting (complete, whole, fractional, square root fractional) and limiting the number of publications (at researcher and institution levels) on the results of a national research evaluation exercise across fields using Polish data. We use bibliographic information on 0.58 million publications from the 2013–2016 period. Our analysis reveals that the largest effects are in those fields within which a variety publication and cooperation patterns can be observed (e.g. in Physical sciences or History and archeology). We argue that selecting the publication counting method for national evaluation purposes needs to take into account the current situation in the given country in terms of the excellence of research outcomes, level of internal, external and international collaboration, and publication patterns in the various fields of sciences. Our findings show that the social sciences and humanities are not significantly influenced by the different publication counting methods and limiting the number of publications included in the evaluation, as publication patterns in these fields are quite different from those observed in the so-called hard sciences. When discussing the goals of any national research evaluation system, we should be aware that the ways of achieving these goals are closely related to the publication counting method, which can serve as incentives for certain publication practices.     

The influences of counting methods on university rankings based on paper count and citation count

In an age of intensifying scientific collaboration, the counting of papers by multiple authors has become an important methodological issue in scientometric based research evaluation. Especially, how counting methods influence institutional level research evaluation has not been studied in existing literatures. In this study, we selected the top 300 universities in physics in the 2011 HEEACT Ranking as our study subjects. We compared the university rankings generated from four different counting methods (i.e. whole counting, straight counting using first author, straight counting using corresponding author, and fractional counting) to show how paper counts and citation counts and the subsequent university ranks were affected by counting method selection. The counting was based on the 1988–2008 physics papers records indexed in ISI WoS. We also observed how paper and citation counts were inflated by whole counting. The results show that counting methods affected the universities in the middle range more than those in the upper or lower ranges. Citation counts were also more affected than paper counts. The correlation between the rankings generated from whole counting and those from the other methods were low or negative in the middle ranges. Based on the findings, this study concluded that straight counting and fractional counting were better choices for paper count and citation count in the institutional level research evaluation.     

An examination of the Counting Talk Test’s ability to discern individual variability in exercise-induced metabolic stress

The purpose of this study was to determine if the counting talk test can be used to discern whether an individual is exercising above or at/below maximal lactate steady state. Twenty-two participants completed VO₂peak and counting talk test incremental step tests followed by an endurance test at 65% of work rate at VO₂peak (WR_VO2peak). The change in relative count time during endurance exercise decreased in those exercising above maximal lactate steady state only (p < .01); however, this change was less than 1 second. Despite a significant correlation during the incremental step test, large changes in counting talk test performance and blood lactate concentration occurred at different points and there was considerable inter-individual variability in counting talk test performance at a given blood lactate concentration. These results suggest that the counting talk test cannot discern whether an individual is exercising above maximal lactate steady state and that it cannot be used to accurately prescribe intensities targeting specific blood lactate concentrations.     

第一和第三直曲段交界处弧线起跑线的计算原理和方法

依据《田径竞赛规则》中“应使运动员跑进的距离相等”的规定,本文为了实际应用中操作的精准和方便,对田径场第1和第3直曲段交界处弧线起跑线进行弦量法和放射量法的推导和计算,给出每1步骤的计算过程并计算出我国目前较广泛使用的半径为36m、36．5m、37m、37．898m半圆式田径场地的有关丈量数据。     

基于容斥原理计数公式的推广及应用

介绍容斥原理及计数公式,依据容斥原理提出20个计数公式并给出证明。并给出应用实例。     

The value and credits of n-authors publications

Collaboration among researchers is becoming increasingly common, which raises a large number of scientometrics questions for which there is not a clear and generally accepted answer. For instance, what value should be given to a two-author or three-author publication with respect to a single-author publication? This paper uses axiomatic analysis and proposes a practical method to compute the expected value of an n-authors publication that takes into consideration the added value induced by collaboration in contexts in which there is no prior or ex-ante information about the publication's potential merits or scientific impact. The only information required is the number of authors. We compared the obtained theoretical values with the empirical values based on a large dataset from the Web of Science database. We found that the theoretical values are very close to the empirical values for some disciplines, but not for all. This observation provides support in favor of the method proposed in this paper. We expect that our findings can help researchers and decision-makers to choose more effective and fair counting methods that take into account the benefits of collaboration.     

Strategic counting: A novel assessment of place-value understanding

Children's counting strategies reflect how much they understand the place-value structure of numbers. In Study 1, a novel task, namely the strategic counting task, elicited strategies from kindergarteners and first graders that showed a trend of increasing place-value knowledge – from perceiving number as an undivided entity to seeing it as a collection of independent groups of powers of ten. In Study 2, first-graders' strategic counting task scores at the end of fall semester were better predictors of year-end mathematical achievement than the traditional place-value tasks. In Study 3, a five-item subset of strategic counting was the best among 15 various cognitive predictors of end of second-grade mathematical achievement. Growth curve modeling revealed that low-mathematics achievers at the end of second grade had been lagging behind their peers in strategic counting since early first grade. Implications for early support for children with difficulties in place-value knowledge are discussed.