Model and classification of database replication techniques

Construction of a universal mathematic-logical model of replication processes in data bases is considered. The fundamental definitions of notions for different types of replication are given. The classification of replication techniques is proposed and the respective efficiency criteria are determined. The variants of realization for system architecture, locking strategy, servers interaction, transaction termination, database platforms, correctness criteria of transaction terminator are discussed.Розглянуто побудову універсальної математико-логічної моделі процесів реплікації у базах даних. Наведено фундаментальні визначення понять для різних видів реплікації. Запропоновано класифікацію схем реплікації та визначено відповідні критерії ефективності. Обговорено варіанти реалізації системної архітектури, стратегії блокіровок, взаємодії серверів, завершення транзакцій, платформ баз даних, критерії коректності завершення транзакцій.Рассмотрено построение универсальной математико-логической модели процессов репликации в базах данных. Приведены фундаментальные определения понятий для разных видов репликации. Предложена классификация схем репликации и определены соответствующие критерии эффективности. Обсуждены варианты реализации системной архитектуры, стратегии блокировок, взаимодействия серверов, завершения транзакций, платформ баз данных, критерии корректности завершения транзакций

Inhibition, friend or foe? Cognitive inhibition as a moderator between mathematical ability and mathematical creativity in primary school students

It is still unclear which cognitive factors stand at the base of mathematical creativity. One factor could be inhibition, but results are inconsistent. A possible explanation is that this relation is more complex than the direct relations tested, until now. In the current study, the hypothesis was tested that cognitive inhibition moderated the relationship between mathematical ability and mathematical creativity. The sample included 82 primary school students between 8 and 12 years of age. Mathematical creativity was measured with a multiple solution task and scored on fluency, flexibility, and originality. While there was a direct relation between mathematical ability and mathematical creativity, inhibition did not have a direct effect on mathematical creativity, but it positively moderated this relationship for flexibility and originality. These results indicate that reduced inhibition strengthens the relationship between mathematical ability and mathematical flexibility and between mathematical ability and mathematical originality, but not the relation between mathematical ability and mathematical fluency. These findings are discussed in relation to children with high and low mathematical abilities, measurement of inhibition, and the domain-general/domain-specific discussion of creativity

Counting and number line trainings in kindergarten: Effects on arithmetic performance and number sense

Contains fulltext : 192025.pdf (publisher's version ) (Open Access)Children's early numerical capacities form the building blocks for later arithmetic proficiency. Linear number placements and counting skills are indicative of mapping, as an important precursor to arithmetic skills, and have been suggested to be of vital importance to arithmetic development. The current study investigated whether fostering mapping skills is more efficient through a counting or a number line training programme. Effects of both programmes were compared through a quasi-experimental design, and moderation effects of age and SES were investigated. Ninety kindergartners were divided into three conditions: a counting, a number line, and a control condition. Pretests and posttests included an arithmetic (addition) task and a battery of number sense tasks (comparison, number lines and counting). Results showed significantly greater gains in arithmetic, counting, and symbolic number lines in the counting training group than in the control group. The number line training group did not make significantly greater gains than the control group. Training gains were moderated by age, but not SES. We concluded that counting training improved numerical capacities effectively, whereas no such improvements could be found for the number line training. This suggests that only a counting approach is effective for fostering number sense and early arithmetic skills in kindergarten. Future research should elaborate on the parameters of training programmes and the consequences of variation in these parameters.11 p

Working memory and early mathematics: Possibilities for early identification of mathematics learning disabilities

Item does not contain fulltextAt the beginning of children's school careers, large differences already exist between children in their mathematical skills and knowledge. Preparatory math skills such as counting and Piagetian operations are important predictors of later math learning disabilities. However, little research has been conducted on the underlying processes that could explain or predict these preparatory math skills. Traditionally, intelligence has been viewed, next to language (vocabulary), as an important predictor of school success in general and math performance in specific. However, recent studies suggest that other, more fluid, domain-general cognitive processes, such as working memory and executive functions, are better predictors than traditional IQ scores. This chapter reports on two studies in which the relations between early mathematics and different working memory components are investigated. In the first study, the relations between the Early Numeracy Test (ENT) and five working memory aspects have been studied in a correlational study with 240 kindergartners. The following working memory components can be distinguished: the central executive controlling system, the phonological component, and the visuospatial component. In this study, three distinctive executive functions were measured: inhibition, shifting, and planning. The results show that phonological working memory, shifting, and planning are highly related to children's early math competence. Together, these functions can explain 50% of the total variance in early math. In a second study under 111 kindergartners, it was found that the scores on the ENT are moderately related to the executive function planning. Contrary to the expectations, intelligence was more related to preparatory math skills than planning. However, in a short training study with 15 low performing children, it was found that children's planning scores could better predict their improvement than intelligence: children low in planning did not profit as much from the training as children with higher planning capacities. The results of these studies emphasize the need for further research on the relations between working memory processes and preparatory math skills. These processes seem to play an important role in the origin of math learning difficulties. The results of the second study also suggest that remediation of early math learning difficulties should be adapted according to children's cognitive profiles regarding working memory and executive functions

Readiness-based differentiation in primary school mathematics: Expert recommendations and teacher self-assessment

Contains fulltext : 178260.pdf (publisher's version ) (Open Access)The diversity of students' achievement levels within classrooms has made it essential for teachers to adapt their lessons to the varying educational needs of their students ('differentiation'). However, the term differentiation has been interpreted in diverse ways and there is a need to specify what effective differentiation entails. Previous reports of low to moderate application of differentiation underscore the importance of practical guidelines for implementing differentiation. In two studies, we investigated how teachers should differentiate according to experts, as well as the degree to which teachers already apply the recommended strategies. Study 1 employed the Delphi technique and focus group discussions to achieve consensus among eleven mathematics experts regarding a feasible model for differentiation in primary mathematics. The experts agreed on a five-step cycle of differentiation: (1) identification of educational needs, (2) differentiated goals, (3) differentiated instruction, (4) differentiated practice, and (5) evaluation of progress and process. For each step, strategies were specified. In Study 2, the Differentiation Self-Assessment Questionnaire (DSAQ) was developed to investigate how teachers self-assess their use of the strategies recommended by the experts. While teachers (N = 268) were moderately positive about their application of the strategies overall, we also identified areas of relatively low usage (including differentiation for high-achieving students) which require attention in teacher professional development. Together, these two studies provide a model and strategies for differentiation in primary mathematics based on expert consensus, the DSAQ which can be employed in future studies, and insights into teachers' self-assessed application of specific aspects of differentiation.27 p

Number sense in kindergarten children: Factor structure and working memory predictors

Contains fulltext : 178272.pdf (publisher's version ) (Closed access)In the current study, the factor structure of number sense, or the ability to understand, use, and manipulate numbers, was investigated. Previous analyses yielded little consensus concerning number sense factors, other than a distinction between nonsymbolic and symbolic processing. Furthermore, associations between number sense factors and working memory components were investigated to gain insight into working memory involvement in number sense. A total of 441 Dutch kindergartners took part in the study. The factor structure of number sense and associations with working memory were tested using structural equation modelling. Results indicated that there was a distinction between nonsymbolic and symbolic number processing. Nonsymbolic processing was predicted by central executive performance, and symbolic processing was predicted by both central executive and visuospatial sketchpad performance. This implies that symbolic and nonsymbolic processing are distinguishable at this age, and that working memory involvement in symbolic processing is different from that in nonsymbolic processing.7 p

Readiness-based differentiation in primary school mathematics: Expert recommendations and teacher self-assessment

The diversity of students’ achievement levels within classrooms has made it essential for teachers to adapt their lessons to the varying educational needs of their students (‘differentiation’). However, the term differentiation has been interpreted in diverse ways and there is a need to specify what effective differentiation entails. Previous reports of low to moderate application of differentiation underscore the importance of practical guidelines for implementing differentiation. In two studies, we investigated how teachers should differentiate according to experts, as well as the degree to which teachers already apply the recommended strategies. Study 1 employed the Delphi technique and focus group discussions to achieve consensus among eleven mathematics experts regarding a feasible model for differentiation in primary mathematics. The experts agreed on a five-step cycle of differentiation: (1) identification of educational needs, (2) differentiated goals, (3) differentiated instruction, (4) differentiated practice, and (5) evaluation of progress and process. For each step, strategies were specified. In Study 2, the Differentiation Self-Assessment Questionnaire (DSAQ) was developed to investigate how teachers self-assess their use of the strategies recommended by the experts. While teachers (N = 268) were moderately positive about their application of the strategies overall, we also identified areas of relatively low usage (including differentiation for high-achieving students) which require attention in teacher professional development. Together, these two studies provide a model and strategies for differentiation in primary mathematics based on expert consensus, the DSAQ which can be employed in future studies, and insights into teachers’ self-assessed application of specific aspects of differentiation

Executive functions as predictors of math learning disabilities

In the past years, an increasing number of studies have investigated executive functions as predictors of individual differences in mathematical abilities. The present longitudinal study was designed to investigate whether the executive functions shifting, inhibition, and working memory differ between low achieving and typically achieving children and whether these executive functions can be seen as precursors to math learning disabilities in children. Furthermore, the predictive value of working memory ability compared to preparatory mathematical abilities was examined. Two classifications were made based on (persistent) mathematical ability in first and second grade. Repeated measures analyses and discriminant analyses were used to investigate which functions predicted group membership best. Group differences in performance were found on one inhibition and three working memory tasks. The working memory tasks predicted math learning disabilities, even over and above the predictive value of preparatory mathematical abilities