Young children with limited knowledge of formal mathematics can intuitively perform basic arithmetic-like operations over nonsymbolic, approximate representations of quantity. However, the algorithmic rules that guide such nonsymbolic operations are not entirely clear. We asked whether nonsymbolic arithmetic operations have a function-like…

In the literature on numerical cognition, the presence of the capacity to distinguish between numerosities by attending to the number of items, rather than continuous properties of stimuli that correlate with it, is commonly taken as sufficient indication of numerical abilities in cognitive agents. However, this literature does not take into…

Computational thinking (CT) is a new literacy of 21st century that can be transferred to and applied in different real-world situations, although being derived from the discipline of computer science. Tangible robots or child-friendly digital apps are used to implement coding education with the goal of promoting young children's CT. However, there…

Traditional estimators of reliability such as coefficients alpha, theta, omega, and rho (maximal reliability) are prone to give radical underestimates of reliability for the tests common when testing educational achievement. These tests are often structured by widely deviating item difficulties. This is a typical pattern where the traditional…

Random item effects item response theory (IRT) models, which treat both person and item effects as random, have received much attention for more than a decade. The random item effects approach has several advantages in many practical settings. The present study introduced an explanatory multidimensional random item effects rating scale model. The…

In this article we find the thermodynamics of some large N particles systems and some small N particles classical systems using micro canonical ensemble. Small N particle systems are seldom done in textbooks, since statistical mechanics(SM) systems work for large N systems. We show that small N systems will help the students to get an insight…

The recognition that the development of Computational Thinking (CT) has been achieved in the educational systems of different countries implies, in some cases, the challenge of integrating its development into mathematics lessons. Although various proposals address the development of CT in the early years of schooling, educational robotics emerges…

Throughout a programming course, students develop various source code tasks. Using these tasks to track students' progress can provide clues to the strengths and weaknesses found in each learning topic. This practice allows the teacher to intervene in learning in the first few weeks of class and maximize student gains. However, the biggest…

Computational Thinking (CT) is considered a core 21st century digital skill. The aspect of assessment is crucial and knowing what, who, when, how, and where to assess is important for assessment design. In this study, we conducted an umbrella review to gain insights regarding CT assessment in higher education. In total, we analyzed 11 reviews,…

Computational thinking (CT) is vital for success in numerous domains. However, the nature, definition, and scope of CT are ill-defined, and research on how best to develop CT is very limited. This study focused on how thinking styles and STEM attitudes have effects on computational thinking. Using a proportionate stratified random sampling…

A readily and widely applicable procedure is discussed that can be used to point and interval estimate the probabilities of particular responses on polytomous items at pre-specified points along underlying latent continua. The items are assumed thereby to be part of unidimensional multi-component measuring instruments that may contain also binary…

Bell's theorem is a topic of perennial fascination. Publishers and the general public have a steady appetite for approachable books about its implications. The scholarly literature includes many analogies to Bell's theorem and simple derivations of Bell inequalities, and some of these simplified discussions are the basis of interactive web pages.…

Over the past decade, statisticians have developed methods to improve generalizations from nonrandom samples using propensity score methods. While these methods contribute to generalization research, their effectiveness is limited by small sample sizes. Small area estimation is a class of model-based methods that address the imprecision due to…

This study offers an approach to testing for differential item functioning (DIF) in a recently developed measurement framework, referred to as "D"-scoring method (DSM). Under the proposed approach, called "P-Z" method of testing for DIF, the item response functions of two groups (reference and focal) are compared by…

To present time-varying evidence, cumulative meta-analysis (CMA) updates results of previous meta-analyses to incorporate new study results. We investigate the properties of CMA, suggest possible improvements and provide the first in-depth simulation study of the use of CMA and CUSUM methods for detection of temporal trends in random-effects…