Because error variance alternatively can be considered to be the sum of systematic variance associated with unknown variables and randomness, a tripartite assumption is proposed that total variance in the dependent variable can be partitioned into three variance components. These are variance in the dependent variable that is explained by the…

Previous research includes frequent admonitions regarding the importance of establishing connectivity in data collection designs prior to the application of Rasch models. However, details regarding the influence of characteristics of the linking sets used to establish connections among facets, such as locations on the latent variable, model-data…

Diagnostic classification models (DCMs, also known as cognitive diagnosis models) hold the promise of providing detailed classroom information about the skills a student has or has not mastered. Specifically, DCMs are special cases of constrained latent class models where classes are defined based on mastery/nonmastery of a set of attributes (or…

In this paper we report on a survey designed to test whether or not students differentiated between two different types of problems involving combinations--problems in which combinations are used to count unordered sets of distinct objects (a natural, common way to use combinations), and problems in which combinations are used to count ordered…

This research aimed to compare the G and Phi coefficients estimated in Decision studies in Generalizability theory and obtained in actual cases for the same conditions of similar facets by using crossed design. The research was conducted as pure research on 120 individuals (students), six items and 12 raters. An achievement test composed of six…

Surface modification has been considered as a fundamental item in upper-division undergraduate and master courses. Thus, the development of experiments regarding processes and characterization of surface-modification phenomena is highly desired. In this article, we propose an electrochemical and computational study of widely used…

Coding and computational thinking have recently become compulsory skills in many school systems globally. Teaching these new skills presents a challenge for many teachers. A notable example of professional development designed using Constructionist principles to address this challenge is "ScratchEd". Upon reflecting on her experiences…

The European Commission Science Hub has been promoting Computational Thinking (CT) as an important 21st century skill or competence. However, „despite the high interest in developing computational thinking among schoolchildren and the large public and private investment in CT initiatives, there are a number of issues and challenges for the…

Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data…

The long-standing debate into the potential benefit of developing mathematical thinking skills through learning to program has been reignited with the widespread introduction of programming in schools across many countries, including England where it is a statutory requirement for all pupils to be taught programming from 5 years old. Algorithm is…

Researchers are often interested in whether the effects of an intervention differ conditional on individual- or group-moderator variables such as children's characteristics (e.g., gender), teacher's background (e.g., years of teaching), and school's characteristics (e.g., urbanity); that is, the researchers seek to examine for whom and under what…

Exploratory structural equation modeling (ESEM) is an approach for analysis of latent variables using exploratory factor analysis to evaluate the measurement model. This study compared ESEM with two dominant approaches for multiple regression with latent variables, structural equation modeling (SEM) and manifest regression analysis (MRA). Main…

Children see and describe patterns in the primary grades when they develop the meaning of numbers by composing and decomposing. During their early years, they use patterns to learn properties of operations (Common Core Standards Writing Team 2011). While describing the intent of the third-grade standards for multiplication, the CCSS writers…

Connecting theory and practice in teaching is sometimes difficult, as it requires expensive or delicate equipment, thus limiting the teacher to giving demonstrations in which students are passive participants. Numerical mathematics, as an applied discipline, should be taught on real world examples. By using inexpensive Arduino hardware, we can…

In this study we investigated the development of 245 kindergarteners' mathematics problem solving (MPS) at two time points within 7 months using a cognitive diagnostic test, which measured three cognitive components (mathematical knowledge and skills, semantic understanding, and quantitative reasoning) with eleven cognitive attributes. The effects…