We propose a divisibility criterion for elements of a generic Unique Factorization Domain. As a consequence, we obtain a general divisibility criterion for polynomials over Unique Factorization Domains. The arguments can be used in basic algebra courses and are suitable for building classroom/homework activities for college and high school…

Recently a teacher friend enquired about the S-I-R equations for disease spread, and what follows was stimulated by that exchange. COVID-19 provides an opportunity to put mathematical flesh on verbal bones such as "self-isolation", "lockdown", "herd immunity", "flattening the curve", "closed…

Counting is fundamental to early mathematics. Most studies of teaching counting focus on teachers observing children count. The present study compares mathematical ideas that 12 PK, transitional kindergarten (TK), and kindergarten teachers noticed from observing their own students count during a classroom session of Counting Collections with ideas…

Four operations algorithm is among the major topics occupying a significant position in primary school schedule. Moreover, utilizing alternative strategies during the education process and improving operation flexibility of students also considered important in teaching of mathematics. Flexibility in computing is the ability of solving any…

Large amounts of missing data could distort item parameter estimation and lead to biased ability estimates in educational assessments. Therefore, missing responses should be handled properly before estimating any parameters. In this study, two Monte Carlo simulation studies were conducted to compare the performance of four methods in handling…

Many education systems have recognized the importance of computational thinking and coding skills and are implementing curricular changes to introduce coding into formal school education. A necessary and critical success factor involves the preparation of and support for teachers to teach coding. Thus, understanding the perceptions of teachers…

In the recent years, there has been a push to engage primary and secondary students in computer science to prepare them to live and work in a world influenced by computation. One of the efforts involves getting primary and secondary students to think computationally by introducing computational ideas such as, algorithms and abstraction. Majority…

This article communicates the results of a Danish survey study conducted in 2018 that aimed to examine initiatives relating to computational thinking in primary and lower-secondary schools, as well as the professional development of teachers and the perceptions of school principals in this area. The context is an increasing interest in this field,…

This study explored children's area estimation performance. Two groups of fourth grade children completed area estimation tasks with rectangles ranging from 5 to 200 square units. A randomly assigned treatment group completed instructional sessions that involved a conceptual area measurement strategy along with numerical feedback. Children tended…

The ancient Greek astronomers devised ingenious methods for measuring the size and distances of the Earth, Moon and Sun. The concepts were beautifully simple and although in most cases could only yield approximate results, they have the advantage that they can be understood by anyone with a basic mathematical background. The emergence of…

This paper describes analyses of the K-12 computational thinking (CT) integration activities collected at two NSF-funded workshops, "Developing an Interdisciplinary Framework for Integrating Computational Thinking in K-12 Science, Mathematics, Technology, and Engineering Education," held in August and November of 2017 at Education…

This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

Multidimensional Item Response Theory (MIRT) is widely used in assessment and evaluation of educational and psychological tests. It models the individual response patterns by specifying functional relationship between individuals' multiple latent traits and their responses to test items. One major challenge in parameter estimation in MIRT is that…

This dissertation is composed of a study of estimation methods in classical and test theories and the elaboration and application of a cluster-robust variance estimator. Variance estimators derived from generalized estimating equations are known to be robust to most covariance structures and are therefore well suited for psychometric analysis of…

Due to the nature of the teaching environment, students may often develop perceptions of their lecturers' ability as mathematicians, based on the pre-prepared and well-rehearsed content they present. In reality, performing mathematical calculations and solving problems is a difficult skill, and students may compare their own experiences…