Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are…

Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are…

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…

Stoichiometry calculation competence tends to be particularly poor in the developing world, even among teachers. Various methods, including the unit factor method, have the potential to be effective in developing such competence. To evaluate the likelihood of such a generic proportion method, which downplays traditional formula usage, succeeding…

An onto-semiotic analysis of the mathematical connections established by one in-service mathematics teachers and university students when solving a problem about launching a projectile using the derivative was carried out. Theoretically, this research was based on the articulation between the Extended Theory of Mathematical Connections and the…

We propose a generalization of the classical Remainder Theorem for polynomials over commutative coefficient rings that allows calculating the remainder without using the long division method. As a consequence we obtain an extension of the classical Factor Theorem that provides a general divisibility criterion for polynomials. The arguments can be…

A good formula is like a good story, rich in description, powerful in communication, and eye-opening to readers. The formula presented in this article for determining the coefficients of the binomial expansion of (x + y)n is one such "good read." The beauty of this formula is in its simplicity--both describing a quantitative situation…

This study investigated 11 pre-service middle school teachers' solution strategies for exploring their knowledge of fraction division interpretations. Each participant solved six fraction division problems. The problems were organized into two sets: symbolic problems (involving numbers only) and contextual problems (involving measurement…

Measurement in geometry is one of the key areas of school mathematics, however, pupils make serious mistakes when solving problems involving measurement and hold misconceptions. This article focuses on the possible links between lower secondary pupils' (n = 870) success in solving non-measurement tasks and calculations tasks on area and volume and…

This article presents a case study that examines the level of integration of mathematical knowledge in physics problem solving among first grade students of upper secondary school. We explore the ways in which two specific students utilize their knowledge and we attempt to identify the epistemological framings they refer to while solving a physics…

Formulas, problem types, keywords, and tricky techniques can certainly be valuable tools for successful counters. However, they can easily become substitutes for critical thinking about counting problems and for deep consideration of the set of outcomes. Formulas and techniques should serve as tools for students as they think critically about…

Early in their chemistry education, students learn to do empirical formula calculations by rote without an understanding of the historical context behind them or the reason why their calculations work. In these activities, students use paperclip "atoms", construct a series of simple compounds representing real molecules, and discover,…

In this article, the authors begin by considering symbolic literacy in mathematics. Next, they examine the origins of misuse of the equals sign by primary and junior secondary students, where "=" has taken on an operational meaning. They explain that in algebra, students need both the operational and relational meanings of the equals…

The 43rd meeting of Canadian Mathematics Education Study Group (CMESG) was held at St. Francis Xavier University in Antigonish, Nova Scotia (May 31-June 4, 2019). This meeting marked only the third time CMESG/GCEDM (Groupe Canadien d'Étude en Didactique des Mathématiques) had been held in Nova Scotia (1996, 2003), and the first time it had been…