Bayesian methods to infer model dimensionality in factor analysis generally assume a lower triangular structure for the factor loadings matrix. Consequently, the ordering of the outcomes influences the results. Therefore, we propose a method to infer model dimensionality without imposing any prior restriction on the loadings matrix. Our approach…

This article describes the author's experience designing and implementing an inquiry-based learning (IBL) pedagogical approach to an upper-division undergraduate cryptology course. The author shares the course goals and how the IBL style supports their achievement. The article concludes with sample activities -- in-class exercises that touch on…

Impaired numerosity perception in developmental dyscalculia (low "number acuity") has been interpreted as evidence of reduced representational precision in the neurocognitive system supporting non-symbolic number sense. However, recent studies suggest that poor numerosity judgments might stem from stronger interference from non-numerical…

Over the last decades, a multitude of results in educational and psychological research have shown that the implementation of multiple external representations (MERs) in educational contexts represents a valuable tool for fostering learning and problem-solving skills. The context of science, technology, engineering, and mathematics (STEM)…

In Mathematics Education (ME), research dealing with topic-specific (TS) issues (e.g., what levels of development exist in learning fractions) produces usually local results and is considered less fashionable and attractive for innovative research projects than research dealing with context-specific (CS) issues that have more general and abstract…

This article features a fifth grade mathematics exploration planned to facilitate students' productive struggle. The exploration was a catalyst for a team of educators to unpack the teacher's experience when facilitating students' productive struggle. The team called this "teacher productive struggle" and shares about the construct…

Mathematical competence in school-related contexts is a multidimensional construct that encompasses several content areas and cognitive components. Kindergarten children have experiences with different types of mathematical content. However, empirical research has focused mostly on children's numerical skills, and less is known about their…

In this essay, I examine coloniality as a racializing force within international education curricula. I focus on the British-developed Cambridge Assessment International Education (CAIE) curriculum, previously known as the Cambridge International Education (CIE) curriculum. Using the CAIE as a specific case, I discuss how international curricula…

In this conceptual paper, the author argues that equity research in mathematics education is a genre that operates according to certain implicit ideological and rhetorical rules and assumptions--or discursive formations--that form how one can think about equity and inequity. One such rule that forms the basis of this paper is the axiom of…

Retention of secondary math teachers is a critical issue in the field of K-12 education. This dissertation investigates the internal influences, external influences, and motivators that retain secondary math teachers in the classroom. This study is framed around Bronfenbrenner's Socieoecological Framework, which guided the research questions and…

Research has shown that multiple-indicator multiple-cause (MIMIC) models can result in inflated Type I error rates in detecting differential item functioning (DIF) when the assumption of equal latent variance is violated. This study explains how the violation of the equal variance assumption adversely impacts the detection of nonuniform DIF and…

QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively…

The introduction of statistical concepts into school curricula in Australia and New Zealand in the early 1990s initiated an ongoing research program into the learning and teaching of statistics and probability in both countries. This paper reviews the contribution of Australian and New Zealand researchers to building statistical literacy at…

Research has shown the importance of helping students, especially those with mild-to-moderate learning disabilities, to offload information during problem-solving. When students can get their thoughts onto paper, number line strategies can help them develop a firm foundation in mathematical problem-solving while understanding the relationships…

The development of young children's counting has been extensively researched, yet detailed studies that examine development over multiple years are curiously absent from the literature. This research examined 15 preschoolers' (ages 3-4) use of number words as they engaged in two counting tasks, an oral counting task and counting a collection of 31…