In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a…

The concept of determinant plays a central role in many linear algebra concepts and is also applied to other branches of mathematics and science. In this study, we focus on the application of determinant and inverse matrix concepts, in solving systems of equations by a group of 116 in-service mathematics teachers who were studying the topic at a…

Categorical data become increasingly ubiquitous in the modern big data era. In this dissertation, we propose novel statistical learning and inference methods for large-scale categorical data, focusing on latent variable models and their applications to psychometrics. In psychometric assessments, the subjects' underlying aptitude often cannot be…

Almost all finite groups encountered by undergraduates can be represented as multiplicative groups of concise block-diagonal binary matrices. Such representations provide simple examples for beginning a group theory course. More importantly, these representations provide concrete models for "abstract" concepts. We describe Maple lab…

As educators and school leaders work towards building students' capacity throughout a student's academic career, the goal is to facilitate opportunities for students to develop college and career readiness skills that can be applied to novel and challenging problems long after high school graduation. Hess' Cognitive Rigor Matrix (HCRM) is a tool…

Contemporary science education themes are marked by the inevitable uncertainty of consequences emerging from human actions. They encompass disasters, pandemics and other events that have been marking our present times. Understanding new risks as the ones resulting from human action, even when proposing a solution for an issue, is one of the…

Meta-reasoning refers to processes by which people monitor problem-solving activities and regulate effort investment. Solving is hypothesized to begin with an initial Judgment of Solvability (iJOS)--the solver's first impression as to whether the problem is solvable--which guides solving attempts. Meta-reasoning research has largely neglected…

This study examined the effects of: (1) schema-enriched communication; and (2) computer-based messaging on the sharing of knowledge and problem solving in teams with deaf or hard of hearing (DHH) and typical hearing (TH) postsecondary students. Four-member teams comprising either all DHH, all TH, or two DHH and two TH postsecondary students solved…

Efficient visualizations of computational algorithms are important tools for students, educators, and researchers. In this article, we point out an innovative visualization technique for matrix multiplication. This method differs from the standard, formal approach by using block matrices to make computations more visual. We find this method a…

Exploratory cognitive diagnosis models (CDMs) estimate the Q matrix, which is a binary matrix that indicates the attributes needed for affirmative responses to each item. Estimation of Q is an important next step for improving classifications and broadening application of CDMs. Prior research primarily focused on an exploratory version of the…

To address the societal challenges of global solidarity and sustainable societies there is clearly a need for human rights education (HRE). The question arises as to which school subject is capable of contributing to HRE in which way -- and how different disciplines may ideally collaborate. The situation is particularly challenging for religious…

In most contexts of student skills assessment, whether the test material is administered by the teacher or within a learning environment, there is a strong incentive to minimize the number of questions or exercises administered in order to get an accurate assessment. This minimization objective can be framed as a Q-matrix design problem: given a…

Solving systems of linear equations is of central importance in linear algebra and many related applications, yet there is limited literature examining the symbolizing processes students use as they work to solve systems of linear equations. In this paper, we examine this issue by analyzing final exam data from 68 students in an introductory…

Operations and Supply Chain Management (OSCM) courses may cover supply chain strategies, supply chain classification, and supply chain performance. Familiarity with various manufacturing and logistics firms would help students to better understand such topics. Information on the Dow Jones Industrial Average indexed firms and top 50 supply chain…

Our goal in this article is to organise an epistemological matrix for the concept of rational number that contemplates its different meanings. Aiming at understanding the various ways to signify the rational numbers and based on the theoretical-methodological approach of conceptual profiles, we produce and analyse data from various sources,…