Most methods for fitting cognitive diagnosis models to educational test data and assigning examinees to proficiency classes require the Q-matrix that associates each item in a test with the cognitive skills (attributes) needed to answer it correctly. In most cases, the Q-matrix is not known but is constructed from the (fallible) judgments of…

Intrinsic disorder (ID) is defined as a lack of stable tertiary and/or secondary structure under physiological conditions in vitro. Intrinsically disordered proteins (IDPs) are highly abundant in nature. IDPs possess a number of crucial biological functions, being involved in regulation, recognition, signaling and control, e.g. their functional…

Cognitive Diagnostic Models (CDMs) aim to provide information about the degree to which individuals have mastered specific attributes that underlie the success of these individuals on test items. The Q-matrix is a key element in the application of CDMs, because contains links item-attributes representing the cognitive structure proposed for solve…

This article outlines a problem-centered approach to the topic of canonical matrix forms in a second linear algebra course. In this approach, abstract theory, including such topics as eigenvalues, generalized eigenspaces, invariant subspaces, independent subspaces, nilpotency, and cyclic spaces, is developed in response to the patterns discovered…

Based on the original source document for the Common Core State Standards and tested by 1,000 educators in diverse classrooms across the country, these research-based tools will help readers examine their current practices and adapt existing curriculum. Each of the 40 tools is clearly presented, explained, and exemplified, guiding educators…

Transnational education seeks equivalence in standards and/or relevance of outcomes through the transfer of Western theories, concepts and methods. Utilising a critique-interpretative approach, Jing Qi argues that equivalence/relevance-oriented approaches to transnational education assume the legitimacy of the global knowledge hierarchy.…

Diagnostic classification models (DCMs) are structured latent class models widely discussed in the field of psychometrics. They model subjects' underlying attribute patterns and classify subjects into unobservable groups based on their mastery of attributes required to answer the items correctly. The effective implementation of DCMs depends…

Two-mode binary data matrices arise in a variety of social network contexts, such as the attendance or non-attendance of individuals at events, the participation or lack of participation of groups in projects, and the votes of judges on cases. A popular method for analyzing such data is two-mode blockmodeling based on structural equivalence, where…

Matrices can be diagonalized by singular vectors or, when they are symmetric, by eigenvectors. Pairs of square matrices often admit simultaneous diagonalization, and always admit block wise simultaneous diagonalization. Generalizing these possibilities to more than two (non-square) matrices leads to methods of simplifying three-way arrays by…

An involutory matrix is a matrix that is its own inverse. Such matrices are of great importance in matrix theory and algebraic cryptography. In this note, we extend this involution to rhotrices and present their properties. We have also provided a method of constructing involutory rhotrices.

Martin Gardner wrote about a coin-flipping trick, performed by a blindfolded magician. The paper analyses this trick, and compares it with a similar trick using three cups flipped in pairs. Several different methods of analysis are discussed, including a graphical analysis of the state space and a representation in terms of a matrix. These methods…

The central goals of most introductory linear algebra courses are to develop students' proficiency with matrix techniques, to promote their understanding of key concepts, and to increase their ability to make connections between concepts. In this article, we present an innovative method using adjacency matrices to analyze students' interpretation…

Engineering curricula should be dynamic with a goal of constant improvement and refinement. Unfortunately, this is often not the case; courses are developed, altered, and expanded in a piecemeal manner. Namely, as time progresses many programmes end up with courses that are developed and not a developed curriculum. To remedy this shortcoming…

The idea that multiple measures should be used when evaluating teachers is widely accepted. Multiple measures are important not only because education has multiple goals, but because each measure is an imperfect indicator of any given goal. For a variety of reasons, states and districts use multiple measures in one particular way: to make…

Exploratory factor analysis involves five key decisions. The second decision, how many factors to retain, is the focus of the current paper. Extracting too many or too few factors often leads to devastating effects on study results. The advantages and disadvantages of the most effective and/or most utilized strategies to determine the number of…