In application-oriented mathematics, particularly in the context of nonlinear system analysis, phase plane analysis through SageMath offers a visual display of the qualitative behaviour of solutions to differential equations without inundating students with cumbersome calculations of the plane-phase. A variety of examples is usually given to…

The purpose of the present article is to investigate the definition of matrix multiplication as a central issue in linear algebra courses. Applying both historical and pedagogical approaches, it focuses on the philosophy of generating the usual matrix multiplication, as a special binary operation, with its partly unexpected form compared with the…

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…

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…

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,…

The purpose of this article is to describe the analytic process of a method of data collection known as Q Methodology. This method is an alternative method in collecting data especially suited to research on "points of views" (Coogan & Herrington, 2011, p. 24). The analytic process of Q methodology involves factor analysis, a…

The measurement error in principal components extracted from a set of fallible measures is discussed and evaluated. It is shown that as long as one or more measures in a given set of observed variables contains error of measurement, so also does any principal component obtained from the set. The error variance in any principal component is shown…

Structural equation models play an important role in the social sciences. Consequently, there is an increasing use of meta-analytic methods to combine evidence from studies that estimate the parameters of structural equation models. Two approaches are used to combine evidence from structural equation models: A direct approach that combines…

There is significant controversy over what counts as evidence in the evaluation of social interventions. It is increasingly common to use methodological criteria to rank evidence types in a hierarchy, with Randomised Controlled Trials (RCTs) at or near the highest level. Because of numerous challenges to a hierarchical approach, this article…

The objective of this work is to present a spreadsheet tool that illustrates an ideal case of dynamic matrix control (DMC) calculations. The ideal case presented in this work is a hypothetical single- input-single-output DMC control system for setpoint tracking, in the absence of disturbance and mismatch between the measured and predicted process…

A 2 × 2 matrix identifying four discrete thought processes was presented. The contributions of the first three processes in developing the knowledge base of public administration were detailed as were their limitations. It was argued that the fourth process--insight and its mental powers--builds upon the strengths and overcomes the limitations…

For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

Borrowing from marital research literature, a four-square matrix constructed from the twin dimensions of effort and comfort levels is used to describe a typology of campus and community associations. Results from a study using the Optimal College Town Assessment to measure community member perceptions on town-gown relationships are presented next,…

Lloyd Bond comments here on the Focus article in this issue of "Measurement: Interdisciplinary Research and Perspectives". The Focus article is entitled: "How Task Features Impact Evidence from Assessments Embedded in Simulations and Games" (Russell G. Almond, Yoon Jeon Kim, Gertrudes Velasquez, and Valerie J. Shute). Bond…

Emerging technologies offer an opportunity for the development, at the institutional level, of quality processes with greater capacity to enhance learning in higher education than available through current quality processes. These systems offer the potential to extend use of learning analytics in institutional-level quality processes in addition…