In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

A method is presented which can be used to obtain analytical solutions for boundary value problems (BVPs) using the matrix exponential and Maple. Systems of second order, linear differential equations are expressed as two or more first order equations in matrix form, and their solutions are obtained using the matrix exponential, matrix…

Establishing positive classroom expectations, or norms, that reflect the shared values of a classroom community (i.e., educators, students, families) is an important step toward creating a positive teaching and learning environment. This brief provides guidance for creating and using a classroom teaching matrix to explicitly identify, define, and…

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…

Purpose: Lesson study (LS) is a collaborative form of action research. Collaboration is central to LS methodology, therefore exploring and expanding the understanding of the collaborative features that occur in LS is a priority. This paper explores the features of collaboration in existing publications on LS to consider if, as Quaresma (2020)…

Research has shown that training diagonal targets in a matrix may result in correct responses to the nondiagonal targets within the same matrix and novel targets from a separate matrix. This study replicated prior research using matrix training to teach tact noun-verb combinations to 3 male participants with autism who use a speech generating…

Preschoolers' earliest productions of sentential complement sentences have matrix clauses that are limited in form. Diessel proposed that matrix clauses in these early productions are propositionally empty fixed phrases that lack semantic and syntactic integration with the clausal complement. By 4 years of age, however, preschoolers produce…

As the field evolves over time, shifting from Industrial Arts, to Technology Education, to Engineering and Technology Education (ETE), so too does what teachers teach, how they teach, and the projects that they use. Projects that worked 10 years ago might not hold up today and, as reflective practitioners, they need to be able to align the current…

Children with autism spectrum disorder often lack fundamental play skills, which can aid development with social, language, and imitation skills (Boutot et al. 2005). The purpose of this study was to extend the previous literature that successfully combined video modeling and matrix training. Matrix training is an efficient way of teaching that…

The Culture of Assessment Matrix is a one-page rubric intended to provide institutions of higher education with a simplistic way to quickly gauge the status of their institution's assessment culture and the degree to which the culture is an integral part of the institution's operations, expectations, methods of accountability, and reward systems.…

All cognitive diagnostic models that evaluate educational test data require a Q-matrix that combines every item in a test with the required cognitive skills for each item to be answered correctly. Generally, the Q-matrix is constructed by education experts' judgment, leading to some uncertainty in its elements. Various statistical methods are…

Cognitive diagnostic models (CDMs) have received sustained attention in educational settings because they can be used to operationalize formative assessment to provide diagnostic feedback and inform instruction. A large number of CDMs have been developed over the past few years. An important component of all CDMs is a Q-matrix that specifies a…

People with autism show identifiable impediments in three central aspects, namely communication, social interaction, and repetitive and restrictive behavior, which is called the triad of impairments. The communication observation of children with autism is relatively complex, so a specific procedure to identify their communication is required. A…

This research paper presents a digital game-based learning as an innovative methodology that takes full advantage of the educational potential offered by digital games to aid learning of concepts. It focuses on the use of games as a mode of learning in the classroom while exploring all learning theories that supports it. This mode of learning is…

State and territory child care and early education (CCEE) leaders typically support a range of professional development (PD) opportunities for CCEE providers. This highlight presents the "Professional Development Matrix for Quality Improvement" created by Douglass, Tout, and Doyle. The matrix provides a framework for organizing and…