Many studies provide insights into students' conceptions of various linear algebra topics and difficulties they face with multiple modes of thinking needed for conceptualization. While it is important to understand students' initial conceptions, students' transfer of learning of these conceptions to subsequent courses can provide additional…

Model analysis provides a mechanism for representing student learning as measured by standard multiple-choice surveys. The model plot contains information regarding both how likely students in a particular class are to choose the correct answer and how likely they are to choose an answer consistent with a well-documented conceptual model.…

Experiencing and experimenting how to teach a foreign language in methodology courses in the undergraduate programs of ELT departments is a complex and confusing task at microteaching level. Trainees utilize their instructional capacity using the collection of techniques they compile for the simulation of this sort. Such a construction and…

The gold standard for identifying more effective pedagogical approaches is to perform an experiment. Unfortunately, frequently a hypothesized alternate way of teaching does not yield an improved effect. Given the expense and logistics of each experiment, and the enormous space of potential ways to improve teaching, it would be highly preferable if…

In Brazil we have identified a predilection of the authors of Mathematical History books for the discussion of the fundamentals of Differential and Integral Calculus. On the other hand, when we consider the teaching of Mathematics in the school context, it is essential to know the teaching of the historical and dynamic evolution of the concepts,…

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.

The aim of this paper is to describe the innovative teaching approach used in the Southern Federal University, Russia, to teach accounting via a form of matrix mathematics. It thereby contributes to disseminating the technique of teaching to solve accounting cases using mutual calculations to a worldwide audience. The approach taken in this course…

Various forms of Peer-Learning Environments are increasingly being used in post-secondary education, often to help build repositories of student generated learning objects. However, large classes can result in an extensive repository, which can make it more challenging for students to search for suitable objects that both reflect their interests…

This article presents case study research into a New Zealand primary school enacting a very sophisticated whole school inquiry approach to enhance teacher classroom professionalism and practice. A culture of inquiry manifests as an ontological 'way of being' in this school community, in the daily professional interactions between the teachers and…

Decision matrices are valuable engineering tools. They allow engineers to objectively examine solution options. Decision matrices can be incorporated in K-12 classrooms to support authentic engineering instruction. In this article we provide examples of how decision matrices have been incorporated into 6th and 7th grade classrooms as part of an…

This paper introduces a new matrix tool for the sowing game Tchoukaillon, which establishes a relationship between board vectors and move vectors that does not depend on actually playing the game. This allows for simpler proofs than currently appear in the literature for two key theorems, as well as a new method for constructing move vectors.We…

This study is part of ongoing research in undergraduate mathematics education. The study was guided by the belief that understanding the mental constructions the pre-service teachers make when learning matrix algebra concepts leads to improved instructional methods. In this preliminary study the data was collected from 85 pre-service teachers…

Matrix diagonalization, the key technique at the heart of modern computational chemistry for the numerical solution of the Schrödinger equation, can be easily introduced in the physical chemistry curriculum in a pedagogical context using simple Hückel molecular orbital theory for p bonding in molecules. We present details and results of…

In this article, the authors present a tool, the Cognitive Rigor Matrix (CRM; Hess et al. 2009), as a means to analyze and reflect on the type of questions posed by mathematics teachers. This tool is intended to promote and develop higher-order thinking and inquiry through the use of purposeful questions and mathematical tasks. The authors…

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.