In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)

Computing the mean and covariance matrix of some multivariate distributions, in particular, multivariate normal distribution and Wishart distribution are considered in this article. It involves a matrix transformation of the normal random vector into a random vector whose components are independent normal random variables, and then integrating…

One of the earlier, more challenging concepts in linear algebra at university is that of basis. Students are often taught procedurally how to find a basis for a subspace using matrix manipulation, but may struggle with understanding the construct of basis, making further progress harder. We believe one reason for this is because students have…

The aim of this article is to characterize the 2 x 2 matrices "X" satisfying X[superscript 2] = X + I and obtain some new identities concerning with Fibonacci and Lucas numbers. The recommendations regarding the teaching of the identities given in this article can be presented in two cases. The first is related to the pedagogical aspect. The…

The use of Candecomp to fit scalar products in the context of INDSCAL is based on the assumption that the symmetry of the data matrices involved causes the component matrices to be equal when Candecomp converges. Ten Berge and Kiers gave examples where this assumption is violated for Gramian data matrices. These examples are believed to be local…

The material in this module introduces students to some of the mathematical tools used to examine molecular evolution. This topic is standard fare in many mathematical biology or bioinformatics classes, but could also be suitable for classes in linear algebra or probability. While coursework in matrix algebra, Markov processes, Monte Carlo…

The study examines the agreement among raters on children's problematic behaviors. A multitrait-multimethod (MTMM) matrix was applied to a normative sample of elementary school-aged children (N = 841). The participants were rated by their physical educators, using the Motor Behavior Checklist for children (MBC; Efstratopoulou, Janssen, &…

In this paper, we present a study of a large corpus of student logic exercises in which we explore the relationship between two distinct measures of difficulty: the proportion of students whose initial attempt at a given natural language to first-order logic translation is incorrect, and the average number of attempts that are required in order to…

The main purpose of this note is to present and justify proof via iteration as an intuitive, creative and empowering method that is often available and preferable as an alternative to proofs via either mathematical induction or the well-ordering principle. The method of iteration depends only on the fact that any strictly decreasing sequence of…

If the purpose of secondary schooling is to educate the upcoming generation to become active participants in society, evaluation of teaching and learning in the information-rich digital age should be underpinned by relevant theories and models. This article describes an evaluation tool developed using emerging ideas about knowledge creation and…

The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.

Little is known about the variety of ways students conceptualize matrix multiplication, yet this is a fundamental part of most introductory linear algebra courses. My dissertation follows a three-paper format, with the three papers exploring conceptualizations of matrix multiplication from a variety of viewpoints. In these papers, I explore (1)…

The Knowledge Society Network (KSN) "takes advantage of new knowledge media to maximize and democratize society's knowledge-creating capacity" (www.ikit.org/KSN). This article synthesizes the principles and designs of this network which were initiated over 15 years ago, and presents an exploratory study of interactions in the KSN over…

Contextual mathematics is an area of mathematics teaching and learning through which researchers and educators believe that mathematics is better taught, and learned, if connected to real-life situations and problems. It is also very helpful if it makes sense in the students' world. Thus, the author decided to start a project by creating a blog,…