This paper discusses findings from an ongoing study investigating mental mechanisms involved in the conceptualisation of linear transformations from the perspective of Action (A), Process (P), Object (O), and Schema (S) (APOS) theory. Data reported in this paper came from 44 first-year linear algebra students' responses on a task regarding the…

Almost all finite groups encountered by undergraduates can be represented as multiplicative groups of concise block-diagonal binary matrices. Such representations provide simple examples for beginning a group theory course. More importantly, these representations provide concrete models for "abstract" concepts. We describe Maple lab…

We present an algorithm for a matrix-based Enigma-type encoder based on a variation of the Hill Cipher as an application of 2 × 2 matrices. In particular, students will use vector addition and 2 × 2 matrix multiplication by column vectors to simulate a matrix version of the German Enigma Encoding Machine as a basic example of cryptography. The…

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.…

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…

As teachers organize classroom schedules to meet curricular demands and time constraints, they strive to seek ways to motivate and sustain student engagement in quality vocabulary instruction, enjoyable learning experiences, and interesting informational books. This article addresses these concerns and describes a vocabulary acquisition strategy…

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…

Discusses Component Display Theory (CDT) as a method of instructional design, and describes a reorganization of CDT meant to increase its utility in the instructional design process. Matrices in the CDT are explained, and a synthesized matrix based on content and performance elements is provided. (six references) (LRW)

Examined the role played by experience with multidimensional stimuli in the child's ability to separate variables. (Author/DB)

Describes how elementary linear algebra can be taught successfully while introducing students to the concept and practice of mathematical proof. Suggests exploring the concept of solvability of linear systems first via the row echelon form (REF). (Author/KHR)

Presents a lesson to teach matrices that emphasizes conceptual understanding and allows students to extend their investigations into important and relevant situations by using graphing calculators after important conceptual understanding has been developed. (KHR)

Suggests 11 dimensions of cognitive style which influence learning, and proposes a three-step instructional design plan to move beyond individual instruction to individualized instruction, so that differences in learners need not result in differences in learning. (Author/JEG)

Describes MATRIX-1, a small group activity that can be used to show interrelationships between various factors. Examples include values clarification; procedural phases; relationships among people; resource allocation; related concepts; and group decision making activities. Modifications to MATRIX-1 are discussed that allow for variations in…

Matrix tasks to assess multiple classifications and multiple seriation skills were administered to 160 children (40 Ss each from preschool, kindergarten, first and second grade levels). Each child received six matrix subtasks (reproduction and transportation of cross classification I, double seriation, and cross classification II) in one of six…

Indirectly, instructor behavior provided two models for using a multitrait-multimethod matrix. Students who formulated their own concept, created empirical indicators, and assessed convergent and discriminant validity had better results than those who, influenced by classroom authority dynamics, followed a poorly formulated concept with a…