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…

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.

In this paper I address the issue of collaboration between content lecturers and language lecturers or educational researchers. Whilst such collaboration is a desirable goal for disciplinary learning in monolingual settings, I suggest it takes on extra significance when two or more languages are involved in teaching and learning a discipline.…

In the School of Education at the University of Adelaide, the use of oral evidence is increasingly common as students engage with reflective practices now dominant in teacher-education programs. These experiences offer both a dynamic perspective and a challenge to academic assessors and raise three questions, each of which are addressed in this…

The approaches to teaching and learning mathematics in Australian preschools and schools can be quite different. These differences arise from what can be termed different "cultures" within the prior-to-school and school settings. Even the first years of school can be characterized by teacher-centered, syllabus-driven lessons and written,…

Mathematics can be perceived as being a difficult subject to learn due to the conceptual leaps required to understand particular mathematical topics. In some areas of mathematics, part of the difficulty may be associated with applying sufficient imagination to visualize a particular mathematical concept, and applying sufficient visio-spatial…

A heuristic procedure can be used to teach organizational skills to students of technical writing. Designed to allow students on their own to explore ways that numbers can be used to give a definite shape to technical information, its central feature is a matrix composed of a series of control numbers (horizontal axis) and organizing concerns…

We evaluated an intervention package for teaching generative sociodramatic play activities to a young boy with an autism spectrum disorder. In Phase 1, the boy learned computer activity schedules that featured embedded video models of what to say and do. A 3 x 3 instructional matrix defined 9 activities to be performed involving combinations of 3…