In an earlier issue of "Australian Primary Mathematics Classroom," Sparrow discussed the concept of real-world mathematics and the use of mathematics to explore problems in real-life situations. Environmental issues have provided a context that some teachers have used for teaching mathematics. An example of a particular environmental…

The original shipping strategy of FedEx was to fly all packages to a hub during the afternoon and evening, sort them there, and then fly them to their destinations overnight for delivery the next day. This leads to interesting mathematical questions: Given a population represented by points in Euclidean space or on a sphere, what is the location…

We describe a modelling activity for students in a course in which modelling with differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a linear, first-order, ordinary differential equation. The activity…

Considering our atmosphere as a steady viscous gaseous envelope that co-rotates with the Earth, we obtain a solution for the form in which this induced rotational effect decreases as a function of the distances to the centre of the Earth and to the rotation axis. (Contains 1 figure.)

Part of the power of algebra is that it provides students with tools that they can use to model a variety of problems and applications. Such modeling requires them to understand patterns and choose from a variety of representations--numeric, graphical, symbolic--to construct a model that accurately reflects the relationships found in the original…

After learning how to trace the principal rays [Fig. 1(i)] through a thin lens in order to form the image in the conventional way, students sometimes ask whether it is possible to use other rays emanating from the object to form exactly the same image--for example, the two arbitrary rays shown in Fig. 1(ii). The answer is a definite yes, and this…

Problems in projectile motion are a time-honored staple of high school and even first-year university physics. They can become confusing for some students, yet boring for the stronger students. Herein we present two alternative approaches to such questions, one we call "breaking down gravity," which makes these questions easier to solve, and the…

Children playing in damp sand invariably try to make a tower or a tunnel. By providing experiences with a variety of materials, alone and together, teachers set up the conditions for children to learn through their senses and ensure that a class approaches a topic with a common set of experiences to build on. Learning about the properties of…

Connecting mathematical thinking to the natural world can be as simple as looking up to the sky. Volunteer bird watchers around the world help scientists gather data about bird populations. Counting flying birds might inspire new estimation methods, such as counting the number of birds per unit of time and then timing the whole flock's flight. In…

This paper presents an innovative, interdisciplinary, design-and-build course created to improve placement, content, and pedagogy for introductory engineering design education. Infused at the freshman level, the course aims to promote expert design thinking by using problem-based learning (PBL) as the mode of delivery. The course is structured to…

For the students who have just entered colleges, learning university physics would be a challenge. This paper discusses how to make students who have just finished senior high school physics won't feel difficult in learning university physics and how to guide and cultivate the students' interest in the study of physics so to stimulate the…

This paper outlines an innovative game-based approach to learning introductory programming that is grounded in the development of computational thinking at an abstract conceptual level, but also provides a direct contextual relationship between game-play and learning traditional introductory programming. The paper proposes a possible model for,…

In society, courage gets associated with soldiers, police, firefighters--those men and women who risk their lives in ways that are public and visible and immediate. For school heads also, as a different dictionary definition puts it, courage is demonstrated through "strength in the face of pain or grief" and the ability to do something that…

The senior school Mathematics syllabus is often restricted to the study of single variable differential equations of the first order. Unfortunately most real life examples do not follow such types of relations. In addition, very few differential equations in real life have exact solutions that can be expressed in finite terms. Even if the solution…

Challenges, mistakes, and problems are inherent every day in learning activities and social interactions. How children think about and respond to those difficult situations has an impact on how they see themselves as being able to shape their own learning and on how they handle the next problem that comes their way. Building resilience means…