This paper discusses recent paradigm changes in linguistics as well as other scientific disciplines in order to stress how such changes affect interactional approaches to health care. It argues that moving from a reductionist to a more holistic and trans-disciplinary approach to human interactivity entails a rethinking of both theory and…

In an attempt to engage primary-school students in a hands-on, real-world problem-solving context, a large urban district, a mathematics and science institute housed in a college of education, and a corporate sponsor in the southwest United States, joined forces to create a mathematics and science trail for fourth- and fifth-grade students. A…

The eight mathematical practices explored in the Common Core Math Standards are the following: (1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (4) Model with mathematics; (5) Use appropriate tools strategically; (6) Attend to…

The Dodgson winner seems very intuitive and reasonable: when a Condorcet winner doesn't exist, pick the candidate that is closest, under some measure, to being a Condorcet winner. However, Dodgson's method is computationally intensive. Approximate methods are more tractable. By placing these methods in a geometric framework, we can understand how…

This paper was first motivated by the following question: "A pair of twins, R and S, each gives the "same" hard push on a block. R's block is on a rougher floor than S's. Who does more work?" It is shown that S will do more work on his block if there is no constraint on the distance over which the force is applied. On the other hand, if the…

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 describes the use and benefits of Microsoft's Adventure Works (AW) database to teach advanced database skills in a hands-on, realistic environment. Database management and querying skills are a key element of a robust information systems curriculum, and active learning is an important way to develop these skills. To facilitate active…