Research into virtual role-based learning has progressed over the past decade. Modern issues include gauging the difficulty of designing a goal system capable of meeting the requirements of students with different knowledge levels, and the reasonability and possibility of taking advantage of the well-designed formula and techniques served in other…

Students are provided with a mystery concerning dogs that are paralyzed. This motivates a laboratory exercise to measure parameters from the dog's "blood" to determine whether the paralysis is due to pesticide poisoning or an autoimmune attack on nerve myelin. Most of the materials are available from the grocery store. The real-world nature of the…

In this article, the author explores her personal views on mathematics and how she solves problems. She experiences some personal revelations while attending a "Mathsjam". Organised by some of the more prominent names in the popularisation of mathematics, "Mathsjam" was billed as the UK's first Gathering for Gardner, an event…

The separation of content between science, math, engineering, and technology education should not exist. Working with the relationship between these content areas enhances students' efforts to learn about the physical world--and the Bungee Jump offers one great way to go about it. This article describes an activity called the Egg Bungee Jump which…

A chain assumes the well-known shape known as a catenary when it hangs loosely from two points in a gravitational field. The correct solution of the catenary was one of the early triumphs of the newly invented calculus of variations at the end of the 17th century. Here we revisit the catenary and show that, for a chain hanging from a horizontal…

We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…

In this activity, I show how high school students apply their knowledge of density to solve an unknown variable, such as thickness. Students leave this activity with a better understanding of density, the knowledge that density is a characteristic property of a given substance, and the ways density can be measured. (Contains 4 figures and 1 table.)

Some simple chemistry is used to demonstrate how Fe(II) ions, formed during iron corrosion in acid aqueous solution, can reduce toxic Cr(VI) species, forming soluble Cr(III) and Fe(III) ions. These ions, in turn, can be precipitated by neutralizing the solution. The procedure provides a treatment for industrial wastewaters commonly found in…

Problem posing is a higher-order, active-learning task that is important for students to develop. This article describes a series of interdisciplinary learning activities designed to help students strengthen their problem-posing skills, which requires that students become more responsible for their learning and that faculty move to a facilitator…

Children learn from a very early age what it means to get their "fair share." Whether it is candy or birthday cake, many children successfully create equal-size groups or parts of a collection or whole but later struggle to create fair shares of multiple wholes, such as fairly sharing four pies among a family of seven. Recent research suggests…

Making problem solving a central part of teaching may be challenging to teachers who have limited experiences in learning and teaching mathematics in this way. Math Teachers' Circles were developed with the aim of establishing a "culture of problem solving" among middle school mathematics teachers. This culture could then be carried back into…

We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…

This article presents the methods, materials, and manpower required to create a strategic leadership program for promoting, sustaining, and advancing institutional significance. The functionality of the program is based on the Original Case Study Design (OCSD) methodology, in which participants are given actual college issues to investigate from a…

I argue for the inclusion of topics in high school mathematics curricula that are traditionally reserved for high achieving students preparing for mathematical contests. These include the arithmetic mean--geometric mean inequality which has many practical applications in mathematical modelling. The problem of extremalising functions of more than…

Many optimization problems can be solved without resorting to calculus. This article develops a new variational method for optimization that relies on inequalities. The method is illustrated by four examples, the last of which provides a completely algebraic solution to the problem of minimizing the time it takes a dog to retrieve a thrown ball,…