"When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data," notes the Common Core State Standards Initiative (2010, p. 72). This exploration of the recursive process in the Devil and Daniel Webster problem reveals that the symbolic spreadsheet fits this bill.…

This story is a chemical mystery with an emphasis on qualitative analysis. It is, as well, part of a body of work that presents a scientific problem in mystery format in the context of the popular and beloved characters of 221B Baker Street. A break within the story allows readers to ponder and solve the mystery. Holmes and Watson provide the…

There is growing worldwide interest in Japanese lesson study as a model for professional learning, with large-scale adaptations of lesson study taking place in many countries. This paper describes how teachers and researchers collaborated in a lesson study project carried out in three Victorian schools. It describes Japanese lesson study and the…

One of the main challenges in tapping the full potential of modern educational software is to devise mechanisms to automatically analyze and adaptively support students' problem solving and learning. A number of such approaches have been developed to teach argumentation skills in domains as diverse as science, the Law, and ethics. Yet,…

Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…

Loyola University Chicago's Teaching, Learning, and Leading With Schools and Communities (TLLSC) program is an ambitious break from traditional university-based teacher preparation models. This clinically based initial teacher preparation program, fully embedded in local schools and community organizations, takes an ecological perspective on the…

Although the human mind resists confusion, this feeling of disequilibrium nurtures learning. Newkirk, the author quotes, says intelligence is not a matter of being smart--it is the capacity to view difficulty as an opportunity to stop, reassess, and employ strategies for making sense of problems. These same habits of mind define reflection, a…

Over the last four years of the senior capstone seminar at Western Carolina University, we have redesigned the course substantially to comply with our institutional Quality Enhancement Plan for engaged student learning and to follow the guidelines proposed by the Mathematical Association of America's Committee on Undergraduate Programs in…

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.)