This article presents key steps in the design and analysis of a computer based problem-solving assessment featuring interactive tasks. The purpose of the assessment is to support targeted instruction for students by diagnosing strengths and weaknesses at different stages of problem-solving. The first focus of this article is the task piloting…

Several decades ago, V. A. Krutetskii conducted a multiyear study to investigate the various types of thinking that academically advanced, or as he called them, gifted mathematicians used. Following an in-depth look at Krutetskii's nine ways of thinking, a model is proposed that will provide direction for teachers in selecting problems. The model…

In recent times experiential learning attempted to assist student development in almost every field. More specifically regarding business studies, instructors have used experiential learning projects in a variety of ways, depending upon the business function. The described learning project progression holds the potential to be useful to…

Districts face increasing pressure to improve students' mastery of curriculum in the fields of science, technology, engineering and mathematics (STEM). Yet the number of students enrolling in science and math courses drops dramatically in middle and high school. At Sylvester Middle School, Chinook Middle School and Cascade Middle School of the…

The problem of angle trisection continues to fascinate people even though it has long been known that it can't be done with straightedge and compass alone. However, for practical purposes, a good iterative procedure can get you as close as you want. In this note, we present such a procedure. Using only straightedge and compass, our procedure…

This article explores phenomena related to fitting polynomials with data sets with equally spaced x-values.

The well-known "hats" problem, in which a number of people enter a restaurant and check their hats, and then receive them back at random, is often used to illustrate the concept of derangements, that is, permutations with no fixed points. In this paper, the problem is extended to multiple items of clothing, and a general solution to the problem of…

The "matching" hats problem is a classic exercise in probability: if "n" people throw their hats in a box, and then each person randomly draws one out again, what is the expected number of people who draw their own hat? This paper presents several extensions to this problem, with solutions that involve interesting tricks with iterated…

In a recent article, Iain MacInnes analyzed the static equilibrium of a system consisting of a wine bottle and a wine butler. After discussing that composite system, students can be asked to consider only the bottle (and its contents) as the system. An interesting challenge for them is to describe the forces on the bottle in static equilibrium.

Psychology has largely ignored the distinction between constructs and events and what comprises a scientific construct, yet this distinction is basic to some of the major divisions of thought within the discipline. Several kinds of constructs are identified and compared with events, and improper use of constructs is noted of which the mind…

A puzzle was developed as a resource for teaching intermediate chemistry students where they need to use general intelligence and logic skills. The puzzle involves identification of name, age, subdiscipline of chemistry and position of 6 students around the table by using certain data provided to them.

This article describes the use of Fermi questions as a problem-solving tool.

As is known, a semi-magic square is an "n x n" matrix having the sum of entries in each row and each column equal to a constant. This note generalizes this notion and introduce a special class of block matrices called "block magic rectangles." It is proved that the Moore-Penrose inverse of a block magic rectangle is also a block magic rectangle.

This book presents a schoolwide model of instructional support designed to make the most of available time, resources, and personnel--one that is also fully compatible with other problem-solving models, such as response to intervention. The authors provide a comprehensive and cohesive framework for linking assessment and intervention. They show…

This 21st Century Skills Map is the result of hundreds of hours of research, development and feedback from educators and business leaders across the nation. The Partnership for 21st Century Skills has issued this map for the core subject of World Languages. [Funding for this paper was provided by EF Education.]