The paper reports the results from 16 versions of a simple probability estimation task, where probability estimates derived from base-rate information have to be modified by case knowledge. In the bus problem [adapted from Falk, R., Lipson, A., & Konold, C. (1994), the ups and downs of the hope function in a fruitless search. In G. Wright & P.…

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…

We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.

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 article describes an experiment using a novel gasometric assembly to determine the thickness and number of atomic layers of zinc coating on galvanized iron substrates. Students solved this problem through three stages. In the first stage, students were encouraged to find a suitable acidic concentration through the guided-inquiry approach. In…

This article describes an exploratory study of question prompts and online mentoring (specifically a lateral or peer mentoring experience) in a field-based practicum that focused on teaching ill-structured problem solving of classroom discipline. Data were gathered on 26 in-service practicum teachers through online observations, online journal…

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 report presents the results of an experiment conducted in Alabama beginning in the 2006/07 school year, to determine the effectiveness of the Alabama Math, Science, and Technology Initiative (AMSTI), which aims to improve mathematics and science achievement in the state's K-12 schools. This study is the first randomized controlled trial…