Martin Gardner wrote about a coin-flipping trick, performed by a blindfolded magician. The paper analyses this trick, and compares it with a similar trick using three cups flipped in pairs. Several different methods of analysis are discussed, including a graphical analysis of the state space and a representation in terms of a matrix. These methods…

How many ways may one climb an even number of stairs so that left and right legs are exercised equally, that is, both legs take the same number of strides, take the same number of total stairs, and take strides of either 1 or 2 stairs at a time? We characterize the solution with a difference equation and find its generating function.

Spatial reasoning, a crucial skill for everyday actions, develops gradually during the first several years of childhood. Previous studies have shown that perceptual information and problem solving strategies are critical for successful spatial reasoning in young children. Here, we sought to link these two factors by examining children's use of…

This paper describes a forward approach to an inverse problem related to detecting the nature of geological substrata which makes use of optimization techniques in a multivariable calculus setting. The true nature of the related inverse problem is highlighted. (Contains 2 figures.)

Grading can be accelerated to make time for more effective instruction. This article presents specific time management strategies selected to decrease administrative time required of faculty and teaching assistants, including a multiple answer multiple choice interface for exams, a three-tier grading system for open ended problem solving, and a…

In this article, we present a proposal for fostering learning in the management classroom through the use of student-produced video assignments. We describe the potential for video technology to create active learning environments focused on problem solving, authentic and direct experiences, and interaction and collaboration to promote student…

Strictly teaching algorithms or procedural computations can "encourage children to give up their own thinking" (Kamii and Dominick 1998). Although such procedures are valid for finding solutions, students often know only how to use them, and they lack the understanding of why a procedure works. In 2001, the National Research Council…

This paper describes a unique integrative business case appropriate for use in a managerial accounting course or other business courses related to economics or marketing. The case describes a scenario in which a managerial accountant is assisting in business decisions relating to factors influencing the profitability of a small manufacturing…

Paraprofessionals (also referred to as paraeducators or instructional assistants) who work in inclusive early childhood classrooms are facing increasing responsibilities in supporting teachers and children with diverse learning needs (Deardorff, Glasenapp, Schalock, & Udell, 2007; Downing, Ryndak, & Clark, 2000; Giangreco, Broer, &…

A connection between creativity and curiosity may seem self evident, and, indeed, psychologists and philosophers have long held that creativity and curiosity are related. It seems logical enough. One can imagine that the typical individual is satisfied by the usual solution to a problem or the usual way to conceptualize a situation, but the…

Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

When designing lessons and units of study, teachers prepare problems that will make learning accessible, challenging, and targeted to goals. Experienced teachers often can predict classroom dialogue. This sense of déjà vu is even stronger when they teach the same course several times a day. The questions from the students are familiar and almost…

Based on the popular television show the "Iron Chef," an innovative marketing activity called the "Iron Inventor" is introduced. Using the creative problem-solving approach and active learning techniques, the Iron Inventor facilitates student learning pertaining to the step-by-step processes of creating a new product and…

The consultant role remains a critical function for school psychologists and other educators, and a number of choices exist regarding how to enact the role. Preservice training, assumptions and beliefs regarding practice, and work context all influence professional practices; so may contribute to misunderstandings about particular approaches. In…

Root cause analysis is a powerful method schools use to analyze data to solve problems; it aims to identify and correct the root causes of problems or events, rather than simply addressing their symptoms. In this webinar, veteran practitioner, Roni Silverstein, talked about the value of this process and practical ways to use it in your school or…