Internationally, evaluation of group-based trauma recovery programs has relied upon normative outcome measures, with no studies systematically analyzing children's subjective experience for program development. In contrast, the current study explored children's experience of a Gazan recovery program "in their own words." Twenty-four…

The article provides a review of recent research on human performance on the traveling salesman problem (TSP) and related combinatorial optimization problems. We discuss what combinatorial optimization problems are, why they are important, and why they may be of interest to cognitive scientists. We next describe the main characteristics of human…

We consider a version of an optimal stopping problem, in which a customer is presented with a finite set of items, one by one. The customer is aware of the number of items in the finite set and the minimum and maximum possible value of each item, and must purchase exactly one item. When an item is presented to the customer, she or he observes its…

Research in physics education indicates that the use of multiple representations in teaching and learning helps students become better problem-solvers. We report on a study to investigate students' difficulties in solving mechanics problems presented in multiple representations. We conducted teaching/learning interviews with 20 students in a…

This article reviews some key ideas about the nature of proof, kinds of proofs, and the way of reasoning called proving. This provides background for a discussion of the teaching of proof, in which some important aspects of teaching that support students' proving are described, and the ideas of a tool-box of accepted premises and local…

Three clinical interviews were conducted with each of 15 sixth grade students to test conjectures about the relationship between their level of multiplicative reasoning and their solution of combinatorics problems that could involve single and multi-digit multiplication. The problems that involved multi-digit multiplication were designed with the…

In this paper, we review the rules and game board for "Chutes and Ladders", define a Markov chain to model the game regardless of the spinner range, and describe how properties of Markov chains are used to determine that an optimal spinner range of 15 minimizes the expected number of turns for a player to complete the game. Because the Markov…

The development, in an introductory differential equations course, of boundary value problems in parallel with initial value problems and the Fredholm Alternative. Examples are provided of pairs of homogeneous and nonhomogeneous boundary value problems for which existence and uniqueness issues are considered jointly. How this heightens students'…

A question posed by a teacher can often serve as an effective and engaging way to start a class. Sometimes, however, interesting questions arise from comments made by students. The investigation presented in this article arose from a student's very simple question: "Is there a perfect rectangle for folding origami?" The initial investigation was…

We provide several constructions, both algebraic and geometric, for determining the ratio of the radii of two circles in an Apollonius-like packing problem. This problem was inspired by the art deco design in the transom window above the Shadek Fackenthal Library door on the Franklin & Marshall College campus.

In order to be able to adapt successfully to eco-challenges, interest in change-oriented learning is growing around the world. The authors of this paper aim to assess the occurrence of learning for effective action-taking in successive fishery problem-solving interventions in the municipality of Grand-Popo, South-Western Benin, where interventions…

The Schrodinger equation for the ground state of a hydrogen atom confined at the centre of an impenetrable cavity is treated using variational perturbation theory. Energies calculated from variational perturbation theory are comparable in accuracy to the results from a direct numerical solution. The goal of this exercise is to introduce the…

Two studies examine how the time at which problem solving is suspended relative to an impasse affects the impact of incidental hints. An impasse is a point in problem solving at which a problem solver is not making progress and does not know how to proceed. In both studies, work on remote associates problems was suspended before an impasse was…

While many school psychologists agree that part of the satisfaction in their profession lies in the challenges, dealing with these challenges daily can be exhausting. With NASP's 2010 "Model of Comprehensive and Integrated School Psychological Services" (also known as the NASP Practice Model), school psychologists are challenged to take time to…

Research has demonstrated that instruction that relies more heavily on example study is more effective for novices' learning than instruction consisting of problem solving. However, "a heavier reliance on example study" has been implemented in different ways. For example, worked examples only (WE), example-problem pairs (WE-PS), or problem-example…