Kirschner, Sweller and Clark (2006) suggest that minimally guided instructional methods are not as successful or efficient as guided instructional approaches. The goal of the current study was to address both the issue of learner performance and knowledge transfer when problem solving in anchored instruction was used for mathematical instruction…

Two people take turns selecting from an even number of items. Their relative preferences over the items can be described as a permutation, then tools from algebraic combinatorics can be used to answer various questions. We describe each person's optimal selection strategies including how each could make use of knowing the other's preferences. We…

Ever had a roommate? Then you know that it can be difficult to share housekeeping duties. This article uses game theory to analyze situations in which there is a task to be done and two people who might do it. We then use our analysis to consider what game theory tells us about the gendered division of household labor.

Convexity-based measures of shape compactness provide an effective way to identify irregularities in congressional district boundaries. A low convexity coefficient may suggest that a district has been gerrymandered, or it may simply reflect irregularities in the corresponding state boundary. Furthermore, the distribution of population within a…

In this essay Angelo Caranfa maintains that what education should be engaging in is a ceaseless effort of cultivating in the students attention to the things of the spirit--that is, the world of aesthetic apprehension as described by such figures as Plato and Simone Weil. Caranfa attempts to show that in Plato and in Weil, we receive a vision of…

We have developed a two-week guided-inquiry laboratory in which first-semester general chemistry students investigate a suspected arson using gas chromatography--mass spectrometry and paper chromatography. In the process of evaluating evidence from the crime scene, students develop and test hypotheses and learn the fundamentals of chromatography,…

The jigsaw technique has been used in a fourth-year biochemistry course to increase problem-solving abilities of the students. The jigsaw method is a cooperative-learning technique that involves a group structure. Students start with a "home" group. That group is responsible for learning an assigned portion of a task. Then the instructor separates…

Background: The present work is aimed at analysing executive function (EF) in adolescents with Down Syndrome (DS). So far, EF has been analysed mainly in adults with DS, showing a pattern of impairment. However, less is known about children and adolescents with this syndrome. Studying adolescents with DS might help us better understand whether…

This geometrical account of primitive Pythagorean triples was stimulated by a remark of Douglas Rogers on a recent paper by Roger Alperin (Alperin, 2005). Rogers, in commenting on this paper, noted that Fermat in the 17th century had posed a challenge problem on Pythagorean triples that suggested he knew how to construct a sequence of them,…

This article presents the partial results obtained in the first stage of the research, which sought to answer the following questions: (a) What is the role of intuition in university students' solutions to optimization problems? (b) What is the role of rigor in university students' solutions to optimization problems? (c) How is the combination of…

Diagrams and figures play a central role in science and science education. Research has indicated that, when presented and used properly in a classroom setting, these external representations can contribute to students' understanding of scientific concepts; however, it is apparent that students do not always use, understand, interpret, or value…

This study presents and interprets some conceptual difficulties junior-level physics students experience with Ampere's law. We present both quantitative data, based on students' written responses to conceptual questions, and qualitative data, based on interviews of students solving Ampere's law problems. We find that some students struggle to…

In this article, we propose to introduce the differential of a function through a non-classical way, lying on hyperreals and infinite microscopes. This approach is based on the developments of nonstandard analysis, wants to be more intuitive than the classical one and tries to emphasize the functional and geometric aspects of the differential. In…

The authors used the operand-recognition paradigm (C. Thevenot, M. Fanget, & M. Fayol, 2007) in order to study the strategies used by adults to solve subtraction problems. This paradigm capitalizes on the fact that algorithmic procedures degrade the memory traces of the operands. Therefore, greater difficulty in recognizing them is expected…

Taking part in the United States Department of Energy's Real World Design Challenge (RWDC), the author describes how four technology education students at Cumberland Valley High School in Mechanicsburg, Pennsylvania, took on the challenge to redesign an aircraft wing, attempting to make it more efficient than one currently in operation. The…