Several jeeps are poised at base camp on the edge of a desert aiming to escort one of them as far as possible into the desert, while the others return to camp. They all have full tanks of gas and share their fuel to maximize penetration. In a friendly desert it is best to leave caches of fuel along the way to help returning jeeps. We solve the…

The "N" queens problem is a classic puzzle. It asks for an arrangement of "N" mutually non-attacking queens on an "N" x "N" chessboard. We discuss a recent variation called the "N" + "k" queens problem, where pawns are added to the chessboard to allow a greater number of non-attacking queens to be placed on it. We describe some of what is known…

Two independent lines of research--mental simulations and thought experiments--provide strong arguments about the importance of perceptual modalities for the instructional practices in science education. By situating the use of mental simulations in the framework of thought experiments, this study investigated the nature and the role of mental…

Some years ago, Hatano differentiated between routine and adaptive expertise and made a strong plea for the development and implementation of learning environments that aim at the latter type of expertise and not just the former. In this contribution we reflect on one aspect of adaptivity, namely the adaptive use of solution strategies in…

The "box problem" from introductory calculus seeks to maximize the volume of a tray formed by folding a strictly rectangular sheet from which identical squares have been cut from each corner. In posing such questions, one would like to choose integral side-lengths for the sheet so that the excised squares have rational or integral side-length.…

This article is a conversation-analytic examination of situations where one speaker responds to another in a way that publicly exposes that the two speakers hold an incompatible position on a same matter, and in a way that claims that the respondent holds epistemic authority over the matter. These types of responsive actions (i.e.,…

A secretary has "n" letters and "n" addressed envelopes. Instead of matching each letter with the corresponding envelope, she inserts the letters in a random manner. What are the chances that every letter will be in the wrong envelope? In this article, the author presents a solution to this problem and discusses possible ways of placing the…

This study investigates effects of multimedia on cognitive load, self-efficacy and learners' ability to solve multiple rule-based problems. Two hundred twenty-two college students were randomly assigned to interactive and non-interactive multimedia groups. Based on Engelkamp's multimodal theory, the present study investigates the role of…

Teachers can use geometric patterns to promote students' understanding of functional relationships. In this article, the authors first look at a problem-solving process that supports the use of figural reasoning to explore and interpret geometric pattern tasks and generalize function rules. Second, the authors discuss a framework for…

This research uses cognitive load theory and theories of visual literacy to provide a theoretical underpinning for techniques to improve students' ability to recognise designers' styles in higher education. Using a lecture followed by tutorial format, students were required to learn the characteristics needed to identify a designer's work either…

Successful learning sometimes requires that the learner abandons or rejects one or more prior concepts, beliefs, or intuitive theories. Such "nonmonotonic changes" are widely believed to have a low probability of occurring spontaneously and to be difficult to promote with instruction. A theory of nonmonotonic cognitive change should explain both…

In an accompanying study, Alibali et al. [Alibali, M. W., Ockuly, K. M., Fischer, A. D. (2009) "Learning new problem-solving strategies leads to changes in problem representation." "Cognitive Development, 24," 89-101.] present an important experimental result: introducing a new strategy can affect conceptual aspects of children's problem…

This paper describes a framework for learning where learners undergo experimentations with the phenomena at hand according to progressive and staged goals. Bowling is used as a case study in this paper. The premise for experimentations is that learners can experience hidden efficacies, including the formation of "bad habits." A distinction is made…

These problems and activities have been used to demonstrate the uses of multiple representations as well as provide opportunities for students to practice using multiple representations in solving problems. (Contains 3 figures and 2 tables.)

This article explores, in general, three areas for leadership communication that women in business need to master. Indeed, there are more than three, but the focus here is on: the need to master the art of successfully confronting the problem when it appears, the process of leading a team, the special requirements of communicating with men. An…