A very common Applied Optimization Problem in Calculus deals with minimizing a distance given certain constraints, using Calculus, the general method for solving these problems is to find a function formula for the distance that we need to minimize, take the derivative of the distance function, set it equal to zero, and solve for the input value,…

A large and growing body of work has documented robust illusions of area perception in adults. To date, however, there has been surprisingly little in-depth investigation into children's area perception, despite the importance of this topic to the study of quantity perception more broadly (and to the many studies that have been devoted to studying…

There is a large body of literature concerning the potential of dynamic geometry software (DGS) in the problem solving process. However, questions regarding how teaching should take place to prepare students to use DGS as a heuristic tool in non-routine problem situations seem to be overlooked. To address this gap in the literature, the current…

This article gives an example for using Dynamic Geometry Software to encourage making conjectures, reasoning, and experiencing mathematics as a process.

The article reports three experiments designed to explore heuristics used in comparing the lengths of completed Euclidean Traveling Salesman Problem (E-TSP) tours. The experiments used paired comparisons in which participants judged which of two completed tours of the same point set was shorter. The first experiment manipulated two factors, the…

Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…

Admittedly, the study of Complex Analysis (CA) requires of the student considerable mental effort characterized by the mobilization of a related thought to the complex mathematical concepts. Thus, with the aid of the dynamic system Geogebra, we discuss in this paper a particular concept in CA. In fact, the notion of winding number v[f(gamma),P] =…

This paper investigates how detailed a linguistic representation is formed for descriptions of visual events. In two experiments, participants watched captioned videos and decided whether the captions accurately described the videos. In both experiments, videos depicted geometric shapes moving around the screen. In the first experiment, all of the…

The Pedagogical Agents (PAs) for Mobile Learning (m-learning) must be able not only to adapt the teaching to the learner knowledge level and profile but also to ensure the pedagogical efficiency within unpredictable changing runtime contexts. Therefore, to deal with this issue, this paper proposes a Context-aware Self-Adaptive Fractal Component…

The scientific study of creativity has proven a difficult undertaking. Researchers have employed a diversity of definitions and measurement methods. As a result, creativity research is underrepresented in the literature and the findings of different studies often prove difficult to draw into a coherent body of understanding. A heuristic framework…

Recent studies on a computationally hard visual optimization problem, the Traveling Salesperson Problem (TSP), indicate that humans are capable of finding close to optimal solutions in near-linear time. The current study is a preliminary step in investigating human performance on another hard problem, the Minimum Vertex Cover Problem, in which…

This paper reports a study on the effect of using the Lakatosian heuristic method to teach the surface area of a cone (SAC) on students' achievement according to Bloom's taxonomy levels. Two groups of students (experimental and control) participated in the study. The experimental group (n = 20) was taught using the Lakatosian heuristic method…

This article describes how students at North Central College do-si-doed their way to a deeper understanding of fractals, fractions, and abstract algebra. As part of the college's "Verandah" curriculum, David J. Schmitz, an associate professor of mathematics, led seven undergraduates, mostly math majors and minors, through an adventure in "math in…

Students learn new abstract concepts best when these concepts are connected through a well-designed analogy, to familiar ideas. Since the concept of the relativistic spacetime distance is highly abstract, it would be desirable to connect it to the familiar Euclidean distance, but present the latter in such a way that it makes a transparent contact…

Illustrates how heuristics can provide a psychological narrative of Hippocrates' and Archytas' thinking on the duplication of the cube. Four general heuristic techniques were used. (YP)