This article is an excerpt from a master's thesis developed in Brazil, in which we approach recurrent and linear sequences, given some intriguing particularities in their definitions and the scarcity of discussion of this topic in the literature of the History of Mathematics, especially with regard to its geometric representation. Thus, we aim to…

FINDIF is a Windows application that numerically solves the one-dimensional (1D) Schrödinger equation and displays the eigenstates, eigenvalues, and probability density of the system. FINDIF accepts both nonperiodic and periodic 1D potential energy functions as input and uses the finite difference method to evaluate the energy of the quantum…

This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to…

The main purpose of this study is to determine the effects of using dynamic mathematics software on pre-service mathematics teachers' ability to infer the shape of a cross section of a three-dimensional solid, as well as on their spatial visualization skills. The study employed a quasi-experimental design with a control group; the Purdue Spatial…

Several years ago we presented an experimental, discovery-learning approach to the active learning of greedy algorithms. This paper presents GreedEx, a visualization tool developed to support this didactic method. The paper states the design goals of GreedEx, makes explicit the major design decisions adopted, and describes its main characteristics…

Imagine high school students glued to computer screens--not playing video games but applying their mathematical knowledge of functions to the design of three-dimensional sculptures. Imagine these students engaging in rich discourse as they transform functions of their choosing to design unique creations. Now, imagine these students using…

Recursion is a concept that can be used to describe the phenomena and natural occurrences in many different fields. As many applications utilize computer software to model recursion, recursion is a particularly important concept in the computing discipline. However, it is a difficult concept for many undergraduate students to master. A Recursion…

There is an active research community concentrating on visualizations of algorithms taught in CS1 and CS2 courses. These visualizations can help students to create concrete visual images of the algorithms and their underlying concepts. Not only "fundamental algorithms" can be visualized, but also algorithms used in compilers. Visualizations that…

This study proposes an innovative solution to the problem of multiobjective engineering design optimization by integrating desktop VR with genetic computing. Although, this study considers the case of construction design as an example to illustrate the framework, this method can very much be extended to other engineering design problems as well.…

jGRASP has three integrated approaches for interacting with its dynamic viewers for data structures: debugger, workbench, and text-based interactions that allow individual Java statements and expressions to be executed/evaluated. These approaches can be used together to provide a complementary set of interactions with the dynamic viewers. Data…

This article reviews successful educational experiences in using program and algorithm visualizations (PAVs). First, we survey a total of 18 PAV systems that were subject to 33 evaluations. We found that half of the systems have only been tested for usability, and those were shallow inspections. The rest were evaluated with respect to their…

This article reports on an experiment undertaken in order to evaluate the effect of a program visualization tool for helping students to better understand the dynamics of object-oriented programs. The concrete tool used was BlueJ's debugger and object inspector. The study was done as a control-group experiment in an introductory programming…

Online learning material that students use by themselves is one of the typical usages of algorithm animation (AA). Thus, the integration of algorithm animations into hypertext is seen as an important topic today to promote the usage of algorithm animation in teaching. This article presents an algorithm animation viewer implemented purely using…

Hypertextbooks for Computer Science contents present an interesting approach to better support learners and integrate algorithm animations into the learning materials. We have developed a prototype for integrating a selection of the functionality of such a hypertextbook into the established Moodle LCMS. This article describes the goals and…

The study of a real function of two real variables can be supported by visualisation using a Computer Algebra System (CAS). One type of constraint of the system is due to the algorithms implemented, yielding continuous approximations of the given function by interpolation. This often masks discontinuities of the given function and can provide very…