A central topic in Bioelectricity is the generation of the extracellular potential that results from the propagation of a transmembrane action potential along the muscle fiber. However, the way in which the extracellular potential is determined by the propagating action potential is difficult to describe, conceptualize, and visualize. Moreover,…

The work deals with the study of the roots of the characteristic polynomial derived from the Leonardo sequence, using the Newton fractal to perform a root search. Thus, Google Colab is used as a computational tool to facilitate this process. Initially, we conducted a study of the Leonardo sequence, addressing it fundamental recurrence,…

The objective of this work was to evaluate the implementation of a metavisual strategy for students to revise and self-regulate concepts arising in a study of a chemical reaction between ions. For this purpose, two chemistry education undergraduate students at a Brazilian public university carried out an investigative activity, involving…

In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

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] =…

In this paper we introduce a new collaborative technique in teaching and learning the epsilon-delta definition of a continuous function at the point from its domain, which connects mathematical logic, combinatorics and calculus. This collaborative approach provides an opportunity for mathematical high school students to engage in mathematical…

A teaching experiment-using Mathematica to investigate the convergence of sequence of functions visually as a sequence of objects (graphs) converging onto a fixed object (the graph of the limit function)-is here used to analyze how the approach can support the dynamic blending of visual and symbolic representations that has the potential to lead…

In this paper we describe the results that we have obtained while integrating algorithm visualization (AV) movies (strongly tightened with the other teaching material), within a first-year undergraduate course on algorithms and data structures. Our experimental results seem to support the hypothesis that making these movies available significantly…

The importance of visualisation and multiple representations in mathematics has been stressed, especially in a context of problem solving. Hanna and Sidoli comment that "Diagrams and other visual representations have long been welcomed as heuristic accompaniments to proof, where they not only facilitate the understanding of theorems and their…

A heuristic approach to explaining of the Black-Scholes option pricing model in undergraduate classes is described. The approach draws upon the method of protocol analysis to encourage students to "think aloud" so that their mental models can be surfaced. It also relies upon extensive visualizations to communicate relationships that are…

Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)

Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)

Presents methods for teaching two mathematical concepts that utilize visualization. The first illustrates a visual approach to developing the formula for the sum of the terms of an arithmetic sequence. The second develops the relationship between the slopes of perpendicular lines by performing a rotation of the coordinate axes and examining the…