Dynamic, interactive simulations for enhancing student learning

We present a study of the use of on-line interactive simulations and associated learning packages to enhance student understanding of course material. We have implemented such an approach across undergraduate courses in mathematics and physics. Feedback showed that students found the simulations were both beneficial and enjoyable as part of the learning process

The 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Ngā mihi aroha ki ngā tangata katoa and warm greetings to you all. Welcome to Herenga Delta 2021, the Thirteenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics. It has been ten years since the Volcanic Delta Conference in Rotorua, and we are excited to have the Delta community return to Aotearoa New Zealand, if not in person, then by virtual means. Although the limits imposed by the pandemic mean that most of this year’s 2021 participants are unable to set foot in Tāmaki Makaurau Auckland, this has certainly not stopped interest in this event. Participants have been invited to draw on the concept of herenga, in Te Reo Māori usually a mooring place where people from afar come to share their knowledge and experiences. Although many of the participants are still some distance away, the submissions that have been sent in will continue to stimulate discussion on mathematics and statistics undergraduate education in the Delta tradition. The conference invited papers, abstracts and posters, working within the initial themes of Values and Variables. The range of submissions is diverse, and will provide participants with many opportunities to engage, discuss, and network with colleagues across the Delta community. The publications for this thirteenth Delta Conference include publications in the International Journal of Mathematical Education in Science and Technology, iJMEST, (available at https://www.tandfonline.com/journals/tmes20/collections/Herenga-Delta-2021), the Conference Proceedings, and the Programme (which has created some interesting challenges around time-zones), by the Local Organizing Committee. Papers in the iJMEST issue and the Proceedings were peer reviewed by at least two reviewers per paper. Of the ten submissions to the Proceedings, three were accepted. We are pleased to now be at the business end of the conference and hope that this event will carry on the special atmosphere of the many Deltas which have preceded this one. We hope that you will enjoy this conference, the virtual and social experiences that accompany it, and take the opportunity to contribute to further enhancing mathematics and statistics undergraduate education. Ngā manaakitanga, Phil Kane (The University of Auckland | Waipapa Taumata Rau) on behalf of the Local Organising Committ

Una introducción al método de dominio colorado con GeoGebra para la visualización y estudio de funciones complejas

There are various methods to visualize complex functions, such as plotting their real and imaginary components separately, mapping or transforming a region, the analytical landscapes method and the domain coloring method. The latter is one of the most recent methods and takes advantage of certain characteristics of color and its digital processing. The basic idea is to use colors and brightness or shadows as additional dimensions and to visualize complex numbers a real function is used that associates a specific color to each complex number. The complex plane can then be visualized as a color palette constructed from the HSV scheme (from Hue, Saturation, Value - Hue, Saturation, Value). As a result, the domain coloring method allows to visualize zeroes and poles of functions, branches of multivalued functions, the behavior of isolated singularities, among others properties. Due to the characteristics of GeoGebra in terms of dynamic colors, it is possible to implement the colored domain method to visualize and study complex functions, which is explained in detail in this articl

Una introducción al método de dominio colorado con GeoGebra para la visualización y estudio de funciones complejas

ABSTRACT There are various methods to visualize complex functions, such as plotting their real and imaginary components separately, mapping or transforming a region, the analytical landscapes method and the domain coloring method. The latter is one of the most recent methods and takes advantage of certain characteristics of color and its digital processing. The basic idea is to use colors and brightness or shadows as additional dimensions and to visualize complex numbers a real function is used that associates a specific color to each complex number. The complex plane can then be visualized as a color palette constructed from the HSV scheme (from Hue, Saturation, Value - Hue, Saturation, Value). As a result, the domain coloring method allows to visualize zeroes and poles of functions, branches of multivalued functions, the behavior of isolated singularities, among others properties. Due to the characteristics of GeoGebra in terms of dynamic colors, it is possible to implement the colored domain method to visualize and study complex functions, which is explained in detail in this article.RESUMO Existem vários métodos para visualizar funções complexas, como plotar seus componentes reais e imaginários separadamente, mapear ou transformar uma região, o método de superfície analítica e o método de domínio colorido. Este último é um dos métodos mais recentes e aproveita certas características da cor e seu processamento digital. A ideia básica é usar cores e brilho ou sombras como dimensões adicionais e, para visualizar números complexos, é usada uma função real que associa uma cor específica a cada número complexo. O plano complexo pode então ser visualizado como uma paleta de cores construída a partir do esquema HSV (de Matiz, Saturação, Valor - Matiz, Saturação, Valor). Como resultado, o método do domínio colorido permite visualizar zeros e pólos de funções, ramificações de funções com múltiplos valores, o comportamento de singularidades isoladas, entre outras propriedades. Devido às características do GeoGebra em termos de cores dinâmicas, é possível implementar o método do domínio colorido para visualizar e estudar funções complexas, o que é explicado em detalhes neste artigo.RESUMEN Existen diversos métodos para visualizar funciones complejas, tales como graficar por separado sus componentes reales e imaginarios, mapear o transformar una región, el método de superficies analíticas y el método de dominio coloreado. Este último es uno de los métodos más recientes y aprovecha ciertas características del color y su procesamiento digital. La idea básica es usar colores, luminosidad y sombras como dimensiones adicionales, y para visualizar números complejos se usa una función real que asocia a cada número complejo un color determinado. El plano complejo puede entonces visualizarse como una paleta de colores construida a partir del esquema HSV (del inglés Hue, Saturation, Value – Matiz, Saturación, Valor). Como resultado, el método de dominio coloreado permite visualizar ceros y polos de funciones, ramas de funciones multivaluadas, el comportamiento de singularidades aisladas, entre otras propiedades. Debido a las características de GeoGebra en cuanto a los colores dinámicos, es posible implementar en el software el método de dominio coloreado para visualizar y estudiar funciones complejas, lo cual se explica en detalle en el presente artículo

On Coloring Different Objects of the Same Class

Every object created in GeoGebra has a color property that can be easily changed by the user. This is useful for identifying different objects of the same class. However, if we create lists of objects of the same class (e. g. a list of circles) and try to change the color of this list, then we notice that all the objects change color. How can we create a set of objects of the same class, such that each element has a different color? In this article, I will show an efficient method to color different objects of the same class

Developing prospective mathematics teachers in Mexico: a lesson on the relationship between integration and differentiation

Mexican authorities and universities are actively working to improve mathematics teaching and learning across the education system. Thus, efforts are underway to raise the historically low performance in mathematics, which include theoretically grounded pedagogy and curriculum development to raise mathematical knowledge in teacher education programmes. The purpose of this article is twofold. Firstly, I give an overview of the educational system in Mexico by outlining the evolution of the mathematics curriculum and teacher preparation programmes. Secondly, I describe and discuss, from my own practice, a lesson using dynamic tools for helping prospective teachers to understand the relationship between integration and differentiation within the context of the current literature from Mexico and abroad. While Mexico faces distinct issues within its educational system, challenges in how future mathematics teachers understand mathematical content appear universal. Thus, teaching mathematical content while modelling effective mathematical pedagogical practices is of relevance to all of us striving to enhance the quality of future mathematics teachers

Trigonometric Interpolation Using the Discrete Fourier Transform

The Fourier transform (and all its versions, discrete/continuous/finite/infinite), covers deep and abstract mathematical concepts, and can easily overwhelm with detail. In this paper I provide some intuitive ideas of how the discrete Fourier transform (and its version with low frequencies) works and how we can use it to approximate real periodic functions and parametric closed curves by means of trigonometric interpolation

Números : revista de didáctica de las matemáticas

Resumen basado en el de la publicaciónTítulo, resumen y palabras clave en español e inglésSe presenta el método de dominio coloreado para representar funciones complejas y damos algunas sugerencias didácticas para su uso en el estudio y análisis de variable compleja. Asimismo, mostramos cómo se puede implementar fácilmente este método con el programa GeoGebra, el cual cuenta con el potencial de graficar usando colores dinámicos y además con el álgebra de números complejos.ES