North American GeoGebra Journal (GeoGebra Institute of Ohio)
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88 research outputs found
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Modeling the Gyroid in GeoGebra
No full textThe gyroid is a triply periodic minimal surface (TPMS) with intriguing geometric and aesthetic appeal. However, it is a challenging structure to model in GeoGebra. Starting with the implicit equation, we first derive a parametric equation to model the gyroid unit surface patch in light of its intrinsic symmetries. Next, we demonstrate how JavaScript codes and GeoGebra Sequences can be employed to create 3D scatterplots of the gyroid unit cell. Through this process, we showcase the interplay between GeoGebra's capabilities, its limitations, and the computational complexity involved in gyroid modeling
Expanding the Semiotic Scope of GeoGebra by Teaching It to Speak
No full textThis paper discusses the integration of JavaScript and Google's Text-to-Speech (TTS) technology in GeoGebra, adding voice synthesis to enhance the software's educational use. This allows for verbal communication of concepts, increasing interactivity, accessibility, and semiotic range. Such innovation promotes inclusive education, especially for individuals with disabilities, by making learning materials more accessible and engaging. We highlight this advancement with practical examples, underscoring its significant impact on making education more flexible and inclusive through enhanced GeoGebra functionalities
Rate of Change: Degrees vs. Radians
No full textIn this article, we will discuss using GeoGebra to present and connect multiple representations. The purpose of the activities shared is to help students reflect on the consequences of different units when graphing trigonometric functions. Specifically, the activity should help students compare the consequences, with respect to the rate of change, of using radians or degrees when graphing trigonometric functions
Filling vessels: An exciting way to investigate functional dependencies
No full textWhen discussing and analyzing functional dependencies, schoolbooks, and teachers often use different filling curves—asking students to match various vessels with their corresponding graphs. After presenting the three basic ideas of functional thinking, the authors demonstrate ways of determining functional equations from analyses of filling data and discuss the use of dynamic applets with students
Challenging misconceptions about the coefficient of determination (R^2) with a dynamic Geogebra applet
No full textThe authors present an applet, R2 Explorer, that can be used to explore how the value of R2 is related to data points and to challenge the misconception that R2 measures “percentage of fit” of a regression line
Origami paper cup: From paper folding to data analysis and algebraic explorations
No full textWe present the case of an origami paper cup and its extensions to data collection, analysis, and dimensional reasoning in K--12 teacher education, featuring the integration of GeoGebra. The paper cup case has been implemented numerous times in our K--12 mathematics methods classes, targeting a variety of issues of mathematics teaching and learning---multiple representations, mathematical discourse, intuitive perceptions, rational reasoning, data analysis, as well as hands-on engagement and ownership. To implement the instructional tasks, we need an adequate supply of commercial or self-made origami paper, copy paper of various sizes, and a few pounds of pinto beans or similar beans that are safe for classroom use as well as access to GeoGebra
Building an Analog Clock with Complex Numbers
No full textIn this article, we describe a lesson that enabled 10th and 11th grade students to create an analog clock using GeoGebra. This self-directed, exploratory lesson is built on students’ prior knowledge of complex numbers and vector transformation and relies on the technological features of GeoGebra
Projective Geometry: A Historical Overview and Perspectives for Education
No full textThis article aims to bring a discussion focused on the historical evolution of projective geometry and perspectives that aim at its application in the educational context, especially with the use of GeoGebra for the presentation of its concepts. The historical bias of this geometry field was analyzed in the light of the possibilities of its approach in basic education. The research methodology of this work is of a qualitative nature, bibliographic in nature, where we relate materials that bring the evolution of projective geometry from its genesis to the present day. In the meantime, we bring a perspective of transition between the Euclidean-projective geometries, as a way to elucidate some concepts of projective geometry and facilitate its understanding from the visualization with the contribution of GeoGebra
Trigonometric Interpolation Using the Discrete Fourier Transform
No full textThe 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
The Arithmetic Average of Altitudes From Vertices of a Parallelogram to a Straight Line: A Sketch and Proof
No full textThe author illustrates a method for motivating mathematical generalization with students using GeoGebra. Building on student interest in amusement parks, the author connects an initial question about Ferris wheel riders to general quadrilaterals in the plane. In a culminating activity, students construct a rigorous algebraic proof confirming their initial conjectures