North American GeoGebra Journal (GeoGebra Institute of Ohio)
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Engaging Students with Linear Functions and GeoGebra: An Action Research Study
No full textSoots completed an action research study with pre-algebra students during a unit on linear functions. The goals of this study were to increase student-led technology engagement and utilize a graphing application that would allow students to make connections between multiple representations of linear functions. The use of GeoGebra combined with a student-led approach to instruction positively impacted the classroom environment, allowed students to make connections between representations of functions, and supported student discovery, especially within the topic of systems of equations
Transformations and Complex Numbers
No full textIn this paper, we use complex-number operations to carry out transformations of geometric shapes and establish connections between geometry and algebra in the high-school curriculum. We use dynamic geometry software to visualize the geometric effect of these algebraic operations and connect complex-number operations to translations, rotations, and dilations. 
GeoGebra Simulations of the Monty Hall Game Show
No full textThe purpose of this exploratory note is to offer teaching/learning ideas in the exploration of the famous Monty Hall Game Show, Let’s Make a Deal, in an introductory probability theory class using GeoGebra spreadsheets in a computer lab in groups of 2 to 3 people
Using Action-Consequence-Reflection Geogebra Activities To Make Math Stick
No full textIn this article, the author discusses the Action-Consequence-Reflection cycle for promoting conceptual understanding with technology in the mathematics classroom, along with some cognitive science research support. Several Geogebra activities are presented that capitalize on this process, covering common curricular topics in secondary math. Throughout, the author shares strategies for classroom implementation that encourage reflection and enhance student learning
Graph Theory in GeoGebra
No full textGraph theory is a visual field of mathematics. GeoGebra, although user-friendly, provides no automated way to make or analyze graphs. In the following article, the authors illustrate how JavaScript may be used to extend the capabilities of GeoGebra to build graph theory tools
Teaching Statistics with GeoGebra
No full textIn this article, the author discusses a statistics project that examines the ability of participants to accurately estimate the location of midpoints of various line segments from a GeoGebra sketch. Students explore differences in estimating accuracy for various types of lines among different subgroups of subjects
Models in Demography
No full textIn this article, we present a way to use GeoGebra for working on so called Leslie models. Biomathematicians use these models to describe the demographic development of populations. We have used original statistics on the population of the city of Vienna to provide realistic data. By following the presented tasks students gain insights into the field of demography by starting with the familiar exponential growth model which is successively advanced to a simple Leslie model that takes into consideration the age structure of the population. GeoGebra serves as an ideal tool for implementing these models and allows for some predictions for the future development of the population being considered
Visualizing Functions Of Complex Numbers Using Geogebra
No full textThis paper explores the use of GeoGebra to enhance understanding of complex numbers and functions of complex variables for students in a course, such as College Algebra or Pre-calculus, where complex numbers are introduced as potential solutions to polynomial equations, or students starting out in an undergraduate Complex Variables course. The paper introduces methods to create interactive worksheets for students seeing complex numbers and functions for the first time and for those who have some experience with them, but struggle to visualize their meaning. Acknowledging limitations of GeoGebra concerning complex functions, we create new learning opportunities as we develop workarounds
A Geometric Interpretation of Complex Zeros of Quadratic Functions
No full textMost high school mathematics students learn how to determine the zeros of quadratic functions such as f (x) = ax^2 + bx + c, where a, b, and c are real numbers. At some point, students encounter a quadratic function of this form whose zeros are imaginary or complex-valued. Since the graph of such functions do not intersect the x-axis in the xy-plane, students may be left with the impression that complex-valued zeros of quadratics cannot be visualized. The main purpose of this manuscript is to show that if the zeros of a quadratic function with real-valued coefficients are imaginary, the zeros can be seen if we use an appropriate coordinate system. For illustrative purposes, we have used the software program GeoGebra, which allows us to create a three-dimensional Cartesian coordinate system where imaginary zeros can be viewed simultaneously with the graph of the quadratic function they correspond to. To illustrate this, we will apply geometric transformations to the function given by f (x) = x^2 − 6x + 13 in order to visualize its zeros, which happen to be complex-valued. Then, we will identify a particular set of complex numbers that can be used as inputs for the function f. Using this set of complex numbers, we can construct the exact image that is produced by the geometric transformations. Then, we may deem the two methods as equivalent ways to ultimately construct the geometric images of complex-valued zeros of quadratic functions with real-valued coefficients.Â
Exploring Euclidean and Taxicab Geometry with GeoGebra
No full textTechnology has changed the nature of mathematics learning and instructional practices (Andreasen and Haciomeroglu, 2013; Edwards, 2015; Haciomeroglu, Bu, Schoen, and Hohenwarter, 2011). Dynamic and interactive technology enriches students' learning opportunities and shifts the focus of instruction to understanding and student-centered learning by providing a means of modeling mathematical relationships (Bu and Henson, 2016; Haciomeroglu, Bu, Schoen, and Hohenwarter, 2011). The authors connect Euclidean and non-Euclidean geometries through an exploration of rich tasks of Taxicab geometry, sharing methods for organizing and presenting tasks to enhance students' understanding of geometry concepts