May 2020 For the Love of Mathematics Jokes
Erell Germia and Nicole Panorkou
We present a Scratch task we designed and implemented for teaching and learning coordinates in a dynamic and engaging way. We use the 5Es framework to describe the students' interactions with the task and offer suggestions of how other teachers may adopt it to successfully implement Scratch tasks.
Hamilton L. Hardison and Hwa Young Lee
In this article, we discuss funky protractor tasks, which we designed to provide opportunities for students to reason about protractors and angle measure. We address how we have implemented these tasks, as well as how students have engaged with them.
Over the past 100 years, technology has evolved in unprecedented fashion. Calculators, computers, and smart phones have become ubiquitous, yet school mathematics experiences for many children still remain without many powerful technological tools for the exploration of mathematics. We consider the evolution of some tools as we imagine a future.
The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.
Debasmita Basu, Nicole Panorkou, Michelle Zhu, Pankaj Lal, and Bharath K. Samanthula
We provide an example from our integrated math and science curriculum where students explore the mathematical relationships underlying various science phenomena. We present the tasks we designed for exploring the covariation relationships that underlie the concept of gravity and discuss the generalizations students made as they interacted with those tasks.
Using technology to solve triangle construction problems, students apply their knowledge of points of concurrency, coordinate geometry, and transformational geometry.
Chris Harrow and Lillian Chin
Exploration, innovation, proof: For students, teachers, and others who are curious, keeping your mind open and ready to investigate unusual or unexpected properties will always lead to learning something new. Technology can further this process, allowing various behaviors to be analyzed that were previously memorized or poorly understood. This article shares the adventure of one such discovery of exploration, innovation, and proof that was uncovered when a teacher tried to find a smoother way to model conic sections using dynamic technology. When an unexpected pattern regarding the locus of an ellipse's or hyperbola's foci emerged, he pitched the problem to a ninth grader as a challenge, resulting in a marvelous adventure for both teacher and student. Beginning with the evolution of the ideas that led to the discovery of the focal locus and ending with the significant student-written proof and conclusion, we hope to inspire further classroom use of technology to enhance student learning and discovery.
I always seek activities that might stretch my students yet would be accessible to them; that might require logical thought yet would contain counterintuitive elements; that might provide the opportunity to venture into new mathematical realms yet would have a simple starting point. This article and the activity that inspired it did indeed arise by way of a relatively straightforward problem that I proposed to one of my classes.
Students often have difficulty with the topic of straight-line graphs. Perhaps they cannot relate to the abstractness of the concepts involved. Perhaps the sheer number and complexity of the skills required—reading algebra, substituting values, rearranging formulas, dealing with negative numbers, understanding coordinates and fractions—magnifies any misconceptions or weaknesses that students may have in other areas of mathematics, rendering them unable to come to grips with the topic as a whole.