The Math Education Blog
Ah geometry, how you suffer from a lack of attention in the elementary grades! Rare is the curriculum that doesn’t stuff geometry into its final chapter, waiting patiently in line behind number and operation. But the one geometry topic that does command attention is classifying two-dimensional shapes into categories based on their properties. To quote...
While most numbers lead anonymous lives away from the mathematical spotlight, eiπ occupies hallowed ground. Douglas Hofstadter writes that when he first saw the statement eiπ = −1, “. . . perhaps at age 12 or so, it seemed truly magical, almost other-worldly.” At the risk of deflating the celebrity status of eiπ, what follows is an...
This past semester, I taught a geometry course for teachers at City College here in New York. As you might expect, Sketchpad figured heavily in the course contents. But unlike other semesters when desktop Sketchpad was my tool of choice, this time, I took the plunge and limited myself to Web Sketchpad. Web Sketchpad kept...
This post, inspired by the work of Al Cuoco, uses Web Sketchpad to explore a transformations approach to complex numbers.
Given two segments and their midpoints, what quadrilaterals can you build using the segments as the diagonals of the quadrilateral?
This post examines the connections between origami and geometry in the context of a new book written by Daniel Scher and Marc Kirschenbaum.
This post presents virtual dances based on geometric transformations. As a penguin travels around a polygon, you, as a frog, must match its movements, but with the added challenge of dancing as a reflection, rotation, or dilation of the penguin’s path.
This post presents an abundance of games that find their inspiration in three geometric transformations: reflection, rotation, and dilation.
In geometry, we learn that if we erect squares on the legs of a right triangle, the sum of their areas is equal to the area of the square on the triangle’s hypotenuse. This is visual way to conceptualize the Pythagorean Theorem. But now consider the image below that shows a bust of Pythagoras, scaled...
I was happy to collaborate on this blog post with Dr. Stavroula Patsiomitou, a researcher at the Ministry of Education and Religious Affairs in Greece. Dr. Patsiomitou received her PhD from the University of Ioannina and has written extensively about the field of dynamic geometry environments, including Sketchpad and Web Sketchpad. Her textbook, Conceptual and...