Though sad, this historical event presents an engrossing opportunity for students and teachers to collaborate and engage in interdisciplinary research. It’s a perfect storm of learning. Delving into what lead up to the tragedy allows pupils to explore elements of:
Diving into this and other historical events, using them as case-study investigations into why and how things happen, makes learning more rewarding and allows students to integrate technology resources in a more meaningful manner.
Mathematics involves much, much more than adding, subtracting, multiplying, and dividing. Math has the potential to be an intensely engaging study of patterns and relationships. Math can be a doorway to exciting new ways of thinking and seeing the world around us. We just have to awaken a desire within our students to recognize and embrace what math has to offer. A great place to start is art and design.
Some art and design resonates with order and internal consistency. Greg Egan is a science fiction author and computer programmer. When programming, Greg uses math to create impressive products. His engaging work is an excellent example of how the simplicity and complexity of math can be combined to create stunning works of art that foster higher level thinking. His site contains an amazing applets gallery full of math-powered images. For example, have students take a look at his applet called Escher. Ask them one or more of the following questions:
Have you ever seen anything like this? If so, where? Was it in a video game, an advertisement, a design on clothing, on a building, or something that occurs in nature?
Is there a pattern in the image below? How can you prove that your answer is correct?
If we want to make a copy of this image, what resources offline or online might we use to accomplish the task? What are the steps we’d have to make?
Assuming it was your job to generate designs like this one, how much money would you charge someone who asked you to create a similar design? Would you charge a high fee because it’s difficult to replicate such a design or would you charge a low fee because it’s easy to replicate such a design? What supports your answer?
In Greg’s words, this applet is “inspired by the conflicting orientation cues that are used throughout the artwork of M.C. Escher. The technique of projecting selected faces from hypercubes is adapted from deBruijn‘s method for quasiperiodic tilings.” The topic of (geometric) tiling is an excellent springboard for mathematical thinking. Opening students’ eyes to the world of tiling is a powerful means of helping them become cognizant of the beauty and logic of mathematics.
Are your pupils exploring geometry? Do you have an interactive whiteboard or wireless slate? If so, you’ll want to take a look at two very useful FREE programs that I’ve been sharing that make learning mathematics an engaging experience. Over the weekend, I was fortunate enough to be invited to attend and present at the 2009 Math & Science Summit Conference in Liberty County, Georgia. While I was there, I shared interactive math resources with the system’s high school teachers.
During the course of my presentation, I introduced the teachers in attendance to one of my favorite freebies, a program called GeoGebra. This spiffy tool for thinking helps students create constructions with all the necessary components: points, segments, lines, vectors, and functions. thanks to its dynamic interface, GeoGebra allows users to directly enter and manipulate equations and coordinates. You can download the program or use its Webstart feature. My audience at the Math & Science Summit Conference also appreciated the GeoGebraWiki. It’s a growing repository of all kinds of free teaching materials using GeoGebra.
C.a.R. is another free resource that I shared with my attendees. This application is useful for generating dynamic geometric compass and ruler constructions on a computer. Thanks to the digital nature of the displays created with C.a.R., constructions can easily be altered by simply dragging one of the basic construction points. Like GeoGebra, there is a Java Webstart edition of C.a.R. that is always up to date with the most recent program version. Imagine students discussing and demonstrating their constructions using an interactive whiteboard.
GraphCalc is an open source and GPLed computer program that runs in Microsoft Windows and Linux that provides the functionality of a graphing calculator. I like this program.
MatheGrafix is a program for drawing, presentation and printing graphs of functions.
If you teach elementary mathematics, stop what you’re doing and drop by the flash-powered Ptolemy Primitives page. You’ll be glad you did. Designed by Alec McEachran, a math teacher/software developer, this impressive web-based resource gives students an engaging means of visualizing the structure of numbers, in the context of their prime factors. For even more mathematical musings, read Alec’s blog.