Category Archives: math

Know When To Hold ‘Em, Know When To Fold ‘Em

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Over at Wheatpond, the ever engaging Eric Meltzer shares a spiffy bit of knowledge and skill: the Miura-ori, a captivating method for folding up a sheet of paper. What’s so ginchy about that? Once properly folded, the paper can be opened or closed fluidly, in one smooth mesmerizing motion.

Judge for yourself. You can see the action (pardon the pun) unfold in hosoken2100‘s YouTube video  below.

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History, Poetry, Music, Math, and Science…a Perfect Storm of Learning

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On this day, November 10th, in 1975, the freighter SS Edmund Fitzgerald (a taconite carrier) sank during a storm on Lake Superior. All of the crew, 29 nine men, perished. The event was memorialized in the lyrics of singer Gordon Lightfoot‘s popular ballad, the Wreck of the Edmund Fitzgerald.

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.

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H1N1 Tracking Goes Viral

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Educators and students are visiting the CDC’s  2009 H1N1 Flu website for frequent updates. They’re using technology to enrich their understanding of the disease. That’s fortunate. Why? Science Daily and other sources report that computer models indicate a rapid vaccine rollout is effective in reducing infection rates; however, frustrating shortages of the H1N1 vaccine make the quick and thorough vaccination of the population unlikely. Help your pupils make better health-related choices. Teach them how to use FluTracker to keep up with the spread of the disease.

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Styling with Tiling

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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?

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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.

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Under Construction: Interactive Geometry Resources

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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.

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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.

C.a.R.

Related resources:

  • 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.

I’ve Got Your Number

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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.

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Amaze Your Students

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Here’s a nifty way to practice using interactive whiteboards such as GTCO, Promethean, and SMARTBoard : use the board’s drawing tools to construct a labyrinth. Doing so gives innovative educators and eager students an engaging means of exploring art, mathematics (see Tony Phillips amazing–pun intended–Mazes and Mathematics, for example), and History. Take the plunge. Use your interactive whiteboard to follow a few simple directions and see if you can draw a labyrinth.

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Off the Charts

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I teach a class at a university near my home. Recently, one my students told me about about an assignment in one of the other classes she’s taking. As part of her assignment she’s expected to describe and explain information contained within spreadsheets. She noted how tedious it was to sit through spreadsheet-dominated presentations from her peers and opined that there had to be a more engaging way to get the essential information locked within the confines of all those rows and columns.

I agreed.

“Why don’t you and your classmates liberate that data and make it easier for your audience understand it?” I asked. I suggested that she pay a visit to a few of my favorite data visualizations resourecs:

I’m betting that things are a little more interesting in her class these days.

:-)

Tax Code: Deciphering Where All That Money Goes

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WallStats.com has an impressive visual guide to how Federal tax dollars are spent. The image was constructed by Jess Bachman, a freelance graphic designer who lives in Burlington, Vermont.

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Note: It’s possible that tons of people are going to be hitting WallStats.com so visitors may have to try looking at the image over at HistoryShots.