Geocube is an engaging, FREE, online resource devoted to the exploration of geography. With an interface based on the appearance of a Rubik Cube, its six faces and 54 topics invite users to learn more about our planet.
Two weeks ago, I wrote a post describing how 21st century educators use technology to take a digital pulse of popular culture. I mentioned a site called What the Trend. Today, while I was talking to an acquaintance who works for Google, she kindly pointed out that Google Labs has a nifty resource for comparing and contrasting the popularity of ideas. Upon checking out this resource, I was hooked. To use Google Trends, supply a few related terms (using commas to separate them) and click the Search Trends button. For example, I jokingly supplied bacon, lettuce, and tomato. What I got in return was the following graph.
In terms of search, bacon seems to be gaining in popularity these days though the term tomato was of some importance to folks over the last few years. Admittedly, my example is silly. Think, however, how this resource could be used to generate questions about a number of topics being discussed in schools throughout the world. For example, in a social studies class, pupils might compare trends in terms of Mesopotamia, Indus Valley, and ancient Egypt.
In a language arts class, a teacher might ask students to conduct a little investigation about the popularity of titles by the same author. While studying a lesson on health, learners could examine trends surrounding obesity and anorexia. Google Trends has the potential to generate higher-level thinking and excellent discussions.
XMind is an excellent concept-mapping tool that your learners should be using. Why? For starters, mapping out complex relationships helps pupils see the big picture. Often, creating an image is a very productive means of making outlines more meaningful. Secondly, this program works on computers across platforms–Windows, Macintosh, and Linux all accept it. Finally, it’s FREE!
Working with FreeMind will be well worth your time, especially if you explore Mappio–the Mind Map Library. It’s rich with FreeMind visualized concepts.
Amble on over to TopicScape. There are tons of mind maps there as well.
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.
Although students are often shown simple, iconic images depicting electrons traveling in circles around the nucleus of atoms, these infinitesimal busybodies don’t really behave that way. What’s more, as Jim Clark over at ChemGuide points out, it’s impossible to plot a path for electrons. Instead, electrons have a probability of existing on the surface of an area enclosing or near the nucleus of the atom. It’s an area referred to as a shell or orbital. Science teachers trying to explain this concept should take a gander at Orbital Viewer. It’s a Windows-based program designed by David Manthey for drawing orbitals.
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.
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.
Drawing is a powerful tool for learning. Humans have harnessed the potential of graphic representations for millennia to communicate ideas. With the advent of interactive whiteboards and digital slates like those available from GTCO, Promethean, and SMARTBoard, teachers and pupils still have the option of creating illustrations as a means of presenting, exploring, and refining ideas. Effective 21st century educators consistently model and facilitate the use of digital illustration to
engage pupils,
make learning relevant,
increase the efficiency and effectiveness of instruction, and
build a foundation for lifelong learning.
Employing the built-in features of the software that powers interactive whiteboards and digital slates is worthwhile. After all, each package allows users to create geometric figures with both ease and accuracy. That said, don’t allow the features of the program to confine illustrations to one computer in one classroom. Learners should be able to share drawings with audiences outside a classroom, school, and district. Think beyond the classroom computer to a web-based tool for drawing.
Check out Odosketch. It’s a Flash-powered drawing resource that’s been around since 2006, thanks to Odopod, a digital agency that works with a number of major brands. This bare-bones artist tablet and colors doesn’t create accurate geometric shapes. However, users don’t need an account to use Odosketch (although, registering for one makes it possible for artists to save their work). Visitors who want to draw need only mouse over the toolbar at the bottom of the canvas. Colors, brush strokes, and other options will appear. It’s a simple means of sketching quick or detailed pictures.
By allowing pupils to use an interactive whiteboard or digital slate in conjunction with Odosketch, educators facilitate the kind of powerful communication skills explored in Dan Roam’s primer for creating problem-solving pictures, The Back of the Napkin.
Playing with sound is fun. Don’t believe me? Check out ToneMatrix over at aM Laboratory and you’ll immediately understand what I’m talking about. In fact, there a number of intriguing items worthy of inspection in Andre Michelle’s repository of cognitive coolness.
Aside from just being wonderfully fun to play with and listen to, ToneMatrix is an excellent example of what learning ought to be like. The people I’ve talked to tell me that it’s practically addictive. Why isn’t learning about Mathematics, Science, History, Literature, and other academic pursuits like this? What does it take to make exploring a concept, process, or viewpoint habit-forming? Any thoughts?
Related links:
If you like ToneMatrix, look at a project called Muxicall. It was created by Diana Antunes as part of her work for the New Technologies of Communication degree at the University of Aveiro in Portugal. A particularly spiffy feature of Muxicall is that Diana integrates ideas proposed by good old Sir Isaac Newton (1642–1727) creating a pleasing, visible interface between notes of music and color.
Trying to help students get a better handle on Civics and Government? If so, consider teaching pupils how to use Watchdog.net to get a better picture of elected officials. This site handily collects information about votes, lobbying records, and campaign finance reports related to representatives and makes everything available in one place.
Related resource:
Make a point to explore the Center for Civic Education. This site helps students learn more about the history and structure of the government of the United States.
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