Useful Math Visualizations

Over the years I've made some useful applications for people, which is very gratifying. Currently I'm seeing a program from a couple years ago come back around to see usefulness in the geometry classroom at my school due to the curiosity and insight of one of our math teachers, Matt DeGraff. He observed that such visualizations do aid in his students understanding of a problem and help them think about describing it in mathematical terms. His use of the program and our discussions about it are giving me the idea that a few different programs I've developed around it should be integrated into one to allow students to visualize a certain problem as an aide to seeing solutions and explaining them. Briefly, here are the three programs, more explanation to come:

Polygon vertex problem visualized as polygon

Cool Tool

Paraphrasing, The most important tool of industrial designers is the factory.
-Masamichi Udagawa of Antenna Design

Notes on Mayer, Moreno, "Nine Ways to Reduce Cognitive Load in Multimedia Learning"

• "The goal of [their] research is to figure out how to use words and pictures to foster meaningful learning," and the biggest hurdle to doing that successfully is minimizing cognitive overload.
  
• This paper is a summary of the entire Cognitive Science I syllabus. Every paragraph represents at least a paper or chapter. Wow, it's chock-full.
  
• I think my website design avoids the split attention effect and reduces incidental processing by allowing only one section to be open at a time. So while you are looking at the information in one section you aren't distracted by what's going on in another section, like a video or school assignments. This is done with this nice little bit of JavaScript:
  

  collapseprev: true,

• Signaling: tell them how to use the information.

Facebook

Now I know why Facebook is so popular. It's the ease with which people can communicate in multimedia formats. The only one that's missing is audio messages. Text, pictures, and video are all there mixed together. The brilliance is how easy it is to relate objects to one another through comments, tags, and probably other ways I don't know about in a very fluid way.:)

Tutorial on Using The Book

I was laughing so hard at this this morning and I hadn't even had my coffee. A monk from the middle ages gets tech support as he upgrades from the scroll to the book.


Here's the link and what it says on YouTube. "This video makes fun of moderns newbie computer users by illustrating - in a way fully understandable to them - how silly some of their questions are by creating a similar problem 500 years ago.

It's from a show called Øystein & Meg (Øystein & I) produced by the Norwegian Broadcasting television channel (NRK) in 2001. The spoken language is Norwegian, the subs in Danish. It's written by Knut Nærum and performed by Øystein Bache and Rune Gokstad."