This blog carnival seeks to promote seven principles:
1. Connection between and among different mathematical concepts
Sol Lederman at Wild About Math shares a video of an Incredible Magic Square.
Antonio Gutierrez at Go Geometry has a fascinating golden rectangle puzzle that connects with the Droste effect.
2. Connections between math and real life; use of real-life contexts to explain mathematical concepts
John D Cook at the Endeavor shares that there isn't a googol of anything.
Grrrl Scientist suggested this article from her guardian.co.uk blog about "How the leopard got its spots" that has some literally beautiful mathematics.
Consider this beautiful film by Cristóbal Vila - Nature by Numbers. Or this collection of Hands On Math Movies.
David Cox has just been sharing a ridiculous amount of great stuff lately. For example, projectile motion.
It's been widely shared, but you have to check out Kate Nowak's money take on special right triangles at f(t).
3. Clear and intuitive explanation of topics not discussed in textbooks, hard to understand, or difficult to teach
James Tanton has two videos explaining the principles for math genius thinking. Hat tip: Denise at Let's Play Math. You might also like Sue Van Hattum's interview of Dr. Tanton for the Math 2.0 interest group.
For that matter, Sue's post at Math Mama Writes about E is for Eigenvectors and Eigenvalues belongs in this category. Has the great first sentence: "This post is about fear."
I spent some time recently looking at trigonometric function visualizations and making a couple Geogebra sketches for them and their inverses. Seems silly to link, since it's right down there.
4. Proofs of mathematical theorems in which the difficulty of the explanation is accessible to high school students
No one nominated entries in this category, but it makes me think of work like James Tanton's explanation of Euler's proof that every even perfect number is triangular, or Alexander Bogomolny's proofs at Cut-the-Knot of the addition and subtraction formulas for sine and cosine. (Both of these sites I've had occasion to look up recently!)
5. Intuitive explanation of higher math topics, in which the difficulty is accessible to high school students
Derek Bruff has put together a fascinating interactive Cryptography Timeline. I'd love to see some of these for some important math concepts.
6. Software introduction, review or tutorials
Guillermo Bautista, the founder of this here carnival, at the Math and Multimedia blog, has a roundup of essential tools for every math blogger. Also be sure to check out his terrific Geogebra tutorials while at his site.
Maria Anderson has video of her presentation from MAA-Michigan up, Math Technology to Engage, Delight and Excite. Also watch as her new blog, Edge of Learning, gets up and running.
Chris Betcher has some terrific Scratch (the programming language) resources and videos.
You might try one of these 15 mind-mapping tools. (Many are free.)
7. Integration of technology (Web 2.0, Teaching 2.0, Classroom 2.0), in teaching mathematics
David Wees has an interesting meditation on the importance of interactivity in math teaching.
Cybraryman has a long list of math/tech integration resources and lessons.
If you're looking for Five tunes, Take 5, or try Gimme 5 from Sesame Street, High Five from They Might Be Giants, Dino 5 (who also have a great counting rap called What About 10)?, or maybe the best (in terms of math) ...
If you have ever posted a blog carnival, you know that you receive a lot of obvious spam. But some can seem relevant, so I like to have a Best of the Spam category. For example, the Top 40 sources for open courseware video.
And if you are mistakenly put here, or your post did not appear, please let me know and I will correct it posthaste.
Images were obtained from Creative Commons search. Attributions are in the picture title - click on the image and you will see the source from Flickr.
If you enjoyed the carnival, please consider nominating a blogpost, your own or someone else's, for the sixth edition, to be held at Great Maths Teaching Ideas by William Emery. It's a very active blog with many K-12 activities, so don't wait a month to check it out!
Congratulations if you recognized the five connection for each of the images above. I tried to slip in some tricky ones.
If the carnival is done, must be time to head over to the Five Bells. Cheers!