Without education

we are in horrible and deadly danger…

The end of Al Kwarizmi’s foreword to The Compendious Book on Calculation by Completion and Balancing (Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala).

One benefit of a graphic designer doing game design is getting cool images  of fundamental ideas. From a post by Daniel Solis, with a link to a great Richard Garfield video.

This is a note so I’ll remember, from the conclusion of Tamara Nelson,  Holmlund, “Teachers’ collaborative inquiry and professional growth: Should we be optimistic?” Science Education, v93 n3, http://dx.doi.org/10.1002/sce.20302

“After 2 years of research with these and other PLCs, we are confident in making two strong assertions. First, it is not sufficient to merely create opportunities within a school day or in addition to teachers’ traditional work for teachers to come together as a PLC. Teachers need support for both the processes of inquiry and for the creation of an environment that models, nurtures, and embeds an inquiry stance. Second, targeted support is critical to move teachers past problematic areas: refining ambiguous inquiry questions, developing the trust needed to share student work, making sense of that student work in relation to their inquiry question, and promoting a willingness to wonder and ask critical questions about instructional decisions, classroom practices, and student learning.”

1. Opportunity is not enough
2. Ambiguous questions
3. Sharing student work
4. Making sense of student work
5. Willingness to wonder and question

Excellent advice from Watterson over at Brain Pickings. Check out the whole article.

My favorite topological construction. Equivalent to a ball?

the-sorcerer:

Alexander horned sphere

Saw this great image at Peano’s from Elijah Porter, (see his Flickr for much more mathart) and had to play around with it.

I love reptiling. So this GeoGebra sketch has a tool that divides up any quadrilateral in the trapezoid reptile pattern. Have fun! (At GeoGebraTube.)

Inspired by Geometry Daily #441, I had to see about making this multiples image. You see multiples, too? Maybe this is some king of math Rorschach test.

Which GeoGebra version do you like better? I think I like the criss-cross version… so that’s what I uploaded to GeoGebraTube. (Mobile version.)

A dynamisized version of Euclid’s proof of the Pythagorean Theorem. Steps, but you can still change the triangle to any right triangle.

At the ‘tube: http://www.geogebratube.org/material/show/id/38900

So what do you think about “dynamisized”? Dynamicized? Dynamicalled?

matthen:

The bending of a light ray depends only on the angle it hits the lens, and not on the thickness of the glass. This means thick lenses can be made thinner, as shown here.  This is called a Fresnel lens, and is used to make magnifying sheets as well as in lighthouses. [more] [video] [code]