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This slide show demonstrates some techniques that would be suitable for an experimental geometry project. The basic shapes of square and circle are explored using open source Geogebra and Dr Geo geometry software. The examples includes exercises in geometric construction, novel solutions and recursive (spiral) constructions. This is mathematics that can be done without algebra. There is some algebra on slide 18, to calculate the radius and area of a semicircle inscribed in a square.

Students in grades 5+ practice reflections, rotations, and translations.

"Use the display and the slider to see how shapes up made up from their nets." Nice visual showing one net for each solid 'fold' up to make it.

A book by Reuben Hersh and Vera Johnson on the "hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians."

Mathematicians at Ohio State University have developed new equations to "describe the shape and motion of single cells for laboratory analysis."

4 Middle School math games: Decimal Detective, Bridge-It (geometric shapes), Fraction Junction, Golf (analyzing angles)

It would be interesting to build a set a links to similar research results as this and discuss the implications this has for what we do as math teachers in our classrooms.

New research from Vanderbilt University has found students benefit more from being taught the concepts behind math problems rather than the exact procedures to solve the problems. The findings offer teachers new insights on how best to shape math instruction to have the greatest impact on student learning.

This just confirms what all the other research has been saying. The issue is getting all of us who didn't learn math conceptually, and who were not trained in college conceptually, to teach this way.

Can you eyeball these geometric shapes?

Part of a virtual tour of geometry math movies. Representing 4D shapes as projections in 3D.

Abstract: "Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry. "

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by David Berlinski, published January 2013. "In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements. Berlinski shows that, for centuries, scientists and thinkers from Copernicus to Newton to Einstein have relied on Euclid's axiomatic system, a method of proof still taught in classrooms around the world. Euclid's use of elemental logic-and the mathematical statements he and others built from it-have dramatically expanded the frontiers of human knowledge. The King of Infinite Space presents a rich, accessible treatment of Euclid and his beautifully simple geometric system, which continues to shape the way we see the world."

A review of Paul Lockhart's new book with a focus on mathematical reasoning and geometry, with a video of the author.

Published in 2014, tells the story of how, in the seventeenth century, Italian Jesuit authorities evidently tried to suppress the idea of infinitesimals in mathematics and how subsequently their flourishing led to the development of calculus and shifted the balance of world culture and the influence of nations.

A great flash based angle finding and protractor whiteboard resource. See a variety of angle measuring activities and use the virtual protractor to solve them. http://ictmagic.wikispaces.com/Maths

A great maths site with flash resources, online tests and worksheets on a range of maths topics to print or use on your whiteboard. http://ictmagic.wikispaces.com/Maths

A fun maths angles game where you must find the attacking ninja at the correct degrees before he attacks you. There are three levels of difficulty. http://ictmagic.wikispaces.com/maths

Review of 1999 book on cosmology demonstrating universal phenomena contingent on six numbers. "Forget those 1,000 things you need to do before you die, the 10 commandments and seven deadly sins. Concentrate instead on six impossible things that, as the White Queen advised Alice, you must try to believe before breakfast. Without them there would be no galaxies of stars, no chemistry, no people, no books and no breakfast."

Several photos of Robert Wexler's work, also featured in the recent Money issue of the New Yorker.