5

This is not what you seek, because it compares two different physical manipulatives, rather than physical vs. virtual. But I find it interesting partly because my own research involves studying nets of polyhedra. Scott, Jacqui, Anton Selvaratnam, and Lynden Rogers. "Using Bendable and Rigid Manipulatives in Primary Mathematics: Is One More Effective Than ...


4

I have used polydrons with 5th-grade students through to college students:           A store in Massachusetts used to sell them, but recently I've had to purchase them from England.


4

Here's a piece comparing virtual manipulatives to traditional teaching without manipulatives, in the context of community college remedial courses: Violeta Menil and Eric Fuchs, "Teaching Pre-Algebra and Algebra Concepts to Community College Students through the Use of Virtual Manipulatives", Improving Undergraduate Mathematics Learning, CUNY Office ...


3

Here's a piece comparing virtual manipulatives to traditional teaching without manipulatives, in the context of community college remedial courses: Violeta Menil and Eric Fuchs, "Teaching Pre-Algebra and Algebra Concepts to Community College Students through the Use of Virtual Manipulatives", Improving Undergraduate Mathematics Learning, CUNY Office ...


3

Sphere: No problem. Torus: Swim Ring. Double Torus: Figure Eight (rock climbing), but could be to small for your purposes. $n$-Torus: Craft them yourself fronm Polystyrene and cover them with paper to draw upon. Non-orientable, bounded surfaces: Hmm, not possible, if you really want to draw triangles upon them.


2

A planimeter is a wonderful little device that measures the area surrounded by a simple closed curve by tracing it. It is based in the version of Green’s Theorem that computes area by integrating vertical/horizontal displacements along the curve.


2

In chemistry, it is still common to integrate some test results by cutting the curve out and weighing the paper.


1

There are several vendors, but I was unable to find shapes that differ in holiness. Instead, they are different in size, color, shape and thickness. They seem to go by the name attribute blocks or logic blocks. They are available at amazon or, as @AmyB said in the comments, here: http://www.minilandeducational.com/en/logical-blocks/


1

Usual bubbles can be freezed. See Bubbles freezing at -26°C and Frozen Bubbles 01-24-11. According to WikiHow no special bubble mix is required. Obvious idea: use very cold water to minimize the required time.


1

For spheres, balloons would work well. Everyone could have a balloon and a marker and draw their own triangulations. You can imagine the awesome squeaking noise. An advantage of this would be that people could try to draw really funky triangulations to test if the Euler characteristic actually worked. I feel starting with spheres (ie balloons) and trying ...


1

Instead of finding a pre-built object and drawing triangles on it, we've settled on just building the objects up from scratch using Zometools, which is a more engaging plan anyway. There is a small problem where when you build a torus out of these toys, it's hard to tell which "faces" are faces and which ones are not, so the solution is to stick your arm ...


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