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

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 ...


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 ...


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

I don't know if this is the right dollar amount, but I think getting access to a 3d printer and making some useful manipulatives of your choice with it would be cool. That is, if you are in a large district and have enough time to invest in trying them out - I don't think it's a one-off process! As an example, Henry Segerman's website has some absolutely ...


4

Secondary math is a pretty broad subject for something as individualized as manipulatives, but this is a list of things I'd love to have if I were teaching every subject in the same year for some reason. A two-pan balance scale and a bunch of clearly-labeled weights (Algebra I) - I feel that it can be really evocative how an equation like $3x+4=16$ can lead ...


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.


3

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

I have a browser-based app I use where students wiggle the mouse and see graphs of position, velocity, and acceleration. These are the tasks I use with this. task 1 Your goal is to produce an x-t graph that looks like a staircase going down and to the right. Discuss with your group (a) how you would need to move the mouse in order to accomplish this, and (...


2

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


2

I might think about some iconic objects of the past that excite interest, perhaps mainly in geometry. Drafting table (probably $500 for a professional one, but you can check second hand). French curve as Rust mentioned. Slide rules. Parallel rulers and 10 point dividers (good for poking people when bored...I would know). Sextant. Abacus. Towers of ...


1

As a no-cost option that gives you so many capabilities besides the conventional black/white-board, I always use geogebra. Not only as a demonstration tool, but also as a functionality for the students to investigate almost anything in precalculus or algebra. By simply adding, e.g. some moving graphics you can easily explain why, say, $e^x\approx\left(1+\...


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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