## Props and Equipment for Paradigms Activities

### Spins OSP Software

The Spins software, an elegant and simple simulation of the Stern--Gerlach experiment, is used extensively in the Spins and Quantum Measurement Paradigm.

### The Partial Derivative Machine

The Partial Derivative Machine is used as a method of physically interpreting the concepts behind partial derivatives. Instructions for making your own can be found at Building the PDM: Instructions.

### Whiteboards

We use three different sizes of whiteboards for various activities:

#### Wall-Mounted Whiteboards

These whiteboards are large and vertically mounted on the walls (like the front blackboard). We use these for activities where student groups present their results/calculations to the rest of the class.

#### Tabletop Whiteboards

These whiteboards are about $2'\times3'$ and lie flat on the groups' table/desks. We use these for most small group activities as a workspace for students to share their ideas with other members of their group (and so that the instructor can easily monitor the group's progress!).

#### Individual Small Whiteboards

These whiteboards are ideally $12''\times18''$ and are for individual use. Students can each respond to a Socratic question and the instructor can collect these whiteboards for discussion with the whole class.

You should be able to purchase the whiteboard material at any home improvement store (e.g. Home Depot). It is technically melamine, but that word just confuses many employees; instead ask for “that shiny white shower board stuff.” It should come in $4'\times8'$ sheets, plywood-size, approximately \$10/sheet. Make sure that it is smooth and shiny and on a thin backing. Backing should NOT be plywood (it comes this way, but is too heavy). Thickness maybe $\frac{1}{4}"$. You can get five medium sized whiteboards ($2'\times3'$) out of one sheet (if you are clever) and 24 small white boards. Often the home improvement store will cut them for you at a small charge per cut.

If you buy framed whiteboards, ready-made for classroom use, they will be much more expensive. For large, wall-mounted whiteboards, you can build a frame yourself. Don't forget a “chalk” tray! But, if you are going to use the wall-mounted boards for many classes over many years, it is probably worth investing in professional enamel-on-steel boards available from classroom suppliers.

### Model Observer

We use a small model (about 10--15 cm) of a person to help students learn how to do proofs by contradiction when using Gauss' and Ampere's Laws. Index cards or cardboard cutouts allow the students to decorate them (which a large percentage do).

### Spheres and Cylinders

• Spheres: various size balls (e.g. basketball, soccer ball, tennis ball, ping pong ball, etc.).
• Cylinders: a piece of thin cardboard or cardstock can easily be taped or stapled into a cylinder.

### Butterfly Net

Make a "butterfly net" with a hanger or other wire loop and a cloth lingerie bag. The butterfly net is a used when discussing Stokes' Theorem. By changing the shape of the net, you can demonstrate how different surfaces might have the same closed boundary. By bending the wire, you can show what it means to change the boundary.

### Cube

Similar to the butterfly net, storage cubes can be used to help students visualize flux through a cube. By stacking the storage cubes together, it is possible to show how the flux out of one small cube is the negative of the flux out of the adjacent cube---this is the fundamental idea in the proof of the Divergence Theorem.

### Coordinate Axes

Students encounter a variety of orthogonal coordinate systems in their courses on electrodynamics. To illustrate orthogonal coordinates, the instructor can use a set of coordinate axes with which they may place different labeled unit vectors, allowing students to visualize the coordinate system they are working with.

A paddle wheel (in this case, made out of snap-together constructive toys) can be used to demonstrate the effect of a vector field on a physical system as part of a discussion of curl. Geometrically, the direction of the curl is the direction of the axis of the paddle wheel when the wheel is oriented in the plane of maximum circulation.

### Pumpkin Quarters

A pumpkin that has been sectioned into quarters can be used as an interactive physical representation of a spherical coordinate system.

### Pineapple Sections

Canned pineapple sections can be used as an interactive physical representation of a cylindrical coordinate system.

### Surfaces

We use plastic “surface” graphs of multivariable functions that are dry-erasable, transparent, and lightweight. The surfaces were created as part of the Raising Calculus to the Surface and Raising Physics to the Surface projects. Surface Kits include a surface, its corresponding laminated contour map, and a slope measurement tool.

### Contour Maps & Vector Maps

We print out contour maps or vector maps and put them in dry-erasable sleeves. Often, our maps correspond to plastic surfaces.

### Equipment Primarily Used In Labs

• Force Meters
• Oscilloscopes
• Coaxial Cable
• Thermometers
props equipment