#### Visualizations

I am a visual learner and have found most students understand better with visual aids as well. To this end I have used and developed many visualizations to help students make connections. Recently we were working in my Calculus II class on pumping problems and were pumping from a hemispherical tank. We'd drawn the tank on the board but as class was ending, several students were not getting the picture so that they could use the geometry of the problem to find what was needed. I returned to my office and built a visual that we started class with the next day. (see video below)

I also went out into my husband's shop the previous night and rounded up some metal to help students visualize the triangular trough we'd been working on as well. After showing them that visual aid, when I asked them what a cross-sectional slice would look like, every one of them had it. As technology has evolved, so have many of my visualizations as there are some great things on the Internet shared by other faculty, but the low tech foam pieces I bought and cut and rounding up scrap metal pieces work great too!

Shoeboxes make nice vector spaces and jumbo legos are great for thinking about a collection of vectors of which you can build any element in the vector space and for talking about linear independence (can you build any of the collection of vectors witha combination of some of the others?) and visualizing a basis for the vector space.

## Foam for washers and shells, nested bowls for chain rule, 3D axis welded by my husband, torque demo & triangular trough.

Here is a collection of a few of my favorite visualizations I've built over the years.