Activities, Writings, and Videos by Debra K. Borkovitz
Use the slider to change the value of k, and to see dynamically how the graph of \(h(x)=k^x-x^k\) changes. Negative values have \(x^k>k^x\). Which value of k gives a graph that is never negative? Why? Here is a very pretty … Read More
Which is bigger, the sine of 40\(^{\circ}\) or the sine of 50\(^{\circ}\)? This is a great trigonometry assessment question. Unfortunately, virtually none of my college students who haven’t used trig for a while can answer it (without a calculator). For … Read More
The handshake problem is an old chestnut — if everyone in the room shook hands with everyone else, how many handshakes would there be? Then generalize. What I have to add to teaching the problem is a handout (doc version, … Read More
This is a great first day of class activity, which works well with math phobic students (I use it in a math for elementary teachers class). Students make a list 1:00, 2:00, etc. on a piece of paper — however … Read More
This is a classic problem solving activity that I first saw many years ago in Mathematics: A Human Endeavor. The NCTM has a nice applet to test cases one at a time. Since I like playing with Excel and … Read More
I made this video when I was thinking about ways to teach the basics of linear transformations and matrices by illustrating their connections to computer graphics. I wanted to show the actual matrix calculations that lead to the graphics, as … Read More
Puzzle books I had as a kid often asked what the intersection of three cylinders looked like. Even looking at the answer in the back, I still had trouble seeing it. Making this video helped a lot. The Sketch Up … Read More
This is my first Sketch Up video. It is surprising how many shapes the cross-section of a cube can take on, and how hard they are to visualize (for most of us). The Sketch Up file I used is in … Read More
Visual Quadratic Reciprocity
This one’s harder.