A New School Year, a New Approach

I’ve written a few posts over the past few years about flipping some of my courses. Flipping a course involves recording a screencast of the content and having students view the screencast for homework. When they come to class the next day, the teacher is available to work with them on the problems. So, the lecture part of teaching is “flipped” with the homework part.

This year, I’ve decided to hold my students more accountable for watching and understanding the material in my screencasts, and after talking with my department chair, I’m making some changes.

First, before they watch a screencast, I will hand out a worksheet (see attached file below for a sample) with the problems and examples that I cover in it. Students are expected to write the solutions to the examples as they watch, as well as fill in blanks where appropriate.

Second, I will ask them to solve one or two similar problems on their own before they come to class. I will check to make sure they’ve done them.

Third, I will see each student individually and ask her to solve a typical problem while I’m watching to make sure she has mastered the material.

Hopefully these steps will help my students take responsibility for learning the material I am including in their course’s screencasts.

Here’s the first worksheet for my College Algebra and Trigonometry Course:

Sec. 1.2 Worksheet

And here’s the corresponding screencast:


Visualizing in 3D

I introduced my precalculus students to vectors in 3D space yesterday. They have a hard time visualizing the 3-dimensional axis system, especially since the familiar XY-plane is now on the “floor”:

3D axes

To help them understand how 3D coordinates work, I paired the students up, and gave them a slip of paper that read:

This landmark is ( ______, ______, ______ )

steps from the northwest corner of Mr. Wert’s classroom.

Using the northwest corner of my room as the origin, they went all over campus and picked a spot to put their label on. They had to keep track of how many steps they walked in the x-direction, the y-direction, and the z-direction. Here’s an example:

3D landmark

Actively keeping track of their position using 3D coordinates really helped them understand how the x, y, and z coordinate system. works. After this, they were ready to work with vectors in 3 dimensions.

Fractals and Kindles

I just can’t help myself. Whenever I get a new gadget, I have to customize it. When my wife and daughters gave me a Kindle four years ago, I was thrilled. It’s a Kindle 3, and it opened to me the amazing world of ebooks. My library now includes collections of G. K. Chesterton, Charles Dickens, Fyodor Dostoyevsky, and Shakespeare. I like the fact that the screen isn’t backlit, so there is no eye strain. It’s a wonderful device that has completely changed the way I purchase and read books.

However, I thought the screensavers that Amazon preloaded on the Kindle were really unattractive, so I tried to replace them with images more to my liking. Easier said than done! I assumed that all I had to do was locate the folder containing the screensaver files and dump my own in there. It turns out Amazon does not want you poking around in there, so that folder is hidden.

Fortunately, after a little research online, I was able to hack into my Kindle and change the screensavers. There are thousands of great images online to choose from (just Google “Kindle screensavers”), and I had a blast exploring them. Then it occurred to me that I could create my own fractal screensavers – all that is necessary is to make sure they are gray-scale images that are 600 by 800 in size.

I decided to use Chaoscope to create my screensavers. (I posted a tutorial on how to use Chaoscope here.) Make sure you render them in either Gas or Liquid mode. My first batch is posted below. They are already correctly sized – just click on a thumbnail to access the full-size image, and then save it to your computer. Enjoy!