This Could Have Been an Email - Teaching Edition

I have two pet peeves in this world: people wasting my time and me wasting other peoples time. I recently realized that I've been wasting my students' time and my time by creating videos that could be Blackboard announcements. I've decided to stop making as many videos and focus on other ways of connecting with students.

During my online teaching professional development, I was taught to use introduction videos to help students start to form a connection with their instructor. Of course, I can't stop with just one video. I have to make a video for each week of the course. Since I'm terrible on camera, these videos take longer to make than is reasonable. Also, no one watches the videos after the second week of the semester.

To try to maintain some personal connection, I plan to record the weekly posts as an audio file and upload it next to the script. That way students can choose either option. This also covers my bases for accessibility. Because audio files are easier to edit and looking good on camera isn't an issue, the whole process goes faster.

A welcome message for Liberal Arts Mathematics. There is an audio file player above the written text.
Student view of a finished welcome message.

Also, it is possible to use the recording process to create videos as well. It works pretty well to solve a problem and scan each step in the process. I can create PowerPoints with the scans and other text and then save the whole thing as a series of images. A video editing program can assemble the images with the narration. It is possible to do this entire process in PowerPoint, but I like to edit the audio first. This post from the Audacity wiki shows exactly how I edit my audio.

Long term, I'd like to assemble all of the audio recordings into a single file for students to download. This is an idea I picked up from Michael Wesch. It may not work as well with math as it does with anthropology, but that's a problem for later.

Since my perfectionist tendencies have to be appeased somehow, I decided to build a recording area in my messy garage. With $45 worth of PVC pipe and Harbor Freight moving blankets, I managed to pull something together. There is a frame built out the PVC pipe and some fittings. The blankets are clamped to the frame. It's not professional quality, but a little effort goes a long way.

Two shelves hold some moving blankets.
I can fit myself, a microphone, and a recorder in there.

A piece of lumber holds up a PVC pipe frame. A moving blanket is clamped to the frame
Close-up of the frame and blankets.

One-Upping the Stand Up Mathematician?

In October of 2021, Matt Parker - number 3 on my list of YouTube man crushes - and Hannah Fry released a video on YouTube demonstrating how to measure the radius of the Earth using a tall building and protractor. Their attempt was moderately successful despite facing several obstacles. On a recent family vacation, I realized I had the perfect opportunity to make a more accurate measurement. Keep reading to see how our estimates compare.

Hannah and Matt

The process outlined in the video requires an observer to climb to a high point and measure the angle of declination down to the horizon. Using your elevation, the angle of declination, and some surprisingly elementary trigonometry, you can calculate the radius of the Earth. This method was devised by 10th Century mathematician al-Biruni. Using his method, al-Biruni was able to calculate the radius with surprising accuracy.

Hannah and Matt had several difficulties to overcome in their experiment. The main problem was getting their measuring equipment through building security. Additionally, Matt insisted on measuring the height of The Shard through trigonometry.

The duo's results are:

  • Height of observation deck: 263m (Actual: 244 m)
  • Angle of Declination: 1.5 degrees
  • Radius of Earth: 875 km (Actual: 6371'ish km)

Visiting the Perfect Location

Visiting the perfect location for this experiment was a lucky coincidence for me. There was a mountain with high elevation located close to the sea on our vacation itinerary: Haleakala. The lack of building security is a plus.

Haleakala Visitors Center sign. Elevation 9740ft or 2969 m.
Photo Credit: Emily Sears

Standing on the top of a volcano was the one experience I wanted out of the trip. We took a tour bus up for sunrise. The pickup time was 2:30 am, which sucked. The rest of the trip was amazing.

There was a healthy crowd at the Visitor Center. Fortunately, everyone was respectful. That is not always a guarantee, but the Aloha Sprit was with us tourists. The light of sunrise played nicely with the cloud layer below. I was able to poke around the crowd to get a few shots. The thinner air at the top made moving around more difficult. I hiked up to the higher observation area, and had to stop every few minutes to catch my breath.

Silhouettes of people watching a sunrise over Haleakala.
Silhouette of the Crowd. Photo Credit: Chris Sears

The sun rises of a cloud layer.
The view from the top. Photo Credit: Chris Sears

The clouds enhanced the natural beauty, but they worked against my secondary objective for this trip. Finding the horizon turned out to be a problem. The clouds started to break enough to see the ocean. If we had stayed for an extra half hour or so, the view of the horizon would have been clearer. With the tour bus loading, I made the best measurement I could.

A measurement of 0.95 degrees seemed good enough for me. I remembered that Hannah and Matt should have measured around 0.5 degrees from The Shard. A larger angle is expected from a higher height. I was happy with the result. My family was happy I stopped talking about math for the rest of the morning.

View of the Pacific Ocean from Haleakala. Clouds obscure the horizon.
The view of the horizon. Photo Credit: Chris Sears

A digital level reads 0.95 degrees.
0.95 degrees was the best I was going to get. Photo Credit: Connor Sears


After returning to the mainland, it was time to crunch the numbers. Here are the results:

  • Height of observation: 2960 m (Rounded to three significant digits and adjusted for standing below the Visitor Center)
  • Angle of declination: 0.95 degrees
  • Radius of Earth: 21500 km (Actual: 6371'ish km)
Well, that is disappointing. Matt and Hannah were off by 86.3% of the actual value. I was off by 238%. Looks like I'll be eating the humble pi tonight.

It is possible to work backward to find the proper angle measurement for a height of 2.96 km. I should have measured 1.75 degrees. This is one time where aiming for the clouds was the wrong thing to do.

The video below shows how I made the computations.

Site Updates - June 12, 2022

The past month has served as a sieve for my interests and priorities. Now that I'm off contact for the academic year, the pressure to perform is gone. The main realization born of this freedom is how much energy I spend on existential crises. I worry so much about leaving a legacy that I forget to get stuff done. I'll spare you the manifest of the contents of my navel and move on to the actionable bits.

The most recent change is deleting my regular site. The purpose was to serve as a virtual filing cabinet of all my materials. Blogger is capable of serving this purpose with less upkeep. Best to move it all to one place. The pages of this site will expand over the summer. Also, the URL now directs to the blog.

I deleted my TikTok account. If social media were food, TikTok is cake. Baking a cake can be an act of high skill and artistry. However, the nutritional value is always low. YouTube is saturated with instructional videos, so TikTok looked like a fertile place to stake a claim. After some reflection, I realized it is very difficult to post meaningful instructional videos on TikTok. The format is designed to keep a person's attention on the site, not to watch a few videos and start their homework.

Admitting that I'm late to the YouTube game and cannot possibly catch up to other creators is actually liberating. I'll never be Sal Khan or James Sousa. (I never wanted to be the former.) I can make the videos I need for teaching and be happy about it. Keeping one eye on the YouTube algorithm leaves only eye to create content.

My potential calculator channel on YouTube is getting repurposed. The plan was to have a separate channel for short calculator tutorials. YouTube Shorts gets higher views than regular videos. Conventional wisdom says that mixing shorts with regular videos will confuse the algorithm. Since I don't care about appeasing the YouTube algorithm with my math channel, I'm going to give up on the idea of a separate calculator channel. Instead, I'll create a coding channel instead. I have a natural niche in how I use computer programming. Building a channel out of that should be both fun and an opportunity for self-expression.

Site Updates - May 11, 2022


A view of the Worksheets page on
I had a busy day updating my worksheets for Foundations of College Algebra. After scrambling all year to get above water, I finally arranged to get the help I needed. The rest of the department and I are sharing our materials. I have been polishing my worksheets to share. As I finish them, I'll post them on my main site.

Worksheets landing page.

Site Updates - May 5, 2022


Now that the semester is winding down, I can turn my focus to lower priority tasks. That includes updating my site. My goal is to put an entire Calculus textbook on TikTok and collecting the videos in the website. To get caught up, I made the following changes:

  • Set the URL to point to the Google site and not this blog.
  • Add subpages to the Video Calculus Textbook for Introduction to Calculus, Fundamental Theorem of Calculus, and Integral by Substitution.
  • Remove the subpages from the site navigation.
  • Embed four TikTok's into the pages above.

I'm still on the fence about using YouTube or TikTok for math videos. My mind says YouTube and my heart says TikTok. More on that later.

Getting Back on Track


Photo of "Charting Your Course" by Richard Pregent and Anger from "Inside Out."

Toward the end of each semester I get a feeling that I could be doing better at teaching. That thought hit me today. In addition to the COVID pandemic, our college has been without a president for two years. The lack of leadership meant extra inertia with returning to pre-pandemic teaching practices. The interviews for the new president are concluding while I am writing and an announcement of the pick is due to be announced by the end of the day Thursday. With a sense of closure on the COVID era pending, it is time to get back to work.

The largest struggle during the pandemic was online teaching. All of the training I received about online teaching was related to creating course shells in Blackboard and audio-visual technology. Blackboard is not easy to use but I can manage to get around. My hobby is photography and making videos, so I am already comfortable with those. Where I struggle is managing students in an online class. I am aware that there is more to online teaching than babysitting a Blackboard shell, but I do not know what the extra activities should be.

After visiting the library and gossiping with the librarian, I decided to go back to the very basics. Charting Your Course: How to Prepare to Teach More Effectively by Richard Prégent is as close to Teaching for Dummies that I could find. It seems like a quick read so far. It will be worth going through it even through it will cut into my TikTok time.