cheesemonkey wonders

cheesemonkey wonders

Monday, May 30, 2011

Unmediated Experience, part 2 —
another use of primary texts in the math classroom

While gathering problems for my logarithms and exponential functions unit from some of my favorite textbook sources, I noticed that John Napier's birth and death dates (1550-1617) looked kind of familiar — really familiar, in fact.

And they're awfully close to Galileo's birth and death dates too (1564-1642).

So why not at least mention the historical context of logarithms?
I had translated Napier's Latin preface to his Description of the Wondrous Canon of Logarithms and was thinking about formatting it as a handout for students. So when Kate Nowak asked if she could publish an early version of my translation. Then Sam Shah e-mailed me about his inspiring idea of having his kids read my translation aloud in class. So I decided to follow their always excellent examples!

I played some Renaissance dance music from very close to the period as students entered the classroom — Calliope's album Calliope Dances: A Renaissance Revel ( ) is a great choice for this. If you only want one song, choose Praetorius' Galliarde (1), which is Track 1 on this album ( ).

I then gave a very brief mini-lecture on how Napier's invention of logarithms were to Renaissance astronomical calculations as our ubiquitous pocket calculators (and calculator iApps) make such calculations for us today.

We then did a practice activity based on Kate Nowak's "Add 'Em Up" practice structure but for solving logarithmic equations (students working in groups of four are given four different colored sheets each with four problems on them; each person does a problem and passes the sheet around to the next person in their group. When all the problems are done, the group adds up their answers/approximations and compares them to the color-coded answers posted on the side wall).

Students seemed to enjoy the change of pace and liked knowing how and why the mathematics they were learning arose and what it was related to historically.

Next time I might have students read and do something with James Tanton's excellent "Story of Logarithms" write-up.

Here is a link to the Napier preface handout, formatted as a PDF and available freely on : Wondrous Canon of Logs

Here is a link to my Add 'Em Up homage to Kate Nowak's practice activity:  Add-Em-Up-Logarithmic-Eqns



  1. There's a growing interest at the university level in making use of primary texts in mathematics classes. One of the driving forces is David J. Pengelley of New Mexico State University, and his webpage ( is a gold mine of resources.

    I've only seen primary sources used once at the high school level, Euler's Calculus (accessed on Google Books, not sure the exact work) but I'm not sure this course was implemented effectively.

    I'm currently re-tooling my Abstract Algebra course for pre-service teachers to include primary sources as an essential component. I might just blog about it...

  2. @TheMathWizard- This sounds amazing. Pre-service teachers definitely need to hear about the idea of using primary sources. In my program, the only reason people heard about it was that I would not shut up about it. ;-)

    I love David Pengelley's materials and web site. They are a treasure trove. I found his (first) textbook used and I hope to use at least one of his units next year. For those who don't know about his work, there's a rich overview at .

    He and his research partners wrote a terrific article about their experience using these materials with high school students in a summer workshop:

    I will watch your blog with great interest for more about your Abstract Algebra course!

  3. Hi,

    I came across your blog via David Wees, and I love this particular article about how all three have similar dates! That's the kind of "wow" things that kids love.

    As a fellow mathematics educator I thought you might be able to help in spreading the word about an educational TV show about math that we're putting together. "The Number Hunter" is going to do for math education what Bill Nye The Science Guy did for science education. I’d really appreciate your help in getting the word out about the project.

    I studied math education at Jacksonville University and the University of Florida. It became clear to me during my studies why we’re failing at teaching kids math. We're teaching it all wrong! Bill Nye taught kids that science is FUN. He showed them the EXPLOSIONS first and then the kids went to school to learn WHY things exploded. Kids learn about dinosaurs and amoeba and weird ocean life to make them go “wow”. But what about math? You probably remember the dreaded worksheets. Ugh.

    I’m sure you know math is much more exciting than people think. Fractal Geometry was used to create “Star Wars” backdrops, binary code was invented in Africa, The Great Pyramids and The Mona Lisa, wouldn’t exist without geometry.
    Our concept is to create an exciting, web-based TV show that’s both fun and educational.

    If you could consider posting about the project on your blog, I’d very much appreciate it. Also, if you'd be interested in link exchanging (either on The Number Hunter site, which is in development, or on which is a well-established site with 300,000 page views a month) please shoot me an email. We're also always looking for input and ideas from other math educators!

    Thanks in advance for your help,