Who Invented Calculus: A WebQuest

A few weeks ago, I tried my first WebQuest. If you don’t know what they are, you aren’t alone. I in fact only learned about themfrom randomly stumbling across it during one of my many hours of traipsing around in the internet aimlessly. In a nutshell, a WebQuest is an assignment that you put on the web with instructions for kids to follow — and all the work they are doing comes from resources on the web.

With a spare day to kill, and a non-AP class full of seniors who generally seem to like writing papers more than they like writing equations, I decided to try it out. I had a few goals:

1. This was early enough in the year that my kids were in the middle of limits. They didn’t know anything about derivatives or integrals, or what calculus is, except for my rant. I wanted them to do some research on their own to learn what calculus is.

2. I wanted my students to learn that math was (and is) not done by robots in ivory towers, simply working to torture them. It was (and is) made by real people, forged in the crucible of a historical and cultural moment.

3. The history of math might bring more interest to some of the ideas my kids were studying (and will study).

So I modified a WebQuest I found and created this (click picture below):

The name is misleading. As my kids read each of the tabs carefully, so they knew my expectations, they soon learned that I wanted them to investigate Newton and Leibniz. And instead of asking “who invented calculus” they were supposed to take a side on who they think deserves the most “kudos” for calculus. They were then supposed to write an editorial defending that position.

As a former historian of science, I know that it’s a terrible question. As a math teacher, I don’t care. It got them talking and interested!

The implementation:
I gave students one 50 minute class period to work on their pro-con lists for Newton and Leibniz. They of course used their laptops, and were allowed to pair up — but only for those 50 minutes. Then over the weekend, they were asked to finish their research and write their editorial individually. They were asked to turn in a paper copy of their notes, their editorial, and their bibliography (and turn in an electronic copy of their editorial to share with the rest of the class).

The analysis:
Overall, I think it was a great use of time. Many of my kids really got into it, watching the videos and reading the articles. They found some of the reading really hard to follow, but I believe that is part of the skill set they should be acquiring in high school. Given a lot of information (a.k.a. the internet), how do you sort it and make sense of it? During classtime, a few kids did slack off a bit, not fully taking advantage of 50 minutes of research. Their papers suffered as a result of it. I really liked how much my students got into trying to figure out what an infinitessimal was, what a fluxion was, and — the biggest point of intrigue for every kid — did Leibniz plagiarize? Those who are great writers had a place to shine in my class.

If you want to see their papers (remember, they didn’t have a long time to write them, so give ’em some slack), browse ’em here.

I am definitely using this WebQuest again next year. However, I had some thoughts. First, so many students had such great research that being limited to just 1.5 pages double spaced was hard. They couldn’t use all their work. Maybe I’d make the assignment longer (two class periods to work, a week to write the paper)? Second, I’d really refine the question. “Who deserves the most kudos” needs more fleshing out or rewriting for the kids. Third, I’d like to get some primary source documents to throw into the mix. Fourth, and most importantly, I wonder if I would wait a bit until we at least had started derivatives before using this WebQuest again. It would be so exciting for kids who have just learned basic derivatives to read about infinitessimals and philosophy!

Anyway, feel free to use the WebQuest if you have a spare day and don’t know what to do.

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5 comments

  1. How about –

    Bell:Telephone as _____:Calculus

    Although Bell is credited with the patent, there are numerous inventors who claimed they invited it first. Bell just had a better sense of PR. Given what you said about your goal of the project, I wonder if that title might steer your students toward the idea of who should get their name associated with Calculus without getting bogged down in a question you’re not crazy about.

    1. I thought about that, and in fact one of my kids brought it up, but I wanted them to really learn about Newton and Leibniz. No reason you can’t add Archimedes in the mix though.

  2. Asking who invented calculus is really like asking who wrote A Thousand and One Nights, or Cinderella, or the Old Testament: it is a compendium of ideas, stories, and applications that have accrued over time, set to print by more than 1 person, and have origins in the misty contrails of history. But for my money Leibniz is the man. His original works look more like what we see in calculus books of today than any other. Principia Mathematica is more a work of physics and because of his obscure invocation of fluxions got Berkeley’s underrobes in a bit of a wad. Leibniz with his monadic concepts of infinitesimal at least had more philosophical substance with which to analyze things. I still think that philosophers make much better pure mathematicians than physicists – take that Kaku!

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