Arithmetical Frames

Back to Math Words Alphabetical Index

The first part of this is from a blog I wrote, which is self explanatory, and as I find more detail, I will add below.

I've been teaching for a while, ok, a long while, and one of the ways I pay back my dues for all the folks who helped me out along the way is by being an associate at T2T, a site hosted by Drexel University where teachers can get questions about teaching answered... so everyone doesn't have to reinvent the wheel.. It's free and if you are lucky, one of the clever associates will answer your question before I get to it, but be warned, if it is about word origins or the history of math teaching, it might fall to me...

On just such an event a few weeks ago, a young man named Sal wrote and asked about the teaching machine shown at the top that had been found when a high school closed in New Paltz, New York in the Forties...(Another picture is located here ....

I sent off notes to all my ususally clever friends, and eventually one of them turned me on to Ms. Peggy Kidwell, the curator of mathematics at the Smithsonian Museum... now aren't you impressed that the Smithsonian has a curator for Math... I'm impressed. It turns out that this question was right down Ms. Kidwell's alley. She is a co-author of Tools of American Mathematics Teaching, from the Johns Hopkins University Press, which is brand new this year.

Ms. Kidwell wrote, "I have never seen this particular device. It has some similarity to an instrument, patented in 1864, that had a series of rotating slats, with several digits painted on each side of each slat. By rotating the slats and marking off problems with a thread, teachers could provide a wide range of arithmetic problems. The inventor of this “arithmetical frame,” a teacher named Henry K. Bugbee, even provided a written Key which gave answers to the questions."

She went on to add that,The arithmetical frame was slightly modified by John Gould in the 1880s." [For an image, see here]

I even went on to suggest that the machine Sal had sent me pictures of would allow the teacher to pull down the shades over some of the digits to reduce the difficulty of a problem for different levels or ages of students.

So, not a bad day all in all, I learned a little about the history of math education, and one note struck me as particularly interesting that I found on the Smithsonians site for the image above. It said, "It was very popular in Catholic schools in New York State." It seems very strange to me that parochial schools would have been more attracted to a particular type of math teaching machine than public, or other private schools... Guess you really do learn something everyday.

In the blog I left off one more piece of information Ms. Kidwell shared on the development of frames, "Another form of arithmetical frame was patented in 1881 by one Frederick B. Ginn of California . In it, there appear to have been continuous strips that ran around the back of the machine (see here