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Figuring It Out: Children's Arithmetical Manuscripts 1680–1880
Publisher: Huxley Scientific Press (2012)
Details: 59 pages, Paperback
Topics: Mathematics Education, History of Mathematics
MAA Review[Reviewed by Marion Cohen, on 10/25/2012]
My usual rule is: short books, short reviews. Let’s see whether I can adhere to that rule.
At first I thought the book might turn out to be boring. At first.
Well, there’s no really interesting math in it. And there’s a fair amount of history, my booby-prize subject throughout elementary and high school. True, there are plenty of pictures, but they’re not of flowers or people, and not in color; rather, they’re rectangles of writing, often unintelligible. In general, my first former-child’s impression was, dull dull dull, like a dictionary or Accounts Payable.
But then I got past the first couple of pages. Then I got past the next couple of pages. And then I realized I couldn’t put it down. It was 12:10 AM. I kept reading to the end.
I originally selected this book from this site’s list of “reviewables” because I’m interested in the math education, and the math itself, of young children. For eight years I was a home-schooling parent, or rather my two youngest were home-schooling children. Our approach was about as unstructured as a family can get. I did very little actual teaching of math, or arithmetic, reasoning that since arithmetic was a huge part of life, the kids would pick it up. We also played a card game involving arithmetic, only because we liked the game and not because I felt it would be educational. From that game the very youngest learned the basic arithmetical operations, including powers. (He was especially motivated to learn that one to any power is one, because each ace = one was worth one point out of a possible eleven.) Otherwise I didn’t do much math teaching, figuring also that they’d derive something out of their mother being a mathematician. At any rate, I’m interested in the history, not only of math, but of math education.
I learned a lot. The author is a retired math teacher and a collector of the manuscripts which are the subject of this book. Another name for them is “copybooks.” Teachers would teach, with or without textbooks, and the students, usually boys aged nine to fourteen, would do the exercises given them in these copybooks. The teachers often did not make comments or corrections. If they did, it was always orally; teachers never wrote in the copybooks. These little books belonged to the students. Each retained, at the end of his schooling, these copybooks, to use as souvenir or reference.
In this book the author frequently refers, with pride and joy, to his collection of copy-books. Page 3: “In my own collection there are books from all parts of England, from Cornwall and Kent to Northumberland and from Lincolnshire to Shropshire, with one or two from Wales and Scotland. I also have 7 from France, 6 from the USA, and 1 from Holland.” And on page 9:
The subject matter? Well, when I was in seventh grade, I got Cs in math. That was not only because seventh grade is, for many, a miserable year socially but also because, at least in my school, the math subject matter consisted of business math — and not the interesting calculus-derived formulas for compound interest or annuities. Much of the subject matter of the kids’ copybooks was of that ilk. No explanations and little, as I’ve said, “mathematician’s math.”
Proportions were taught using The Rule of Three, as well as the Double Rule of Three and the Double Rule of Three Inverse. The examples of problems from that era are interesting historically. Page 15:
Alligation and False Position were two other common topics. I would’ve gotten Cs, maybe Ds!
The book includes a description of school life and copybooks from the early 1800s by Rev. Warren Burton in The District School As It Was, by one who went to it, first published in 1833… The school was in New Hampshire. Pages. 6–7:
Here are some other interesting passages from the book that kept me reading past midnight. Page 23:
All this reminds me of some of my students’ drawings, for example, a cat on the bottom left of the homework sheet because “I had a feeling you’re a cat person.” I smile fondly as I re-read some of this book; kids will be kids, and kids were kids.
Chapter 7, pp. 33–35, is titled “The Wider Curriculum.” Ah, now we’ve made it past seventh grade! “…Included somewhere in the manuscripts there was work on geometry, algebra, trigonometry, conic sections, fluxions, mechanics, and even the arithmetic of infinities…”
Pages 36–45, comprising a large fraction of this small book, are devoted to the lives of the manuscripts’ authors. He calls them by first name and gives details of their personal lives. He seems as fond of these kids as he is of his collection of their copybooks. Page 41:
We, however, do get to read them, including the naughty juicy details of the kids’ lives and psyches. No, this book is not boring at all. Anyone teaching History of Mathematics can refer to parts of it and it will help enliven her course just as the kids’ illustrations enlivened their copybooks.
Marion Deutsche Cohen is the author of “Crossing the Equal Sign” (Plain View Press, TX), a collection of poetry about the experience of mathematics, as well as other literary works with images from math. She teaches at Arcadia University in Glenside, PA, where she developed the course “Truth and Beauty: Mathematics in Literature.”