Math in the late 1800's

Don Potter sent me a link to an interesting 1879 math book in Google Books, "Graded Work in Arithmetic" by S. W. Baird. It has an interesting visual method of showing fractions similar to how they're depicted in Math-U-See. (The unexpected results of web searches, when "Graded Work in Arithmetic" comes up under a search for "phonics charts." There are, of course, ads for phonics charts, McGuffey Readers, and some other books and visual aids at the end of the book.)

Looking through "Graded Work in Arithmetic" prompted me to look up Baird's "American Mental Arithmetic," which was even more interesting. His explanation of fractions for this book used a different method than his 2nd grade book and showed a number line explanation along the lines of Wu.

Also, his preface had the following statement (page 3 in the book, page 5 in google book pages)

"Many who have broken the habit, in adding, of saying "6 and 8 are 14 and 6 are 20," are still saying in subtracting, "6 from 10 leaves 4" ; in multiplying, "9 times 8 are 72, and 4 are 76" ; and in dividing, "12 [divided by sign] 5 = 2 and 2 remaining." Special stress is laid upon the improtance, in performing operations, of dropping all unnecessary words, since the mind reaches results much more rapidly without them."

Interestingly, Don Potter has told me in the past that his father could multiply with lightning quickness and would always say "five 3's are 15" instead of today's common "five times 3 equals 15." I've only taught Mary a few multiplication facts, but I try to follow the two 5's are 10 pattern when teaching her in case there is something to this...I figure it can't hurt and could be helpful. I still teach what the equals sign is and what it means, but I always have her say the shorter are instead of equals when reciting addition and multiplication facts out loud. (Are may also be less abstract than equals as well as shorter.)

Bailey also states,

"Percentage is taught without rules or formulae, and without the use of the terms base, amount, and difference, although one page is devoted to the after the subject has been completed. The student comes to see clearly that the various exercises in percentage do not need special rules, but are familiar cases slightly modified since the symbol "%" is used instead of hundredths. Interest is taught by the 6% mehtod and by the modification of this method in general use among bankers."

His concluding sentence of the preface is,

"Let it be remembered, that he who relies upon thousands of special rules is but a pygmy beside the giant who can apply a score of general principles to millions of particulars."

Perhaps we're the pygmies today for throwing all this out with the bathwater without trying to figure out if there were reasons for some of the things that were taught and some of the methods that were used to teach in the past.