Milne’s Mental Arithmetic

It is not very often that people are without a calculator of some sort close at hand. I’ve seen people whip out various cell phones to calculate tip percentages when at a group dinner. We hardly have a need anymore for true mental arithmetic. But have we lost something in the process of gaining speedy, error-free calculations? In his 1897 book, Milne’s Mental Arithmetic, William J. Milne claimed:

There are many who believe that Mental Arithmetic is one of the most valuable studies in a school curriculum. There can be no doubt that if the subject is properly taught it develops a habit of concentration of mind, which is one of the most desirable ends to be attained by any scheme of education.

Milne’s small book published in 1897 demonstrates his method. The book is not a collection of easy problems designed to give the student practice in the simple processes of arithmetic, but rather 172 pages of exercises of gradually increasing difficulty which enable the student with effort to solve problems whose solution might seem to be almost impossible without resorting to ciphering.

Here’s one of the first problems:

A boy has 2 cents in one pocket and 1 cent in another pocket. How many cents has he?

Before you think the book should be shelved because it is too infantile, consider this problem later in the book:

If I sell one of my two houses for $4500 and the other for $1860, I will gain 6% on the cost of both; but if I sell the dearer house at $4000 and the other at cost, I will lose 5%. What was the cost of each house?

(Don’t get distracted by the cost of housing over a century ago, and don’t pick up a pencil!)

The reason I keep this book and have used it in my math and science classes is because if you can do the first problem, and if you stick with every single step by step increment of increasing difficulty, you will be able to do the last problem.

When I taught algebra I would begin the year by writing “2 + 2 = ___ ” on the board. I would tell the nervous students that if they could do that problem, then they could learn to do algebra. It is all about learning the steps and slowly increasing the difficulty.

Want a quick example of mental arithmetic to wow young kids with? Everyone knows how to do multiples of tens and hundreds (just add a zero onto the multiplicand). Single digit multiplicands and the number 11 are also easy (5 x 11 =55). But what about double digit multiplicands? Quick, what is 17 x 11? You can find the solution quickly by adding together the two digits and putting that sum in the middle. So, 1 + 7 = 8; therefore 17 x 11 = 187. Try 32 x 11…. (3 + 2 = 5, so the answer is 352).

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