## Thursday, August 18, 2016

### Olde School

New School Algebra
by
George A. Wentworth

From the preface, a total of two pages from a small-format text:
The first chapter of this book prepares the way for quite a full treatment of simple integral equations with one unknown number. In the first two chapters only positive numbers are involved, and the beginner is led to see the practical advantages of Algebra before he encounters the difficulties of negative numbers.

The definitions and explanations contained in these chapters should be carefully read at first; after the learner has become familiar with algebraic operations, special attention should be given to the principal definitions.

Where to begin?

First, let's ignore the dated and politically incorrect use of the male pronoun as this was published well before women had the vote in the US or Eleanor Roosevelt published "It's Up To The Women." Then, the text is four hundred seven pages (not counting a whopping six pages of front matter) published in a four and a half by seven inch format starting with definitions and simple equations and covering multivariate equations, imaginary numbers, quadratics and simultaneous equations, properties of series and the binomial theorem. On average the book is more than fifty percent exercises (you know, where the learner does the work of learning by actually solving problems) with Chapter XII comprising fourteen pages with less than a page and a half of text and the remaining space dedicated to 66 exercises. Today's student might wonder what happened to all the pictures, the visual pop-outs of definitions and "further study," and the multi-cultural-correct photos of children having fun doing something that must be related to math if for no other reason than it is in a math book.

Today's pedagogical theorists would dismiss this as antiquated "drill and kill." Obsolete. Ineffective. Out of step with today's students. Nothing could be further from the truth. This is actually "skill and thrill." By progressively working thru exercises that demonstrate and elucidate the principles explained in the text the student learns--masters--techniques and concepts necessary for a deep understanding of and proficiency in more advanced mathematics.

This one book can take a learner from colours and counting to pre-calc. Yet you'll not see this in any modern school today. If you have a child you wish to see as a tiger-cub you don't need to subscribe to modernity in mathematics. Instead you should go to a used book sale and buy a text no less than fifty years old. Have your child learn alongside the minds that put a man on the moon.