Speed Arithmetic Introduction

A word about these pages · Index of Speed Arithmetic Pages · Recommended Books

A word about these pages

After reading a review of this website (October 2002) by a mathematics educator who liked the site but felt it moved too rapidly to advanced topics, I’ve decided to spend more time on basic material suitable for children.

There is a growing home-school movement in this country, hungry for efficient means of teaching kids basic skills. In response, I’m publishing the best basic math methods I can find, in particular, the very fine arithmetic techniques due to Jacow Trachtenberg. These are suitable for teaching to children as young as eight, although an adult must read and understand the methods in order to teach it to children. Fortunately, this is not too hard.

These methods are completely different from the table-based, memorization-intensive basic standard math taught in U. S. public schools. In most cases, the methods are simpler, less error-prone, faster and more readily learnable by children.

Be advised that a partial learning of these techniques mixed with partial standard techniques is probably worse than learning either system completely – I do not believe the systems are compatible. Thus, parents who intend to teach these methods to their children are strongly advised to learn the whole method first, take some time to think about the relative value of the method compared with the standard math they were probably taught, and make a careful decision about committing to one system or the other. Parents with math-challenged children are encouraged to dive right in to this new method, since the standard method has already failed them.

There is one book on Trachtenberg’s method, The Trachtenberg Speed System Of Basic Mathematics, from 1960. I would buy the original book (or borrow it from a library) and work with my kids using pencil and paper on the kitchen table. Practice problems to add, subtract, multiply, and divide can be made up on the spot and checked with a \$10 calculator bought from a grocery store.

Parents are strongly advised to take an active role in their children’s education, personally tutoring them, helping with homework, supervising, checking their work, etc. There is no substitute for the time and attention of the parents.

The methods should be practiced until desired proficiency (doing numbers this large in that much time, consistently) is reached. My feeling is that there is no such thing as too much math proficiency; however, there are certainly other subjects children must master, particularly primary language skills, so that time constraints will naturally limit the math skills any individual student can gain.

The Trachtenberg method covers math up to and including extraction of square roots. After that, it is time for students to tackle algebra. Fortunately, Trachtenberg’s method is fundamentally algebraic in character, so it is to be hoped that learning the method will help students when they later start learning algebra. In any case, students need to learn arithmetic thoroughly prior to trying algebra.

Index of Speed Arithmetic Pages
Speed Arithmetic - Multiplication by Eleven
Speed Arithmetic - Multiplication by Twelve
Speed Arithmetic - Multiplication by Six

Recommended Books

The original, 1960 book that first brought Dr. Trachtenburg's work to the world's attention.  Well written, brief, with plenty of examples.

An inexpensive Dover book that covers the same kind of topics. I haven't read this one (yet), but I have many other Dover titles, and am always happy with them.

(c) Phil Otken 1996-2004. All Rights Reserved except where explicitly noted.