The Cosmic Calculator, A Vedic Maths Course for Schools
The Cosmic Calculator. A Vedic Maths Course for Schools
by Kenneth Williams and Mark Gaskell
Delhi, India: Motilal Banarsidass, 2002; Revised edition, 2005.
This book, designed for 1114 year old school children, is a wonderful introduction to math. Whereas many other approaches to math cause emotional distress, children are often moved to the enjoyment of math by the approach taken in this series of books. This has to do in part with qualities inherent in Vedic math, but it also has to do with the thoughtful organization of the material in this context. The instructional material is organized around concepts and spatial visualization, and it provides brief verbal introductions which consist of more than examples and rules.
The material is organized with the accessibility of concepts in mind. The very first chapter begins by introducing the number 1: “The number 1 represents unity and is the first number. Unity and wholeness are everywhere.” (p.1) The idea that some numbers are larger and smaller than others follows.
The book is divided into short chapters, each of which focuses on a concept. The arrangement of the concepts is not arbitrary, but it is not conventional either. Here are the first ten chapters listed:
1. Arithmetic
2. Digit Sums and the Nine point Circle
3. Large Numbers
4. Digit Sum Check
5. Number Nine
6. Numbers with Shapes
7. Geometry
8. Symmetry
9. Angles and Triangles, Magic Squares
10. By the Completion or NonCompletion
Following basic concepts of arithmetic, together with the concept of arithmetic itself in Chapter 1, digit sums are presented in Chapter 2, together with the Nine point Circle. This way, working with number begins with the shape of a circle, rather than a line. The circle of nines should give the pupil a conceptual boost with arithmetic. The relationship of numbers to one another as they grow in size is likely to be much more meaningful in the context of a circle where there is order, repetition and pattern, whereas the visual concept of a line which seems to go on forever, losing itself ultimately in the clouds, is likely to be less attractive and potentially disturbing.
Large numbers are similarly introduced in Chapter 3 in such a way as to demystify and avoid any potential terror that might be associated with hugeness, namely by presenting first the concept of place value. This circumvents the mental chaos that could attach to a very large number. Attention is also drawn to the words for numbers in connection with the concept of place order, so that by the end of this chapter the student can already spell the terms and can move back and forth easily between the number words and the digits. Place value and work with language and spelling go a long way towards making large numbers manageable.
The digit sum check introduced in Chapter 4 provides a simple and accessible way of adding large numbers. Instead of being delivered to the lions of 4digit adding with carries right off the bat, this approach provides a chance to test oneself with smaller tasks. The authors thoughtfully provide a chance to work with sums without carries before introducing sums with carries. Subtraction follows.
Chapter 5 moves the student forward to the magical shapes and designs, puzzles and tricks associated with the number nine. This way math is art and science at once, as it provides the coding for shapes and forms in the natural world and the potentially infinite forms that can also be created.
Factors, triangles, squares, number sequences and the sieve of Eratosthenes to find prime numbers are introduced within the context of Chapter 6 – “Numbers with Shapes” – in much the way that certain nutrients and spices are put into rice, so that we say we have eaten “rice” when we have really consumed some vital nutrients in concentrated spice form as well. It is impressive to see the way this is done. It is common in math and language instruction for children to become sated with conceptpoor exercises before they are treated to some of the wonders of the universe., but in this case, seemingly foreign concepts are made quite familiar.
In chapters 7, 8, 9 and 10 the child is introduced to geometry, as well as Magic Squares and Magic Stars, and by the time these chapters are over, the child has advanced considerably in the field of geometry.
The verbal introductions to each chapter present just enough material and never too much. These short introductions give a child a chance to get his or her bearings. It is sort of like a quick set of directions for how to get somewhere, not the type that are too detailed, adding to the burdens of your travel, nor the type that are too skimpy, leaving you confused as you set out. Each chapter has a lovely quotation from some fine thinker that places the work in its impressive historical context. Chapter 2 begins with this:
“Even the highest and farthest reaches of modern Western mathematics have not yet brought the Western world even to the threshold of Ancient Indian Vedic Mathematics.” – Professor A. De Morgan (180671). Mathematician and Logician.
The Sanskrit sutras and rules appear in such a way that they are not intimidating but logical. The Teacher’s Guide with its explanations, tests and answers, has a wealth of material to back up the three school books as well. The emphasis is always on finding the simplest, most logical and most elegant way to go about carrying out a task. Let’s hope that Vedic Mathematics, with its logical rules, elegant patterns, creative approach and simple techniques of problemsolving will increasingly be in use through the medium of these thoughtfully designed books.
Review by Robin Jackson
May 8, 2010
