Arithmetic

Title: Arithmetic

Author: Paul Lockhart

Publisher: Belknap Press of Harvard University Press, 2017 (First)

ISBN: 9780674972230

Pages: 223

Even though arithmetic forms only a small subset of mathematics (when you say something about math, it causes no harm using some of its parlance such as subsets), for many people it is the science of mathematics. And, it is the subject that scares away children from appreciating the art and experiencing the joy of doing math. It is forced learning by rote and mechanical procedures for performing arithmetical operations without stopping a moment to perceive what is going on that repels so many children away from it. Clearly, a new paradigm is needed to teach math in elementary schools, making it a participatory experience for the students. However, the sad fact is that most of the teachers were also churned out by the system of memorizing of multiplication tables and doing long division by carefully choreographed procedures which keeps you on tenterhooks until the final result appears. This book is a welcome change to the genre of popular math. It teaches a teacher of math how to teach it to young boys and girls and to make a generation quite confident of dealing with it. The methods and structures detailed in the book are highly oriented to practical learning, while clearly explaining the theoretical aspects in an easy to follow way. Paul Lockhart teaches math at St. Ann’s School in Brooklyn, New York. He is the quintessential teacher who renounced his prestigious career in the university to teach in a grade school. He is the author of two more books on learning math.

Arithmetic is the skillful arrangement of numerical information for ease of communication and comparison. Lockhart makes it categorically clear that being good at it does not make you particularly smart or mathematically inclined. It is like any other craft you can get good at if you wanted to, but it is no big deal either way, assures the author. The book gives an excellent introduction to the two main schemes of arranging numerals – the marked-value and place-value systems. It starts right from the activity of counting where you take stock of something by assigning a numeral to denote something in the real world. Actual examples from the Egyptian, Roman, Chinese and Indian systems are given. It is the place-value system developed in ancient India that revolutionized the way the world did its calculations. Invention of the symbol and concept of zero as a place holder to denote a null value was a novel concept, without which the explosion in information exchange wouldn’t have come into being. The Indian numerical system reached Europe in the thirteenth century through Arab traders. Leonardo of Pisa – better known as Fibonacci – showcased the new ideas in his book Liber Abaci (Book of the Abacus). Strangely, such a fool proof system was slow to catch on with the general public in Europe. Such is the aversion of people to change! Even as late as the eighteenth century, well-educated adults found it confusing and overly technical. Eventually, convenience and increasing availability of inexpensive paper won out over the traditional Roman numerals.

The book is an attempt right from the first page to the last to kindle the spirit of appreciation for mathematical beauty among the readers. In case anyone still ‘feared’ numbers, Lockhart encourages them with sage advice that mathematical operations are only good strategies for encoding and manipulating numerical information, and we can use them in any way we see fit. Instead of thinking in terms of systems and rules, we should think of it more as options and tools at our disposal (p.73). The entire gamut of basic mathematical operations like addition, subtraction, multiplication and division are covered in detail and provide new insight into the heart of the problem. Even those who are well-versed in math would learn one or two new ideas from this impressive book. Lockhart also attempts to detach numbers and its representations from its homologues in the real world. It is not always possible to find a related process happening around us. Math or arithmetic is abstract, making reification – the process of searching for counterparts in the real world – extremely difficult and sometimes impossible. Whether or not it is physically possible, arithmetic imagine or invent some sort of logically coherent structures and forms a part of mathematical reality. This disclaimer is issued in the context of negative numbers which can’t be compared readily to any real thing. But it provides an excellent tool for making calculations to arrive at the result that has real significance. Even though Lockhart doesn’t mention it in this book, complex numbers – which are square roots of negative numbers – are another realm of arithmetic which has no physical meaning, but is immensely useful in calculating and comparing real world data.

There is nothing to be said against the book, except its small type size and the absence of categorization into distinct chapters. The entire volume appears to be divided into several topics of varying lengths, more akin to an encyclopedia rather than a normal work of learning. Even though the focus is on aspiring teachers, the author has cleverly included several practice questions without making it appear as an exercise. The chapter on mechanical calculating machines could’ve been eliminated, as it proves a redundant chapter that doesn’t contribute anything to the general thread of argument. This book is an excellent choice for anyone who has set his heart on becoming a teacher of elementary schools, which will surely help them become an arithmetician of wit and intelligence.

The book is highly recommended.

Rating: 5 Star