Wisdom of ages
Teach the six-year-olds numbers and directions ... the nine-year-olds how to work out days and dates. The 10-year-olds study with a teacher and live away from home learning history, writing and mathematics." Not another revision to the national curriculum, but a translation of instructions for education in the Zhou Dynasty of China, from about 1000 years bc.
The realisation that students have been learning maths in schools, often from written texts, for several millennia is both exciting and sobering. It seems a pity that we don't use the historical perspective more frequently in our own classrooms to help students understand the nature of mathematics and its impact on societies through the ages.
In Exploring Mathematics through History, Ruth Eagle provides a rich treasure-trove of nuggets about how mathematics has been developed and used from antiquity to the 18th century. She links this directly to our own curriculum by providing numerous activity sheets which exploit a historical perspective while initiating problem-solving tasks for 10 to 18-year-olds.
The first half of the book looks at aspects of number, mensuration and geometry in ancient civilisations. The teacher's notes in each chapter provide fascinating insights which can be used when introducing the topic to a class. We learn how the Babylonians were able to generate Pythagorean triples (at least 1,000 years before Pythagoras!), order them according to the size of the smallest angle in the associated right triangle and use this to tabulate design data for altar builders.
Often, minor asides shed light on our own approaches to the subject. For example, in the Jiuzhang suanshu, an ancient Chinese mathematics text, the area of a circle is given as 12Px12D. An accurate and potentially useful formula. Why don't we teach it?
The second half of the book explores the 250 years of rich European endeavour from the Renaissance to the Enlightenment. We see how scholars pushed back the frontiers of understanding while other professionals applied new learning to occupations such as gunnery, navigation and surveying.
Throughout the book the author combines scholarship, enthusiasm and an understanding of school mathematics in a crisp yet accessible manner, illustrating and interpreting many original sources. Inevitably, like the subject itself, a book of this kind raises as many questions as it answers.
Reference notes and an extensive bibliography offer pointers for further investigation.
This is one of the most absorbing school mathematics books I have come across in a long time.
Linton Waters is mathematics inspector for Shropshire