Recently I have started reading the book Unknown Quantity: A real and imagined history of algebra by John Derbyshire. For any history (or mathematics) students, the book is a fascinating read, detailing the development of the number system, algebraic notation and use from over four thousand years ago to as we know it today.
From time to time I have shared with my students snippets of what I have read. For example, the ancient Babylonians didn’t have a conceptual understanding of the numbers 1 to 10. Instead they worked with a base 60 notation, which explains why this same notation appears in various instances of our numerate world today. For my students, who were studying trigonometry and the breakdown of degrees into minutes and seconds, this explanation proved helpful.
Derbyshire’s book has highlighted for me how complex the development of algebraic thinking, language and writing has been. Mathematicians struggled over the course of generations trying to figure out how to represent the unknown number (i.e. a pronumeral or variable, often written as ‘x’). Each step of the way, they didn’t know how their findings would be of use to secondary students today, nor did they often know what had immediately preceded them or was being simultaneously discovered somewhere else in the world.
The study of Algebra today gives many students grief. They struggle with its abstractness and the ideas of simplifying an expression or working with a balanced equation.
Alongside these students, however, there are others who enjoy it and who get a sense of achievement when they find that they do understand this new language they are learning.
In response to recent debate over the worthiness of algebra in the classroom, why limit what our students are learning because it is difficult for some? Learning is not intended to be easy. It is intended to set students up to navigate and make sense of our world. And who knows, maybe there is another Diophantus or al-Khwarizmi growing up today, who will in the years to come make some amazing leap forward in mathematical thinking.
A great contribution to this debate can be found here in an article by Judy Bolton-Fasman.