Robert Recorde (also Record) published the first popular mathematics textbook in English, The Grounde of Artes, in 1542. His style of pedagogy made full use of a dialogue between the Master (teacher) and the Scholar (learner). Unlike Plato’s oft-cited Meno, in which Socrates simply leads the Boy who parrots Socrates’ suggestions (e.g., “Surely, it is!”, ”Why no, upon my word!”, “That’s true.”), Recorde presents a Scholar who asks questions of the Master in ways that illuminate the difficulties of the concepts and procedures that the Master is seeking to convey. The conversation is informal, personal, and designed to popularize and promote the study and use of mathematics. Recorde’s major works consist of The Grounde of Artes (1542) which focused on arithmetic; The Pathway to Knowledge (1551), a practical geometry; The Castle of Knowledge (1556) on geometry and astronomy, and The Whetstone of Witte (1557) on algebra. |
In Mathematics Education Across Time and Place
John Cabber, a priest with mathematical interests in London, (Chapter 4: The Mathematical Practitioners of England) talks about his distress at hearing of the publication of Record’s first work. Cabber had been working for years on a similar book and when it was finished was unable to find anyone to publish it for him.
The year was 1520. King Henry VIII was on the throne, and had been for over ten years. Leo X was the current pope. And I was preaching in Nottingham by day, and writing a mathematics text by night. For the next thirteen years I laboured at this task whenever time permitted. I took ideas from Jordan's Arithmetica (as well as one of his other books, De ponderibus) and from Treviso and made them better. Without the formalism of Latin I was able to make the examples more relevant to the modern Englishman.
In the spring of 1532 it was finished. I titled it Reckoning. It was as comprehensive as any book I had seen. It included Jordan's nine operations: numeration, addition, subtraction, duplation, multiplication , mediation, division, progression, and extraction of roots. As well there were sections on navigation, business, gunnery, and weights and measures. It was a large manuscript, and I realized it would have to be split into two or three volumes (which troubled me because I had come up with only one name).
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… in 1542 another cataclysmic event rocked my world . For many it was insignificant. For me, it was a tragedy. Robert Record published his book The Grounde of Artes, an arithmetic textbook in English. There was nothing in it that hadn't been in Reckoning. But there it was, in all its glory. I was overcome with dread. As much as I loved mathematics, I hated this book.
Obviously, Record had something that I didn't (other than timing). As it turned out, that thing was tenacity. When the English publishers turned him away he didn't give up, and eventually the book was published in Paris.
The year was 1520. King Henry VIII was on the throne, and had been for over ten years. Leo X was the current pope. And I was preaching in Nottingham by day, and writing a mathematics text by night. For the next thirteen years I laboured at this task whenever time permitted. I took ideas from Jordan's Arithmetica (as well as one of his other books, De ponderibus) and from Treviso and made them better. Without the formalism of Latin I was able to make the examples more relevant to the modern Englishman.
In the spring of 1532 it was finished. I titled it Reckoning. It was as comprehensive as any book I had seen. It included Jordan's nine operations: numeration, addition, subtraction, duplation, multiplication , mediation, division, progression, and extraction of roots. As well there were sections on navigation, business, gunnery, and weights and measures. It was a large manuscript, and I realized it would have to be split into two or three volumes (which troubled me because I had come up with only one name).
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… in 1542 another cataclysmic event rocked my world . For many it was insignificant. For me, it was a tragedy. Robert Record published his book The Grounde of Artes, an arithmetic textbook in English. There was nothing in it that hadn't been in Reckoning. But there it was, in all its glory. I was overcome with dread. As much as I loved mathematics, I hated this book.
Obviously, Record had something that I didn't (other than timing). As it turned out, that thing was tenacity. When the English publishers turned him away he didn't give up, and eventually the book was published in Paris.
Mathew Bourne, a mathematical practitioner and instrument maker in London, (Chapter 4) had a much more personal connection with his uncle Robert. The mathematics book to which he refers is likely Record’s The Grounde of Artes, so resented by Cabber.
As a small child I would often go with my mother to visit the house of my Uncle Robert. He was always kind to me and took a great interest in all that I was doing at school. He encouraged me especially in my study of Arithmetick and was able to answer all my questions that my master couldn't. You see, as well as being a physician he was a scholar and a teacher too, for he was Mathematics tutor to the children of several richer merchants. In flattery he told me I was much more astute in Arithmetick than his pupils! It was he who introduced me to the wider studies of Mathematics beyond the Arithmetick. He showed me the geometric shapes and explained how the world is a sphere — which I found so difficult to believe at the age of eight. I remember how I was fascinated by what seemed to me then to be mysterious magical devices which he kept in his study. I now know them to have been navigational instruments — compasses, horologia, astrolabes and the like. He was, he said, writing a book instructing how to use them [likely The Pathway to Knowledge, 1551]. I didn't realize then that he had already written one Mathematics book, which was becoming very popular.
My Uncle removed to Bristol the year I was nine; I missed him sorely. My mathematical education stood still for several years, there being no master at the school who knew as much of the Arithmetick as I had learned from my Uncle. Then when I was eleven he was sent to an employment even farther away, in Ireland. But imagine my delight when, before he left, he presented me with a gift of his new book on Geometrie, a compasse, and a protractor. His gifts gave me many hours of pleasure over the next two years as I followed his instructions for constructing circles, triangles, pentagons, hexagons, and other wonderful shapes, and learned the fascinating theorems of Euclid. How cleverly his book was written — in a dialogue with the master explaining everything so clearly to the scholar, and then the scholar asking just the same questions that I would want to ask. I spent so much time at this study that I would often be in trouble at school for neglecting my home study of Cicero or Erasmus! But how dull those old authors were in comparison to the wonders of Euclid's Geometrie!
As a small child I would often go with my mother to visit the house of my Uncle Robert. He was always kind to me and took a great interest in all that I was doing at school. He encouraged me especially in my study of Arithmetick and was able to answer all my questions that my master couldn't. You see, as well as being a physician he was a scholar and a teacher too, for he was Mathematics tutor to the children of several richer merchants. In flattery he told me I was much more astute in Arithmetick than his pupils! It was he who introduced me to the wider studies of Mathematics beyond the Arithmetick. He showed me the geometric shapes and explained how the world is a sphere — which I found so difficult to believe at the age of eight. I remember how I was fascinated by what seemed to me then to be mysterious magical devices which he kept in his study. I now know them to have been navigational instruments — compasses, horologia, astrolabes and the like. He was, he said, writing a book instructing how to use them [likely The Pathway to Knowledge, 1551]. I didn't realize then that he had already written one Mathematics book, which was becoming very popular.
My Uncle removed to Bristol the year I was nine; I missed him sorely. My mathematical education stood still for several years, there being no master at the school who knew as much of the Arithmetick as I had learned from my Uncle. Then when I was eleven he was sent to an employment even farther away, in Ireland. But imagine my delight when, before he left, he presented me with a gift of his new book on Geometrie, a compasse, and a protractor. His gifts gave me many hours of pleasure over the next two years as I followed his instructions for constructing circles, triangles, pentagons, hexagons, and other wonderful shapes, and learned the fascinating theorems of Euclid. How cleverly his book was written — in a dialogue with the master explaining everything so clearly to the scholar, and then the scholar asking just the same questions that I would want to ask. I spent so much time at this study that I would often be in trouble at school for neglecting my home study of Cicero or Erasmus! But how dull those old authors were in comparison to the wonders of Euclid's Geometrie!