Warren Colburn

In Mathematics Education Across Time and Place
Declan Liam "Bill" Brown (Chapter 7: Canada) received his early education in the monitorial schools of England and, after moving to Canada in 1855, attended the first normal school in Upper Canada for the training of teachers. Bill taught in Ontario for a number of years before completing his teaching career in Calgary, Alberta. Brown highly valued the ideas of Warren Colburn, as shown in the following extract from his autobiography.
The typical texts of this period left much to be desired as they presented and emphasized rules, first and foremost, with little or no concern about understanding, let alone utility. William Slocomb’s The American Calculator (1831) is a prime example. A much superior textbook was Warren Colburn’s First Lessons in Arithmetic on the Plan of Pestalozzi (1825), in which the Rule of Three, and many other rules contained in our usual arithmetic, were abandoned in the interest of the learner and his understanding. I should note that it was not always easy for me, or anyone, to procure American textbooks at that time.
Colburn acknowledged that arithmetic is a very important discipline of the mind, “so much so that even if it had no practical application which should render it valuable on its own account, it would still be well worth while to bestow a considerable time on it.” He added that, while this was an important consideration, it is a secondary one compared with the practical utility of arithmetic.
I must say that I subscribed to Colburn’s thinking about the practical utility of arithmetic and its importance as a consideration in mathematics teaching. As the colonies became more and more thickly populated, and as more and more pupils studied arithmetic, the new system of teaching arithmetic made more and more sense. In Colburn’s system the learner begins with practical examples and simple numbers. Reference to sensible objects assists the learner’s mind greatly. Instead of studying rules in a book, which are for the most part meaningless to him, the student generalizes his own reasoning and makes his own rules after discovering the principle from practical examples. There is more than one way to do a thing, or think of a thing, but so many teachers are products of a system that did not encourage ways of thinking!
When I first started teaching, I used the “rule, example, exercise” approach with the textbook in hand while the pupils copied the rules and examples in their ciphering books. With the new belief that concepts were developed from practical examples, and by reference to sensible objects, a reversal of my previous pedagogy followed. I became obsessed with the notion that arithmetic could be understood, rather than simply carried out using rules, and I went to great lengths to facilitate this with my students.
The typical texts of this period left much to be desired as they presented and emphasized rules, first and foremost, with little or no concern about understanding, let alone utility. William Slocomb’s The American Calculator (1831) is a prime example. A much superior textbook was Warren Colburn’s First Lessons in Arithmetic on the Plan of Pestalozzi (1825), in which the Rule of Three, and many other rules contained in our usual arithmetic, were abandoned in the interest of the learner and his understanding. I should note that it was not always easy for me, or anyone, to procure American textbooks at that time.
Colburn acknowledged that arithmetic is a very important discipline of the mind, “so much so that even if it had no practical application which should render it valuable on its own account, it would still be well worth while to bestow a considerable time on it.” He added that, while this was an important consideration, it is a secondary one compared with the practical utility of arithmetic.
I must say that I subscribed to Colburn’s thinking about the practical utility of arithmetic and its importance as a consideration in mathematics teaching. As the colonies became more and more thickly populated, and as more and more pupils studied arithmetic, the new system of teaching arithmetic made more and more sense. In Colburn’s system the learner begins with practical examples and simple numbers. Reference to sensible objects assists the learner’s mind greatly. Instead of studying rules in a book, which are for the most part meaningless to him, the student generalizes his own reasoning and makes his own rules after discovering the principle from practical examples. There is more than one way to do a thing, or think of a thing, but so many teachers are products of a system that did not encourage ways of thinking!
When I first started teaching, I used the “rule, example, exercise” approach with the textbook in hand while the pupils copied the rules and examples in their ciphering books. With the new belief that concepts were developed from practical examples, and by reference to sensible objects, a reversal of my previous pedagogy followed. I became obsessed with the notion that arithmetic could be understood, rather than simply carried out using rules, and I went to great lengths to facilitate this with my students.