The Historical Perspective

Strange though it may seem at first, it is nevertheless quite clear that addition, subtraction, multiplication and division – comparatively simple operations, which we inflict on our children while they are still quite young – were, in antiquity, far beyond the horizon of any primary school. The widespread use of calculating-tables and counting-machines [abacus] shows that not many people could add up – and this goes on being true to a much later date, even in educated circles.

A History of Education in Antiquity, by Henri I. Marrou, translated by George Lamb, Sheed and Ward, London, 1956, page 158.

[page 204] Before the Reformation there was little or nothing accomplished in the way of public education in England. In the monasteries some instruction was given by monks, but we have no evidence that any branch of mathematics was taught to the youth (some idea of the state of arithmetical knowledge may be gathered from an ancient custom at Shrewsbury, where a person was deemed of age when he knew how to count up to twelve pence. See Tylor’s Primitive Culture, New York, 1889, Vol. I., p. 242.) . . . In the sixteenth century, on the suppression of the monasteries, schools were founded in considerable numbers . . . and for centuries have served for the education of the sons mainly of the nobility and gentry. In these schools the ancient classics were the almost exclusive subjects of study; mathematical teaching was unknown there. Perhaps the demands of every-day life forced upon the boys a knowledge of counting and of the very simplest computations, but we are safe in saying that, before the close of the last century, the ordinary boy of England’s famous public schools [page 205] could not divide 2021 by 43, though such problems had been performed centuries before according to the teaching of Brahmagupta and Bhaskara by boys brought up on the far-off banks of the Ganges . . . . All the information we could find respecting the education of the upper classes points to the conclusion that arithmetic was neglected, and that De Morgan was right in his statement that as late as the 18th century there could have been no such thing as a teacher of arithmetic in schools like Eton. In 1750, Warren Hastings, [page 206] who had been attending Westminster, was put into a commercial school, that he might study arithmetic and book-keeping before sailing for Bengal.

At the universities little was done in mathematics before the middle of the 17th century . . . . During the reign of Queen Elizabeth, fresh statutes were given, excluding all mathematics from the course of undergraduates, presumably because this study pertained to practical life, and could, therefore, have no claim to attention in a university . . . .

[page 207] This scorn and ignorance of the art of computation by all but commercial classes is seen in Germany as well as England.

It was not before the present century that arithmetic and other branches of mathematics found admission into England’s public schools. At Harrow “vulgar fractions, Euclid, geography, and modern history were first studied” in 1829. At the Merchant Taylors’ School “mathematics, writing, and arithmetic were added in 1829.” At Eton mathematics was not compulsory till 1851.

Since the art of calculation was no more considered a part of a liberal education than was the art of shoe-making, it is natural to find the study of arithmetic relegated to the commercial schools. The poor boy sometimes studied it; the rich boy did not need it. In the Latin schools it was unknown, but in schools for the poor it was sometimes taught . . .

[page 217] The first arithmetics used in the American colonies were English works . . . . The earliest arithmetic written and printed in America appeared anonymously in Boston in 1729. Though a work of considerable merit, it seems to have been used very little . . . . In 1788 appeared at Newburyport the New and Complete System of Arithmetic by Nicholas Pike . . . . It was intended for advanced schools . . . . [page 218] Reform in arithmetical teaching in the United States did not begin until the publication of Warren Colburn, in 1821, [page 219] of the Intellectual Arithmetic. This was the first fruit of Pestalozzian ideas on American soil . . . . The success of this little book was extraordinary. But American teachers in Colburn’s time, and long after, never quite succeeded in successfully engrafting Pestalozzian principles on written arithmetic . . . .

A History of Elementary Mathematics with Hints on Methods of Teaching, by Florian Cajori, Ph. D., London: Macmillan Company, 1917, pages 204-207, 217-219.

. . . The American Calculator, first published in 1828 . . . is reasonably typical of the colonial period. This text was used with older students (beginning at about the age of eleven). It was complete in itself, not one book of a series such as the texts that evolved in later years.

Readings in the History of Mathematics Education, edited by James K. Bidwell and Robert G. Clason, National Council of Teachers of Mathematics, Washington, D. C., n. d., page 2.

. . . The study of it [arithmetic] used to be put off to a very late period. Scholars under twelve or thirteen years of age were not considered capable of learning it, and generally they were not capable. Many persons were obliged to leave school before they were old enough to commence the study of it.

Readings in the History of Mathematics Education, page 25, taken from “Teaching of Arithmetic,” text of an address delivered by Warren Colburn before the American Institute of Instruction in Boston, August, 1830, reprinted from theElementary School Teacher12 (June 1912): 463-480.

[In the early seventeenth century, the grammar school curriculum was] almost certainly confined to Latin grammar, the Catechism and Bible study . . . . [P]upils arriving at Oxford and Cambridge frequently did not have any knowledge of Arabic numerals, to say nothing of the elementary arithmetical operations.

A History of Mathematics Education in England, by Goeffrey Howson, Cambridge University Press, Cambridge, 1981, page 30.

You can read the entire article here.

- October 2016
- September 2016
- August 2016
- June 2016
- May 2016
- April 2016
- March 2016
- February 2016
- January 2016
- December 2015
- November 2015
- October 2015
- September 2015
- August 2015
- July 2015
- June 2015
- May 2015
- April 2015
- March 2015
- February 2015
- January 2015
- December 2014
- November 2014
- September 2014
- August 2014
- July 2014
- June 2014
- May 2014
- April 2014
- March 2014
- February 2014
- January 2014
- December 2013
- November 2013
- October 2013
- September 2013
- August 2013
- July 2013
- June 2013
- May 2013
- April 2013
- March 2013
- February 2013
- January 2013
- December 2012
- November 2012
- October 2012
- September 2012
- August 2012
- July 2012
- June 2012
- May 2012
- April 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
- September 2011
- August 2011
- July 2011
- June 2011
- May 2011
- April 2011
- March 2011
- February 2011
- January 2011
- December 2010
- November 2010
- October 2010
- September 2010
- August 2010
- July 2010
- June 2010
- May 2010
- April 2010
- March 2010
- February 2010
- January 2010
- December 2009
- November 2009
- October 2009
- September 2009
- August 2009
- July 2009
- June 2009
- May 2009
- April 2009
- March 2009
- February 2009
- January 2009
- December 2008
- November 2008
- October 2008
- September 2008
- August 2008
- July 2008
- June 2008
- May 2008
- April 2008
- March 2008
- February 2008
- January 2008
- December 2007
- November 2007
- October 2007
- September 2007
- August 2007
- July 2007
- June 2007
- May 2007
- April 2007
- March 2007
- February 2007
- January 2007
- December 2006
- November 2006
- October 2006
- September 2006
- August 2006
- July 2006
- June 2006
- May 2006
- April 2006
- March 2006
- February 2006
- January 2006
- December 2005
- November 2005

March 9th, 2007 at 4:52 am

[…] the mix. Following that, Rebecca Newburn discusses equation solving strategies and Laurie Bluedorn takes a historical view on the age of introduction of formal arithmetic. To finish it up, jd2718 tells us about teaching complex numbers and your humble host has a […]

March 10th, 2007 at 2:47 am

“Formal Arithmetic at Age Ten, Hurried or Delayed?”

Delayed. My son, age 10, could take the derivative or integral of a polynomial if you spoke it to him. He’d visualize the polynomial, calculate the the derivative or integral in his head, and dictate it back to you.

How old were Ramanujan and Gauss when they could do figurate numbers in their heads?

Public schools in the USA have essentially given up, as badly as the prestigious schools in England a couple of centuries ago.

Fortunately, there ARE some good students, good media (the CBS-TV show NUMB3RS for example), many good books, and the Web.

There is no meaningful limit to what a child can learn, given a good teacher and a motivation for the student, and if you start early enough (neural plasticity).

Self esteem? I suggest that it be deserved, by allowing children to succeed with actual content and understanding. Not “teaching to the test.” Not “No child left behind.” Those are red herrings. I mean real education.

For the children.

March 11th, 2007 at 12:06 pm

[…] of mathematics back in the 16th century to the esoterica of modern mathematics2 is mindboggling. « Trivium Pursuit « Carnival of Mathematics #3 (hosted at Michi’s blog) The cited reference doesn’t mean […]

March 29th, 2007 at 3:32 pm

Hello:

It is true that children can learn many math concepts very early, but also it is true that in the last century the advance of the Math has being very poor, I think the only interesting fact was The Demonstration of the Theorem of Fermat, that is.

The math we have comes from those who spend the first years of life learning grammar and logic and then, when they were well prepare they develop the calculus and geometry which our little children play today, but this children miss the enough good foundation to develop something better from there.

So, we as civilization, are not winning teaching complex math concepts to the babies, and little children, we are lose the possibility to develop great minds to solve the science’s problems, the math is a tool of the science, it is the language of the science.