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those connected with abstract numbers , that is to say , with the names of numbers without any reference to present or absent objects . But as children are in a condition to understand easy questions of the second and third sort before they can manage difficult exercises of the first kind , questions of all three sorts have been mingled together , according to their relative difficulty , so that they shall mutually assist each other , and give that variety to the subject which the infant mind urgently requires . 4
The Arabic numerals , or ordinary figures , have been most studiously kept out of sight until near the conclusion of the treatise , because it has been found that , when they are introduced very early , they relieve the pupil from the necessity of examining numbers thoroughly . They present a bright and clear picture to the eye , compared with which all other
impressions and notions connected with number are bIow of acquirement and dim ; and thus their superficial clearness overpowers the more solid properties of their brethren . When kept in proper subordination , and allowed only their fair share of attention , they become most valuable assistants '
' In lieu of tables , a few of the most useful weights and measures should be shown to the pupil ; and such manual , as well as arithmetical exercises , should be performed with them , as are indicated in various parts of this treatise . With these the child would be much delighted ; an agreeable variety of calculation would be attained ; he would never forget what he had seen and handled ; and would take an interest in all future calculations about weights and measures .
' The above remarks will explain , in some degree , the cause of the repetitions , and of the apparently trifling and homely nature of many of the questions , and also of the language in which they are couched . The state of mind of the child frequently prevents us from using the most correct and elegant phraseology and illustration . Variety of expression
and copiousness of illustration , however , must be provided ; and it will soon be found that they who restrict themselves to the most correct and scientific language are unintelligible to children . Great variety of language must studiously be used , or we shall not prevent the pupil from falling into many serious errors , which are certain to result from the invariable use of a single form of words . Before a child can understand
the peculiar language of a science , he must understand something of the science itself . Besides , the general ignorance of children necessarily precludes forms of expression and modes of illustration which might be employed with advantage in teaching adulJLs . ' 4 In the first stage the pupil ' is taught to think and speak in numbers ;
in the second stage lie will continue his former practice , and will unite with it the art of writing numbers ; for there is no reason why we should violate , in arithmetic , those laws of nature which hold good in general life , and which prescribe that we should think before we speak , and that we should both think and speak before we are in a fit condition to learn
to write . A box containing a very useful set of counters , shells , cubes , and measures , may he had of the publishers of the ' Arithmetic for Young Children ; ' and it were greatly to be wished that those ougaged in education would enter into the spirit of this little
Arithmetic for Young Children . 287
Monthly Repository (1806-1838) and Unitarian Chronicle (1832-1833), April 2, 1835, page 287, in the Nineteenth-Century Serials Edition (2008; 2018) ncse.ac.uk/periodicals/mruc/issues/vm2-ncseproduct2644/page/63/