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    firm in the point he has reached hefore another step is presented to him ; and that step it always is in his power to take . There are none of those frightful chasms , or bewildering intricacies with which vulgar minds render the path of knowledge difficult , and even irnpracticable to the learner . The philosophic mind alone is clear and simple . The lessons on arithmetic are preceded by some most excellent c remarks on teaching arithmetic / and directions for the teacher : '

    * In this treatise , ' says the author , ' rules are not mentioned , because it is not necessary to mention them . The pupil discovers them for himself when he wants them . He goes through the various portions of the subject according to their difficulty , and to the light they throw upon each other ; not according to their place in a scientific arrangement . He is , by this means , in a condition to multiply and to divide small numbers , and to perform simple calculations in fractions , long before he can

    attempt the addition of large numbers . And as each operation facilitates the rest , he soon can grapple powerfully with the smaller numbers . For him they really have a meaning ; so far as they go , they are a distinct language , and a clear and powerful instrument of thought . And this knowledge is attained in a space of time that would have been occupied , under ordinary circumstances , in groping painfully , and perhaps fruitlessly , at the very threshold .

    * Although we should not forget that we ought to teach knowledge for the purpose of improving all our faculties , still we must remember that we should also teach it because it is wanted for use in the world ; we must teach it in the way in which it will be wanted and used in the world , and also in conjunction with those things that will render it useful . We should not teach any subject so as to separate it from everything else , and render it practically useless , merely because the

    entire abstraction or separation of a science from all others happens to be best for some other purposes . A child , if sent to a foreign country , will learn the language in a few months . Instruct him at home , by means of scientific works on grammar , by plans and books suited only to the learned or the initiated , and he shall learn less in as many years . The memory is refreshed , and the mind is to a certain extent instructed ,

    by looking over an ordinary scientific work ; but it js little of the real nature of a subject that can be learnt by the beginner from this external labelling and ticketing . A science may be arranged and prepared for the instruction of youth ; it may also be arranged in the most compact and logical form for the use of the philosopher : these arrangements may be equally scientific ; but they must be materially different , because they have a very different purpose to serve .

    ' Some reason has generally existed for the peculiar arrangement of this treatise , though , at first sight , t ^ he work may present no signs of order . When a child sees four counters or two pebbles , he understands their number long before he has any clear notion of the words four and two , used alone . Counting with objects is , therefore , the first stage practicable . Children also remember and understand the numbers of those things with which they are very familiar , before they comprehend abstract numbers : questions respecting familiar absent objects are , therefore , the next in difficulty . And the most difficult questions of all are

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    286 A rithmetic for Young Children .

• Citation
  • Monthly Repository (1806-1838) and Unitarian Chronicle (1832-1833), April 2, 1835, page 286, in the Nineteenth-Century Serials Edition (2008; 2018) ncse-os.kdl.kcl.ac.uk/periodicals/mruc/issues/vm2-ncseproduct2644/page/62/