ON STUDIES MOST SUITABLE FOR ELEMENTARY SCHOOLS. iol 



meet with the approval of most advocates of reform in the teaching of 

 arithmetic in elementary schools. What is now required is that the 

 principles described above should be raised from the plane of pious 

 opinion to that of actual practice. It is not sufficient for the Board of 

 Education or any other body exercising control over the work of 

 elementary schools to point out desirable methods of teaching arithmetic, 

 when it is well known that in most schools no change will be made 

 until it is insisted upon as essential to efficiency. At present the 

 suggestions issued by the Board are regarded merely as sicggestions 

 by the teachers who have taken the trouble to read them, and there- 

 fore outside the sphere of practical politics. The futility of issuing a 

 book of maxims without insisting that they shall be acted upon is obvious 

 to anyone familiar with teachers and schools. There may be differences 

 of opinion upon some of the details of the arithmetic schemes included 

 in the ' Suggestions ' but the spirit of the extracts given above leaves little 

 to be desired ; and if educational authoi'ities would state in unmistak- 

 able terms that they will only countenance work in arithmetic founded 

 upon the principles suggested by the Board of Education, a marked im- 

 pro^ement in the teaching of the subject would soon be seen. 



It is undesirable to give here a detailed syllabus of a school coui'se 

 in arithmetic, but a useful purpote may be served by pointing out some 

 existing defects and indicating directions in which improvements are 

 required. PJxperienced teachers know the intellectual capacities of 

 children and many of them follow methods of instruction which leave 

 little to be desired. In general, however, arithmetic is not made a prac- 

 tical study but a miscellany of processes of doubtful origin and utility. 

 To indicate some of the furbelows which may be usefully discarded and to 

 encourage the adoption of a more reasonable treatment of the subject is 

 the chief object of this report. 



Fundamental Principles. 



So far as possible, all reasoning in arithmetic should be from the 

 concrete to the abstract. Pupils should not be drilled in applying rules 

 they do not understand, but should learn by the manipulation of objects, 

 papei'-folding, the measurement of lines or consideration of other concrete 

 instances, what is meant by simple arithmetical processes and should then 

 be led to arrive at generalisations expressing in abstract form what they 

 have found to be true in the concrete. In other words, the rules should 

 represent results of experience, instead of being academic statements of 

 the order or method in which arithmetical operations should be performed. 

 Excessive precision in the manipulation of large numbers, or rapidity of 

 working should not be considered more important than the development 

 of reasoning powers encouraged by dealing with things instead of words. 



The practice of teaching arithmetic as a collection of devices under 

 different headings, from which a choice has to be made for the solution 

 of any particular problem, cannot be too strongly condemned. Every 

 teacher is familiar with the pupils who want to know whether they 

 should multiply or divide one number by another in a given sum in order 

 to obtain the correct answer ; when this state of things exists it is 

 evident that the calculations are meaningless. When the first four rules 

 are grasped and the meaning of a simple fraction is understood, as the 

 result of familiarity with the subdivisions of a penny or an inch, decimals 



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