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The Aim and Methods of School Algebra1
Published online by Cambridge University Press: 15 September 2017
Extract
§ 1. Definition of aim. A distinguished psychologist recently addressed a body of our American colleagues on the teaching of physics. “Your aim in the teaching of physics,” he told them, “should be—to teach physics” The advice was excellent—especially from one who is apt to be regarded as an intellectual Strong Man, full of esoteric knowledge about the development of mental muscle. Substituting “mathematics” for “physics” we may well adopt the maxim with all its implications, negative and positive.
§ 2. Negative implications. Beginning with the negative implications our amendment of Prof. Baldwin's dictum may be expanded as follows. In the first place, the central purpose in teaching mathematics is not to “train the power” of reasoning, of generalising, of “mental accuracy,” etc. The fallacies embodied in the persistent heresy of “formal training” have been repeatedly exposed, and need not detain us here. The time should soon come when an educational writer may ignore them. The chemist does not feel bound to begin his text-book by rebutting the phlogiston-theory, nor the geographer to demolish the sophistries of the flat-earthers.
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- Research Article
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- Copyright
- Copyright © Mathematical Association 1911
Footnotes
1
These articles contain the substance of the two introductory lectures of a course on Algebra in the Secondary School first given at the London Day Training College in the Michaelmas term of 1909 and repeated in 1910.
References
page 168 note 1 It is difficult to bring girls in at all unless in this category !
page 168 note 2 These distinctions were first developed by the present writer in an article on Science Teaching in Adamson's Practice of Instruction (1906). He described them subsequently in an address on Nature Study given to the L.C.C. Conference of Teachers, Jan. 1907, and in a paper on Epistemological Levels in the Proc. of the Aristotelian Society, 1907-8 (cf. Hodson, Broad Lines in Science Teaching, 1909, Ch. VI.) They are professedly based on observation, but the philosophical reader will note the parallel with the Hegelian triad, “Thing, Law, System.”
page 169 note 1 Set down a column of units. Construct a second column by adding each figure in the first column to the figure to the right of it, and setting the sum beneath the latter. Construct the third, fourth, etc., columns in the same way. The result is the following table (“Pascal's Numbers”):
page 170 note 1 This statement is not meant as a prophecy that no useful results will follow from the labours of these mathematicians. History has often shown the precariousness of such predictions. The statement concerns merely the motives to be assumed behind the intellectual activity that produced the book.
page 170 note 2 Cf. Karl Gross, The Play of Man, and McDougall, Social Psychology, Ch. IV.
page 171 note 1 The laws of commutation, distribution, etc.
page 171 note 2 Prof. Adams’ “Herbartian Psychology” is an account of the doctrine of interest, which has already become an educational classic.