By Morris Kline

*x*, and theorems on differentiation and antidifferentiation bring about a definition of the chain rule and examinations of trigonometric services, logarithmic and exponential capabilities, thoughts of integration, polar coordinates, even more. uncomplicated causes, various drills, illustrative examples. 1967 variation. answer advisor to be had upon request.

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**Example text**

Whatever the word ‘waste’ may refer to materially, we recognise a linguistic use which tells us that it is something to be avoided. Also, whatever describable result is denoted by the phrase ‘social control’ we accept that it may be used to commend this state of affairs. One can often get the right sense merely by considering the people to whom a sentence containing the word is addressed. If we say to a teacher ‘This method will bring emotional and instinctive responses of children under social control’, then, unless he doubts our sincerity, he will probably assume that we are putting forward ‘social control’ as a teaching aim, whatever else we may say about method.

But he is at least alive and ongoing and, other things being equal, is more likely to be a stimulating teacher. All this assumes that the teacher really does want, and will, his theory to affect his practice for the better. Very often this assumption is well justified, particularly when the ‘theory’ is scientific. A good, keen, intelligent teacher both wants to understand more about learning and motivation and the mental development of children, and to translate it into practice, just as a lively intelligent doctor wants to understand the scientific basis of his art in order to help his treatment of patients.

And for understandable economy of speech people have thrown a cordon around the lot and called it ‘education’. Perhaps because this name is too vague, experts in England and elsewhere have devised the term ‘educational theory’ to distinguish those studies which have a more obvious bearing on the actual practice of teaching children. Along with the growth of these special studies that form the core of teacher-training has spread the illusion that they comprise a unified body of expert knowledge by means of which problems of education can be appropriately tackled and solved.