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In addition, the teaching of theories from axioms, or some close imitation of them such as the basic laws of an algebra, is usually an educational disaster.
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p. 739

 

Ivor Grattan-Guinness

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At different stages in the educational process different changes are required. In schools the chief need is for a general change in the attitude towards science, which should be from the beginning an integral part and not a mere addition, often an optional addition, to the curriculum. Science should be taught not merely as a subject but should come into all subjects. Its importance in history and in modern life should be pointed out and illustrated. The old contrast, often amounting to hostility, between scientific and humane subjects need to be broken down and replaced by a scientific humanism. At the same time, the teaching of science proper requires to be humanized. The dry and factual presentation requires to be transformed, not by any appeal to mystical theory, but by emphasizing the living and dramatic character of scientific advance itself. Here the teaching of the history of science, not isolated as at present, but in close relation to general history teaching, would serve to correct the existing atmosphere of scientific dogmatism. It would show at the same time how secure are the conquests of science in the control they give over natural processes and how insecure and provisional, however necessary, are the rational interpretations, the theories and hypotheses put forward at each stage. Past history by itself is not enough, the latest developments of science should not be excluded because they have not yet passed the test of time. It is absolutely necessary to emphasize the fact that science not only has changed but is continually changing, that it is an activity and not merely a body of facts. Throughout, the social implications of science, the powers that it puts into men's hands, the uses they could make of them and those which they in fact do, should be brought out and made real by a reference to immediate experience of ordinary life.

 

John Desmond Bernal

 

"The basic teaching of Buddhism is the teaching of transiency or change. That everything changes is the basic truth for each existence. No one can deny this truth and all teaching of Buddhism is condensed within it. This is the teaching for all of us. Wherever we go this teaching is true. This teaching is also understood as the teaching of selflessness. Because each existence is in constant change, there is no abiding self.

 

Shunryu Suzuki

 

The chief object of the Law, as has been shown by us, is the teaching of truths; to which the truth of the creatio ex nihilo belongs. It is known that the object of the law of Sabbath is to confirm and to establish this principle, as we have shown in this treatise (Part II. chap. xxxi.) In addition to the teaching of truths the Law aims at the removal of injustice from mankind. We have thus proved that the first laws do not refer to burnt-offering and sacrifice, which are of secondary importance.

 

Maimonides

 

All relations are either qualitative or quantitative. Qualitative relations can be considered by themselves without regard to quantity. The algebra of such enquiries may be called logical algebra, of which a fine example is given by Boole.
Quantitative relations may also be considered by themselves without regard to quality. They belong to arithmetic, and the corresponding algebra is the common or arithmetical algebra.
In all other algebras both relations must be combined, and the algebra must conform to the character of the relations.

 

Benjamin Peirce

 

The teaching of axioms should come after conveying the theory in a looser version.

 

Ivor Grattan-Guinness