We may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra.
Interpretation
Algebra must be understandable and practical; if it isn't, it fails its purpose.
This quote by William Kingdon Clifford emphasizes the importance of clarity and practicality in mathematics, specifically algebra. It suggests that if algebra cannot be expressed in straightforward, understandable language and common sense, then it loses its effectiveness and usefulness. The essence of mathematical concepts should be accessible to ensure they can be effectively utilized in real-world scenarios.
In practice
This quote can be used in a math class to emphasize the importance of understanding math concepts.
The aim of scientific thought, then, is to apply past experience to new circumstances; the instrument is an observed uniformity in the course of events. By the use of this instrument it gives us information transcending our experience, it enables us to infer things that we have not seen from things that we have seen; and the evidence for the truth of that information depends on our supposing that the uniformity holds good beyond our experience.
Remember that [scientific thought] is the guide of action; that the truth which it arrives at is not that which we can ideally contemplate without error, but that which we may act upon without fear; and you cannot fail to see that scientific thought is not an accompaniment or condition of human progress, but human progress itself.
Into this, for good or ill, is woven every belief of every man who has speech of his fellows. A awful privilege, and an awful responsibility, that we should help to create the world in which posterity will live.
This sense of power is the highest and best of pleasures when the belief on which it is founded is a true belief, and has been fairly earned by investigation.
It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence.
Some know the value of education by having it. I know it's value by not having it.
Not everyone has equal abilities, but everyone should have equal opportunity for education.
Someday America will have its very own commercial-free TV and radio station devoted to only one thing: to teach people, in their homes, all the essentials of personal achievement.
We inculcate young people with the message that if they don't succeed, it is merely of their own doing. They should have worked harder, we say. They should have made better decisions. This message is especially present in communities of color.
A sympathetic parent might see the spark of consciousness in a baby's large eyes and eagerly accept the popular claim that babies are wonderful learners, but it is hard to avoid the impression that they begin as ignorant as bread loaves.
Respect all the reasonable forms of activity in which the child engages and try to understand them.
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