— James Joseph Sylvester (1814 – 1897)
May not music be described as the mathematics of the sense, mathematics as music of the reason?
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— Tobias Dantzig, about the development of the notion of number, in Number: The Language of Science, Macmillan, 1930
It is not a story of brilliant achievement, heroic deeds, or noble sacrifice. It is a story of blind stumbling and chance discovery, of groping in the dark and refusing to admit the light. It is a story replete with obscurantism and prejudice, of sound judgment often eclipsed by loyalty to tradition, and of reason long-held subservient to custom. In short, it is a human story.
— W.Servais, T.Varga: Teaching School Mathematics, A UNESCO Source Book, 1971.
Learning is much more similar to biological growth than to manufacture, where component parts are first produced, then fitted together.
A short comic thread through numbers
The comics are from the book Understanding and Doing Math – Circle 1 Are natural numbers natural? Do we need zero? Be careful with negative numbers! How to rationally divide two golden bars among three pirates? Secrets of decimal notation Bills can sometimes be irrational.
A Paradox of School Mathematics
School mathematics: Real mathematics:
Which unit of measurement is better: English foot or Croatian elbow?
My neighbor John and I got into a serious disagreement while working on a fence between our houses: will we use an English foot (John’s proposal) or a traditional Croatian elbow (my proposal) to measure the fence? This event helped me solve a problem that has plagued me since elementary
To be vaccinated, or not to be vaccinated, that is the question
Someone proposes the following bet to you. A symmetrical dice will be rolled only once. If is rolled, the challenger gets euros, otherwise, you get euros. The probability of rolling is and the probability of not rolling is , times bigger. Would you accept a bet? What would you do
A Path into Math
Some do math because they have to. Some do math because they think math helps them manage the world. Some do math because they find beauty in it. Not only is there no royal path to math, as Euclid said long ago (for geometry), but there is also no common
— W.Servais, T.Varga: Teaching School Mathematics, A UNESCO Source Book, 1971
Every child, by nature, likes learning just as he likes eating. Children reluctant to eat, and parents using promises and threats in order to make them eat, are not rare, yet they constitute perhaps rather an exception than a rule. In teaching, the situation is worse: to attach rewards and punishments to learning is more a rule than an exception. It is an institutionalized practice supported by social conditioning and by decrees. This practice exerts an unfavorable influence on the natural process of learning.