Delay Method of Errorless Math Practice

Prepare a list of the calculations from the flash cards on a sheet of paper. These can be on a template, with multiplication facts at the appropriate level pulled and copied for the student. On these forms, include three columns next to each multiplication question, labeled “correct repeat,” “correct wait,” and “correct response.” Start with review and confi dence building. For example, show the question 3 × 4 = __ on the card and without any delay say the answer. Th e student re...

 The Question of Methodology

The methodological question. In a previous book I gave a good deal of thought and analysis to the methodological importance f°r work in the human sciences of finding and formulating a first s t eP. a point of departure, a beginning principle.11 A major lesson I learned and tried to present was that there is no such thing as a merely given, or simply available, starting point: beginnings have to be made for each project in such a way as to enable what follows from them. Nowhere in my experien...

 When Science Became a Profession

The possibilities of modem technology were first in practice realised in England by the energy of a prosperous middle class. Accordingly, the industrial revolution started there. But the Germans explicitly realised the methods by which the deeper veins in the mine of science could be reached. In their technological schools and universities progress did not have to wait for the occasional genius or the occasional lucky thought. Their feats of scholarship during the nineteenth century were the ...

 Mathematicians Who Can Only Generalize or Specialize

A mathematician who can only generalise is like a monkey who can only climb UP a tree. ... And a mathematician who can only specialise is like a monkey who can only climb DOWN a tree. In fact neither the up monkey nor the down monkey is a viable creature. A real monkey must find food and escape his enemies and so must be able to incessantly climb up and down. A real mathematician must be able to generalise and specialise. ... There is, I think, a moral for the teacher. A teacher of traditiona...

 Dissecting Crystals

A casual glance at crystals may lead to the idea that they were pure sports of nature, but this is simply an elegant way of declaring one's ignorance. With a thoughtful examination of them, we discover laws of arrangement. With the help of these, calculation portrays and links up the observed results. How variable and at the same time how precise and regular are these laws! How simple they are ordinarily, without losing anything of their significance! The theory which has served to develop th...

 Cooleridge Describes Davy's Work as Methodical

This refusal to allow anything to chance, ‘accident’ or good fortune was exactly the same as Herschel’s insistence that chance played no part in his discovery of Uranus. Coleridge had taken this up as one of the key philosophical problems associated with science, in an essay provokingly entitled ‘Does Fortune Favour Fools?’, which he republished in The Friend in 1818. Here he described Davy, perhaps mischievously, as ‘the illustrious Father and Founder of Philosophic Alchemy’. B...