By Clifton Fadiman

The spouse quantity to Fantasia Mathematica, first released in 1962, this moment anthology of mathematical writings is much more diverse and includes tales, cartoons, essays, rhymes, song, anecdotes, aphorisms, and different oddments. Authors comprise Arthur C. Clarke, Isaac Asimov, Mark Twain, and Lewis Carroll. 19 illus.

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Their teacher will encourage this as one part of their developing ability to communicate. Later on, they might use intersecting circles to draw petals, shapes might be named and tessellated and the familiar counting numbers will be joined by fractions. ’ Mathematical concepts emerge in the course of such activities and the language needed to talk about them becomes more specialised. ’ Later still, during lessons called ‘mathematics’, young students study number sequences and patterns in shape and space.

An important part of your role is to help your students to examine their old knowledge, to recognise that it is partially but not completely true, and to adapt and extend it to ﬁt new, more general situations. 2 Of course, not all school students will go on to study higher mathematics and these students may never ‘need’ to know about complex numbers. Nevertheless, sharing your holistic view of numbers with them is likely both to help students at any level to make better sense of what they are learning and also to affect students’ attitudes towards the subject.

In other words, the order in which topics are taught and learnt is determined by the logic of the subject itself. There is some truth in this. For example, it is difﬁcult to imagine learning to solve quadratic equations without previous knowledge of basic arithmetic and the solution of linear equations (though saying ‘it is difﬁcult to imagine’ does not necessarily mean it is impossible). However, research into learning shows that children often acquire mathematical knowledge in orders that do not match either the apparently logical mathematical hierarchy or the order in which they have been taught (Denvir and Brown, 1986).