Read e-book online A Century of Mathematics in America [3 vols] PDF

By Peter L Duren; Richard Askey; Uta C Merzbach; Harold M Edwards

ISBN-10: 0821801244

ISBN-13: 9780821801246

ISBN-10: 0821801309

ISBN-13: 9780821801307

ISBN-10: 0821801368

ISBN-13: 9780821801369

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Additional resources for A Century of Mathematics in America [3 vols]

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In just two classes, she not only teased out the Grade 3 pupils’ knowledge of tessellations, but helped them articulate it to the Grade 4 pupils, related it to work that the class had done a month earlier on tangrams, taught a quick lesson on colour mixing (we had only the primary colours for silk painting), and had all of the pupils creating several rough sketches of tessellating patterns they might use on their cards. By the end of the first day, the Grade 3 and 4 pupils had established these characteristics and ‘rules’ about tessellations: Tessellations 35 • • • • they make a pattern with shapes, with no space or overlapping; they use shapes like triangles and quadrilaterals; all triangles, quadrilaterals, and even some hexagons tessellate; other shapes can tessellate if you combine them with squares and triangles, like an octagon with a diamond; • you can make patterns on a shape that tessellates (with the corollary that ‘if you make a pattern or design with shapes on a hexagon, it is not a tessellation unless the whole hexagon tessellates too’); • you have to use shapes with straight sides.

In our discussions about the approach we wanted to take to this work, there was a strong consensus that we wished to write in a style that was personal and direct. In choosing to write invitationally, and in attempting to avoid the pomposity and jargon that characterises far too much of the literature of education, our ambition was to make something that interests, stimulates and supports those individuals attracted to a certain type of teaching and learning. This book is intended, therefore, for teachers, parents, and other educators, who are caring, seeking, imaginative, open and intelligent; individuals who might well feel, in some imprecise way, that more might be made of the teaching of mathematics.

And that, at least with respect to mathematics, is supposed to be my stock in trade. As a mathematics educator —among 12 Chapter 1 other things, a teacher of teachers—I occupy that somewhat lonely and hazardous ground between mathematics teacher and research mathematician. Half-caste, hybrid, neither finned nor feathered, easily and frequently incurring the ire and indignation of both sides of the family tree. Perhaps that is where the difficulty arises. Removed from day-to-day contact with challenging adolescents, I am considered by mathematics teachers as out of touch with the realities of the classroom.

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A Century of Mathematics in America [3 vols] by Peter L Duren; Richard Askey; Uta C Merzbach; Harold M Edwards

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