By A. D. C. Peterson
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Additional info for Secondary Education. Techniques of Teaching
Sample text
Classroom Practice. In general, mathematics in secondary schools is taught by class-teaching methods. " Chalk and talk " is the principal medium of teaching. Many lessons begin with a quick oral revision of the preceding lesson, or of that part of earlier work which is to be developed during the lesson. If there is no particular revision to do, the teacher may give five minutes to practice in mental arithmetic. A lesson normally contains some expository material which may take the form of the introduction of new work, or examples worked by the teacher on the blackboard.
L U C H I N S , A . , M e c h a n i s a t i o n in P r o b l e m - s o l v i n g , Psychological Monographs, 54, N o . 6, A m e r i c a n P s y c h o l o g i c a l A s s o c i a t i o n . H I L T O N , P . , " A r i t h m e t i c — d o w n b u t n o t o u t , " Teaching Arithmetic, spring, 1963. M I N I S T R Y O F E D U C A T I O N P A M P H L E T N O . 36, Teaching Mathematics in Secondary Schools, p . 126. M A T H E M A T I C A L ASSOCIATION, Teaching Mathematics in Primary Schools, p. 64. C H O Q U E T , G .
There are some grounds for saying that measurement can lead to a hypothesis, but it does not, in mathematics, lead to facts. It is much better to use some informal demonstration which is independent of measurement. The simplest is to tear off the corners of a paper triangle and lay them adjacent to each other along a straight line. Another method is to fold a triangle cut from paper or cardboard 40 SECONDARY EDUCATION as shown in the diagram. This illustration has the advantage that it is convincing in its own right, could lead to a formal proof later (although not the usual one), and demonstrates at least two other geometrical properties at the same time.