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Uniqueness of patterns generated by repetition

Published online by Cambridge University Press:  23 January 2015

John Mason
John Mason*
Affiliation:
27 Elm Road, Oxford OX2 9JZ
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Consider two related tasks:

A) The diagram below displays a fragment of a pattern known to extend indefinitely and to be generated by an endlessly repeating pattern. What kind of shading will the 137th cell have? What number cell will the 137th white cell be in?

B) What is the next term in the sequence 3, 6, 11, 18, 27, …?

Tasks like the first can provide excellent experience of detecting and expressing generality as one route to algebra, but only if learners are first asked to describe a structural relationship which generates the succeeding items. Tasks like the second feature in intelligence tests, but it is well known that such tasks are mathematically incomplete.

Type
Articles
Information
The Mathematical Gazette , Volume 98 , Issue 541 , March 2014 , pp. 1 - 7
Copyright
Copyright © The Mathematical Association 2014