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The Towers Problem
Pages 133-140

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From page 133...
... ~. ~ Assumec/ background: This task requires children to enumerate in some systematic fashion all possible ways of constructing towers of blocks uncier certain constraints, and then to explain convincingly that all the possibilities have been found.
From page 134...
... You may use the cubes on your table, which include cubes of two different colors. Please build as many different towers as possible.
From page 135...
... Describe aid of the different towers that you have built that are three cubes ball, when you had two colors available to work with. Why were you sure that you had made every possible tower and had not left any out?
From page 136...
... The discrepancy may arise partly because the students know that their smalI-group colleagues will not accept inexact or unclear oral explanations, whereas a written letter provides no immediate feedback. This lack must be addressed, however, because the development of students' communication skills is an important goal of reform.
From page 137...
... Other kinds of colored cubes are often used in elementary school classrooms, but one should be aware that certain brands of cubes can snap together on their sides, so that Lshaped towers can be built. As a result, these cubes are not appropriate for this task unless the students understand that only three-in-a-row towers are to be counted.
From page 138...
... The resulting towers are all different because they differ either in their top color or in the color of one of the tower blocks.
From page 139...
... ,t~`a~0 `1,,~,`~ date - ~ Con-~ ' i~ The letter describes one or more methods for generating new towers, but fails to deal with the question of devising a method that will exhaustively produce all possible towers, and shows no recognition of the need for such a method.


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