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Chapter 12 Discovering Systematic Procedures

In the practical application of theory of equivalent differences as a means of carrying out subtractions, the pupil must either add a value to both the numbers concerned in the subtraction or subtract a value from both. For example, in a subtraction of the type 76–45, the difference is more easily obtained when 40 is subtracted from both numbers and 36–5 used as the equivalent difference. On the other hand, in the case of 76–48, in which ‘borrowing’ is normally used in traditional classes, the difference of 28 is easily obtained by adding 2 to each number and using the equivalent 78–50. If pupils can be taught to understand when it would be best to add and when to subtract a value from the numbers concerned, then, as Gattegno says, all difficulties connected with the operation will disappear. But is there an efficient method of leading pupils to understand and apply equivalent differences for carrying out the operation? First, rod patterns are arranged in such a way that the difference can be easily read without inserting rods in the space that represents the difference. How this might be attempted is briefly illustrated below. 1

Set out the rod pattern showing 17–5 or 17–8. Normally pupils will arrange their rods as illustrated, leaving the space showing the difference on the right.

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The Cuisenaire Gattegno method of teaching Mathematics  
The Cuisenaire Gattegno method of teaching Mathematics  

The Cuisenaire Gattegno method of teaching Mathematics

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