Chapter 6 Teaching The Basic Concepts Of A Fraction

Quotition The example for quotition ‘How many fives in fifteen?’ would be written 15 ÷ 5 = ; this the child should read as ‘fifteen divided by five’. He would use the yellow rod to measure the length representing 15 to find his answer. Gattegno appreciates the difficulty of associating the division sign with ‘How many . . . ’ , and therefore uses numerous examples of quotition throughout the study of operations involving numbers up to 10 and 20, all in the form of ‘How many . . . in . . . ?’ He does not introduce the sign for division until comparatively late in the course. (See exercise 41, Part IV and exercise 48, Part VI of Book I of Mathematics.) His purpose is to let pupils mature with the operation of quotition before introducing the written sign. He goes on to say: ‘It is usually assumed that the inverse operation of multiplication is division. In a sense this is so, but the word is ambiguous and is loosely used to refer to the procedure by which quotient and remainder are found’ (Numbers in Color, p. 8). To perform such a division, he says, one should ‘take one rod and use it over and over again’ to measure how many ‘go into’ the given number. In the opposite sense, division is basically repeated subtraction and 15 ÷ 5 means 15 – 5 – 5 – 5 where the fives are counted successively as one subtracts. Such a notion of division provides the meaning of

115

The Cuisenaire Gattegno method of teaching Mathematics

The Cuisenaire Gattegno method of teaching Mathematics

The Cuisenaire Gattegno method of teaching Mathematics

The Cuisenaire Gattegno method of teaching Mathematics