Chapter 6 Teaching The Basic Concepts Of A Fraction
Other fractions such as , , and so on are similarly introduced, and the following type of questions can be asked: Show me
of the dark green rod;
of the brown rod.
The fact that these fractions are represented with two rods (e.g. a blue and a dark green for of 6) demonstrates that it is the relationship between two whole numbers which is being studied.
Gattegno’s Exercises In ‘Mathematics’ An expression such as × 5 = 1 leads to the concept of a fraction as an operator, operating on a quantity to produce another related to the first. Gattegno uses this concept extensively in his study of numbers to provide an understanding of partition division. It is introduced, in connection with the study of numbers up to five, at the same time as the other basic operations in Part IV, Book I (pp. 39-47) of Mathematics. The fractions are introduced in order and each in turn is dealt with in detail. Concentrating on one half, Gattegno gives a wide variety of exercises with half as an operator, including such examples as 3 – ( × 4) =, 2 + × 2 + × 4 = , and × 2 + × 2 = . He does the same with thirds before proceeding to fourths, and with fourths before proceeding to fifths. From the study of 6 onwards, he treats partition division as a
The Cuisenaire Gattegno method of teaching Mathematics