Chapter 12 Discovering Systematic Procedures

expected to set down in notation what he has done’ (p. 21. Now Johnny Can Do Arithmetic). He continues, referring to the moment when the actual operation has been mastered: ‘Children do not mind what notation is used, and are quite ready to adopt another . . . It is just a matter of language and they are already used to hearing things in different ways; for example: “It’s time you were in bed”, or “Now you must run along to bed”, or “Off you go. You ought to be asleep”. It is the sense of what is said that matters, and variations in the words that give the sense are accepted without question’. Gattegno wrote the above whilst discussing the question of showing pupils 4) 13 as an alternative method of writing 13 ÷ 4. It is clear that if vertical notation is used exclusively, the teacher will find it much more difficult to express certain ideas, and may be tempted to introduce fixed procedures before pupils have understood the reasons for their existence. The reader is recommended to adopt the horizontal notation, introducing the vertical notation at a relatively late stage of the course, and then only as an alternative which condenses the wide variety of informal methods discovered; it should not be introduced until the pupils have mastered the operation concerned. Thus, in a second grade, addition might be shown both as 1

37 + 28 = 50 + 15 = 65

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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