Separating sets, including children's own signs for '='
Separating sets
Children use a wide range of strategies to show that their two amounts are distinct and separate. They do this in a variety of ways, including:
- grouping the two sets of items to be added, leaving a space between them,
- separating theses with words,
- drawing vertical line between the sets,
- drawing an arrow or a personal sign between them.
Equals signs
Young children begin by using their own means to signify the equal’s symbol. For example, Louisa (below) ended her calculations by writing the words "altogether there's '6'" (circled) and John merely wrote "is" before his total, whereas Fred just added the number of their total, without anything to indicate the equal’s sign. In his calculation, Jack used a horizontal line to signify 'equals'.
Louisa's strawberries Louisa (5 years, 1 month), was adding strawberries. Between her two sets she wrote "and four more", then finally wrote "Altogether there's '6' (circled)." Louisa has chosen a means of representing that she felt comfortable without the same time showing that she understands the operation.
methods / explorations with signs and symbols
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 | Adding grapes In this class, the children had been invited to choose some grapes to add, dividing them between two dishes (they could eat them later). John (5 years, 5.5 months), wrote and drew two sets of grapes, leaving a space that allowed this to be read as'4 and 3', then writing the quantity of each to be added. Finally he drew a horizontal line (to signify the equals sign), followed by the total of each calculation.
methods / explorations with signs and symbols
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Fred adds grapes Fred, (5 years, 8 months), was also adding grapes has separated his two sets of grapes with a line (drawn above one finger of the hand). The plus and equals signs are implied, since the whole canoe read as "5 plus1 equals 6." Finally, he wrote the numerals '5' and '1' on' the left, and the '6' beneath as the total.
methods / explorations with signs and symbols
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 | Jack's addition response Jack explored abstract symbols in a diferent way. He has drawn two separate sets of grapes, leaving a gap that allows this to be read as '4 and 3'. Following this he confirmed the amounts to be added by writing the numerals and drawing a horizontal line between these and the final '7' (his answer). The line functions as an equals sign for Jack.
methods
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