Integers as Transformations

Abstract

To investigate whether elementary school students can construct operations of thought for integers and integer addition that are crucial for understanding elementary algebra, 2 sixth graders were taught for 6 weeks in eleven 40-minute sessions using a computerized microworld that proposed integers as transformations of position, integer addition as composition of transformations, negation as an operator upon integers or integer expressions, and representations of expressions as defined words. By the final session, both students had constructed mental operations for negating arbitrary integers and determining the sign and magnitude of a sum and had constructed a rule of substitution that allowed them to negate integer expressions. One student could negate represented expressions.

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