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This article investigates the use of tools in elementary classrooms, highlighting possible tensions that exist when pupils discuss the relationship between physical and intellectual tools while working on multiplication. By analysing the data from three consecutive introductory lessons in eight third-grade classrooms, the aim is to contribute to research and conceptualisation around pupils' tensions in appropriating multiplication. The analysis provides examples of tensions that arose when pupils were required to relate a given physical tool to mathematical symbols, but tensions also exist when the pupils master the use of symbols in multiplication but fail to associate them with physical tools. An important finding is that tensions occur when pupils apply their experiences adding by using tools, the reason being that the same tools are often used in several topics. Another finding is that tensions occur between multiplication and addition when using tools. Some pupils are unable to use tools properly and have problems with the different meanings of repeated addition and multiplication. |
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