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Developing algebraic activity through conjecturing about relationships

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This manuscript contributes to research on how algebraic thinking about operations and properties can develop, and relevant forms of curricular activity. The key question asked is: how can students' early algebraic activity be fostered through focusing on relations involving operations and properties? We adopt Radford's three aspects of algebraic thinking (indeterminacy, denotation and analyticity), which focus on considering, symbolising and operating on unknown objects. We investigate the work of a class of 11-12 year old students in re-analysing data collected over 20 years ago as part of a project exploring algebraic activity. Our findings point to the proposal that a focus on conjecturing about relationships can be a powerful route into early algebra. On the basis of our analysis we propose an extension to Radford's third aspect of algebraic thinking (analyticity) to include structuring a mathematical space, e.g., through a set of conjectures.

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