Indeterminate Operations as a Route into Early Algebra: a Multi-modal Semiotic Analysis of a Chinese Primary Classroom

Abstract

This study examines 9–10-year-old students’ early algebraic reasoning in representing and solving single-variable linear equations. Adopting Radford’s Theory of Objectification, a teaching–learning activity was co-designed in a Chinese primary school with concrete and iconic pan-balance representations. Video and worksheet data from 30 students revealed diverse representations of equality (numbers, letters, Chinese characters, shapes, and balance diagrams), including the culturally embedded Heavenly Stems (天干), ), a potentially novel finding in English language research. Gestures and multimodal actions supported an embodied understanding of equivalence via symmetry and compensatory operations. I argue for an extension to Radford’s framework for algebraic thinking, to include the indeterminate operations.

Keywords

Early algebraSemioticsIndeterminate operationHeavenly stems

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