Abstract
This paper analyzes the interpretations of equality and the equal symbol of the third-grade children who participated in a year long whole-class socio constructivist teaching experiment. These children initially interpreted the equal symbol as a command to perform an arithmetical operation; it was less natural to them to interpret it as a relational symbol to compare two quantities. By the end of the school year, children were able to conceptualize the ‘quantitative sameness’ of two numerical expressions and describe it by using the phrase ‘is the same as’, the words ‘equal’ or ‘equals’, or the symbols ‘=’ or ‘=s’. These children expanded their conceptualizations of equality due to their active role in class discussions, the arithmetical tasks that took into account children's difficulties, and the teacher's intellectual sensitivity to ‘strike a delicate balance between the force of teaching and the freedom of learning’ (Freudenthal, 1991, p. 55).
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Sáenz-Ludlow, A., Walgamuth, C. Third Graders' Interpretations of Equality and the Equal Symbol. Educational Studies in Mathematics 35, 153–187 (1998). https://doi.org/10.1023/A:1003086304201
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DOI: https://doi.org/10.1023/A:1003086304201