From an operational to a relational conception of the equal sign. Thirds graders’ developing algebraic thinking.
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Research Council on Mathematics Learning
Algebraic thinkingAnalyzing expressionsArithmetic equationsEarly-AlgebraEqual signNumber sentencesRelational thinking
Molina, M. y Ambrose, R. (2008). From an operational to a relational conception of the equal sign. Thirds graders’ developing algebraic thinking. Focus on Learning Problems in Mathematics, 30(1), 61-80.
We describe a teaching experiment about third grade students´ understanding of the equal sign and their initial forays into analyzing expressions. We used true/false and open number sentences in forms unfamiliar to the students to cause students to reconsider their conceptions of the equal sign. Our results suggest a sequence of three stages in the evolution of students’ understanding of the equal sign with students progressing from a procedural/computational perspective to an analytic perspective. Our data show that as students deepened their conceptions about the equal sign they began to analyze expressions in ways that promoted algebraic thinking. We describe the essential elements of instruction that advanced this learning.