A symbolizing activity for constructing personal expressions and its impact on a student's understanding of the sequence of partial sums

This paper reports the results from a set of exploratory teaching interviews in which students constructed individualized algebraic expressions (called personal expressions) to describe their meanings for partial sums. Our analysis focused on one student, Emily, who constructed two distinct personal expressions for partial sums, one novel and one based on her image of summation notation. Emily created her novel expression to denote the process of generating the summands to compute the value of a partial sum. Emily adopted summation notation to describe the value of the partial sum. After reflecting on her inscription for a series’ general term of summation, Emily constructed a single expression to describe either the process of computing an arbitrary partial sum or the value of the sum itself. Using Emily's story, we propose three categories for students’ coordination of their meanings for partial sums with a corresponding representation.