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Fostering Students’ Development of Productive Representation Systems for Infinite Series
Ist Teil von
The Mathematics Enthusiast, 2024-08, Vol.21 (3), p.633-672
Ort / Verlag
Missoula: University of Montana, ScholarWorks, c/o Bharath Sriraman
Erscheinungsjahr
2024
Link zum Volltext
Quelle
Electronic Journals Library
Beschreibungen/Notizen
Students' development of reasoning through algebraic symbols is a crucial component of most mathematics courses. This paper reports the journey of one second-semester calculus student, Cedric, as he attempted to reason about and create algebraic representations for arbitrary partial sums and infinite series through two exploratory teaching interviews. We report Cedric's symbolizing activity in terms of Eckman's (2023) expression framework, focusing on Cedric's development and attribution of meaning to a personal expression template for denoting partial sums and series. Specifically, we describe how Cedric leveraged his initial meanings for partial sums to create personal expressions to reason about infinite series. We then describe Cedric's construction of a general personal expression template for partial sums and series, including cognitive and physical modifications he made to his personal expression template as he symbolized various series. Our results show potentially profitable task sequences and lines of questioning that instructors might utilize to help students be more successful in constructing productive meanings for algebraic symbols.