Investigating algorithm-oriented flexibility and structure-informed flexibility in mathematics learning

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Procedural flexibility is a crucial element of deep procedural knowledge involving the selection of “the most appropriate strategy.” However, there exists unavoidable nuance when one attempts to define “the most appropriate” strategy, which leads to two types of procedural flexibility: (a) structure-informed flexibility (Struct-Flex), which refers to a preference for situationally appropriate strategies; (b) algorithm-oriented flexibility (Algo-Flex), which refers to a preference for standard algorithms. The current study investigated the distinction between these two flexibility types and tested potential predictors for both types of flexibility. The study data were collected from 412 Grade 9 through 12 students from 19 math classrooms in the southeastern region of the U.S. Chi-squared tests and regression models revealed that: (a) problem type was strongly correlated to and predictive of a preference for using algorithms in algebra; (b) students’ current high school math course grade was associated with preference for standard algorithms; (c) students’ current high school math course level and their classroom assignment were related to preference for situationally appropriate strategies. The results suggest that, in this sample, Algo-Flex was as prevalent as Struct-Flex, and the two flexibility types had different predictors. This paper can advance our practical knowledge of U.S. students’ strategy choices. The identified predictors of Algo-Flex and Struct-Flex can also inform the design of relevant educational interventions. Future studies may explore longitudinal datasets to untangle the relationship between course level, age, and flexibility, as well as examine flexibility in Asia in comparison to Europe and North America.