The Development of Situational Mathematical Ability Lags behind the Development of Symbolic Mathematical Ability

The ability to apply mathematical knowledge to solve real-life problems is often considered one of the fundamental educational goals. However, more attention in mathematics education has been given to the development of abstract mathematical computations in symbolic form. The current investigation aims to disclose whether there are different trajectories for symbolic mathematical ability and situational mathematical ability (referred to as symbolic ability and situational ability). This cross-sectional study employed six online tasks and three offline paper-and-pencil tasks among 183 sixth-grade students in primary school and 180 seventh- to eighth-grade students in middle school. The results showed that symbolic ability, assessed through fraction division, fraction multiplication and number series completion, increased from primary school to middle school. This ability was also reflected in the procedural understanding involved in the schematic drawing of fractions and word problem composition. Their situational ability, as displayed by the construction of appropriate situations according to a prescribed arithmetic formula, decreased from primary school to middle school. The developmental patterns were consistent for both male and female students. These results suggest that the development of situational ability lags behind the development of symbolic ability. Based on the results, it is recommended that greater attention be given to the development of situational ability in mathematics education, even in higher educational stages.