Bounded and Unbounded Number Line Estimation in Adults: Accuracy, Response Characteristics, and Mathematical Achievement

Source abstract

Number line estimation is widely used to examine numerical magnitude processing and its relationship with mathematics. However,it remains unclear whether mathematical achievement is more closely associated with estimation accuracy or with characteristics ofestimation responses. The present study examined these relationships among 192 adults who completed bounded and unboundednumber line estimation tasks and mathematics assessments covering arithmetic, fractions, algebra, and percentages. Linear,logarithmic, mixed log-linear, proportional judgment, and scallop models were compared to characterize estimation responses. Wealso evaluated the relationships of estimation accuracy and fitted-response characteristics with mathematical achievement. Linearmodels best predicted bounded estimation, whereas mixed log-linear and selected scallop models offered small improvementsfor unbounded estimation. Greater linearity and stronger proportional judgment model fit were associated with greater boundedestimation accuracy, while mixed log-linear characteristics were related to estimation error in both tasks. Bounded estimation accuracywas more consistently associated with mathematical achievement than unbounded accuracy. Most fitted-response characteristicsaccounted for little additional variation in mathematics after considering estimation accuracy, although exploratory analyses indicatedthat mixed-model characteristics contributed modest additional information. The findings highlight the value of distinguishingestimation accuracy from the mathematical characteristics of estimation responses when investigating individual differences inmathematical achievement.