Feder Ami, Lozin Mariya, Neumann Nadav, Pinhas Michal
Department of Psychology, Ariel University, 4070000, Ariel, Israel.
Psychon Bull Rev. 2025 Apr;32(2):705-713. doi: 10.3758/s13423-024-02571-8. Epub 2024 Sep 4.
Exponential expressions represent series that grow at a fast pace such as carbon pollution and the spread of disease. Despite their importance, people tend to struggle with these expressions. In two experiments, participants chose the larger of two exponential expressions as quickly and accurately as possible. We manipulated the distance between the base/power components and their compatibility. In base-power compatible pairs, both the base and power of one expression were larger than the other (e.g., 2 vs. 3), while in base-power incompatible pairs, the base of one expression was larger than the base in the other expression but the relation between the power components of the two expressions was reversed (e.g., 3 vs. 2). Moreover, while in the first experiment the larger power always led to the larger result, in the second experiment we introduced base-result congruent pairs as well. Namely, the larger base led to the larger result. Our results showed a base-power compatibility effect, which was also larger for larger power distances (Experiments 1-2). Furthermore, participants processed the base-result congruent pairs faster and more accurately than the power-result congruent pairs (Experiment 2). These findings suggest that while both the base and power components are processed when comparing exponential expressions, the base is more salient. This exemplifies an incorrect processing of the syntax of exponential expressions, where the power typically has a larger mathematical contribution to the result of the expression.
指数表达式代表如碳污染和疾病传播等快速增长的序列。尽管它们很重要，但人们往往难以理解这些表达式。在两项实验中，参与者尽可能快速且准确地选择两个指数表达式中较大的那个。我们操纵了底数/指数成分之间的距离及其兼容性。在底数 - 指数兼容对中，一个表达式的底数和指数都比另一个大（例如，2 与 3），而在底数 - 指数不兼容对中，一个表达式的底数比另一个表达式的底数大，但两个表达式的指数成分之间的关系相反（例如，3 与 2）。此外，在第一个实验中，较大的指数总是导致更大的结果，而在第二个实验中，我们还引入了底数 - 结果一致对。也就是说，较大的底数导致更大的结果。我们的结果显示出底数 - 指数兼容性效应，对于较大的指数距离，这种效应也更大（实验 1 - 2）。此外，参与者处理底数 - 结果一致对比处理指数 - 结果一致对更快且更准确（实验 2）。这些发现表明，在比较指数表达式时，虽然底数和指数成分都会被处理，但底数更为突出。这体现了对指数表达式语法的一种错误处理，其中指数通常对表达式的结果有更大的数学贡献。
