关键词:  比例推理, 抑制控制, 负启动, 缺值应用题, 数学认知

Abstract:  The overuse of proportional reasoning refers to a phenomenon that students improperly use proportional reasoning to solve non-proportional problems (e.g., addition problems in the present study). No research to date has directly illuminated the cognitive mechanism of the phenomenon since it is widely found in different countries and different ages. Therefore, we aimed to explore the potential cognitive mechanism in the current study from a new perspective based on the Inhibitory Control Model. The model suggests that solving a problem successfully not only requires the grasp of the underlying logic but also the inhibition of the misleading strategies. Accordingly, we proposed a hypothesis that the failure to inhibit the improper proportional thinking rather than the failure to grasp the additive logic would lead to students’ overuse of proportional reasoning since they may have already mastered additive thinking. We conducted three experiments with sixth-grade children, eighth-grade adolescents, and young adults (college students) to test this hypothesis using the Negative Priming (NP) paradigm. Participants performed a pair of problems: an addition problem in the prime stage, a proportion problem in the probe stage. The logic of NP paradigm is as follows: if participants inhibited the proportional strategy in the prime stage, they would pay a price to activate it in the subsequent probe stage as revealed by a slower response or a higher error rate. In experiment 1, we used missing-value word problems. For each test trial, an addition problem served as a prime and a proportion problem served as a probe; for each control trial, a neutral problem served as a prime and a proportion problem served as a probe. Participants’ performance was measured on the probe stage and their performance was compared between test-probes and control-probes. We found a NP effect in all the three age groups, but there was no significant difference among them. In experiment 2, we reduced task difficulty and cognitive load by creating a visual reasoning task and replicated the results in experiment 1. In experiment 3, we manipulated the number ratio (integer vs. non-integer) of the tasks, and the other conditions were the same as those we did in experiment 1 and experiment 2. Again, NP effects were found in missing-value word problem no matter number ratio was an integer or not. However, in the visual reasoning task, the NP effect only existed in the integer ratio condition. These results indicated: First, children, adolescents and adults all need inhibitory control to overcome the overuse of proportional reasoning. This confirms that success in problem-solving requires not only the grasp the underlying logic of the problem but also the inhibition of a misleading strategy. Second, the potential age difference in inhibitory control ability cannot be eliminated though we found no developmental difference in inhibitory control efficiency according to the magnitude of the NP effect in this study. More research with other methods (e.g., ERP, fMRI) is needed to shed light on this. These results also have important implication for mathematic education. Intervention program that aim at improving inhibitory control or meta-cognition ability for students with low math achievement should be considered.

Key words:  proportional reasoning, inhibitory control, negative priming, missing-value word problem, mathematics cognition