The Overuse Of Multiplicative Strategy On Integer Ratio Number Structure And Its Cognitive Mechanism

The integer ratio number structure refers to a set of numbers in which the ratio is integers(e.g.,3 and 12),and the overuse of multiplicative strategy on the integer ratio number structure refers to the phenomenon that students improperly use multiplicative strategy in additive problems in which the number structure is an integer ratio.A large number of previous studies on the overuse of proportional reasoning have demonstrated that integer ratio number structures will induce the use of proportional strategy,but no research to date has illuminated the cognitive mechanism of this phenomenon.Based on the review of related literature,this study proposed that integer ratio number structures preferentially activate multiplicative strategies,leading to the overuse of multiplicative strategies when students solve non-multiplicative problems on integer ratio number structures.Therefore,we aimed to explore the cognitive mechanisms and developmental differences behind them from the perspective of dual processing theory and Inhibitory Control Models.In study 1,based on the dual processing theory,we recruited Grades 3 to 8 and adults as participants to examine the overuse of multiplicative strategy and their developmental characteristics in solving the problems with integer ratio number structures.In study 2,according to the Inhibitory Control Model,Negative Prime Paradigm was used to examine the cognitive mechanisms of overuse of multiplicative strategy on integer ratio number structures from the perspective of behavioral research.In study 3,we used event-related potential technique to further examine the cognitive mechanisms of overuse of multiplicative strategy on integer ratio number structures.The results of the studies indicated that:First,students in elementary and secondary school as well as adults overused the multiplicative strategy in arithmetic problems on integer ratio number structures,shorter responses and lower error rates were found in multiplication problems than in addition problems.There are developmental differences in the overuse of multiplicative strategy,with the overuse in Grades 3 and 5 being most prominent.Second,the negative prime effect was observed in the Negative Prime Paradigm,so students needed to inhibit the overuse of multiplicative strategy when solving addition problems on integer ratio number structures.We found no age differences in the ability to inhibit multiplicative strategy.Third,compared with addition problems,multiplication problems activated larger P2 and P3 amplitude,further demonstrating that multiplicative strategy are intuitive heuristics.Solving integer ratio addition problems required more cognitive resources and the inhibit multiplicative strategy was needed to some extent.