The Effects Of Interactivity Of Problem Representation And Working Memory Depletion On Elementary School Students’ Mental Arithmetic

Mental arithmetic is the basis of mathematical operation,and it is also an important content of cultivating mathematical thinking ability.Interactivity of problem representation refers to the extent to which individuals participate in the construction of problem spaces through actions,which is an important factor affecting the efficiency of mental arithmetic.Specifically,when individuals use external manipulation to increase the degree of interaction with learning materials,the efficiency of their mental arithmetic will be better.But it is unclear whether this efficiency will be affected by individual working memory depletion.Therefore,in the current study,the elementary school students were selected to participate in three experiments,and the effects of interactivity of problem representation and working memory depletion on mental arithmetic efficiency was explored by using mental arithmetic problems as experimental materials.In Experiment 1,69 fourth grade elementary school students were selected as subjects in a 2(interactivity of problem representation: low interaction,high interaction)×2(computational depletion: low computational depletion,high computational depletion)within-subject design to examine the effects of interactivity of problem representation and computational depletion on elementary school students’ mental arithmetic.The results show that under the low computational depletion condition,compared with the condition of high interaction,the accuracy and efficiency of mental arithmetic of elementary school students under the condition of low interaction are higher and the time is shorter,and there was no significant difference in mental arithmetic bias and cognitive load between the two conditions;Under the computational depletion condition,compared with the low interaction condition,the accuracy and efficiency of mental arithmetic are higher,mental arithmetic bias is smaller,the time is shorter and the cognitive load is lower under the high interaction condition.In Experiment 2,69 fourth grade elementary school students were selected as subjects in a 2(interactivity of problem representation: low interaction,high interaction)×2(phonological loop depletion: without phonological depletion,with phonological depletion)within-subjects design to examine the effects of interactivity of problem representation and phonological loop depletion on elementary school students’ mental arithmetic by using low computational depletion tasks as experimental materials.The results showed that under the without phonological depletion condition,compared with the high interaction condition,the mental arithmetic time of elementary school students under the low interaction condition is shorter and the task is less difficult,and there is no significant difference in mental arithmetic correctness,mental arithmetic bias,and mental effort between the two conditions;under the with phonological depletion condition,compared with the low interaction condition,the accuracy of mental arithmetic is higher,the mental arithmetic bias is lower,the time is shorter and the cognitive load is lower under the high interaction condition.The mental arithmetic efficiency of elementary school students under the high interaction condition was significantly higher than that in the low interaction condition,and the mental arithmetic efficiency under the without phonological depletion condition was significantly higher than that under the with phonological depletion condition.In Experiment 3,73 fourth grade elementary school students were selected as subjects in a 2(interactivity of problem representation: low interaction,high interaction)×2(central executive system depletion: without system depletion,with system depletion)within-subjects design to examine the effects of interactivity of problem representation and central executive system depletion on elementary school students’ mental arithmetic by using low computational depletion tasks as experimental materials.The results showed that in the without system depletion condition,compared with the high interaction condition,mental arithmetic time is shorter under the low interaction condition,task difficulty is lower,and mental arithmetic efficiency is higher,and there is no significant differences in mental arithmetic accuracy,bias,and mental effort between the two conditions;in the with system depletion condition,compared with the low interaction condition,the high interaction condition had higher mental arithmetic accuracy and efficiency,lower mental arithmetic bias,shorter time,and lower cognitive load.The following conclusions can be drawn from the three experiments:(1)Under the low computational depletion condition,elementary school students did better in mental arithmetic using the low interaction problem representation form;under the high computational depletion condition,elementary school students did better in mental arithmetic using the high interaction problem representation form.(2)Under the without phonological depletion condition,elementary school students did better in mental arithmetic using the low interaction problem representation form;under the with phonological depletion condition,elementary school students did better in mental arithmetic using the high interaction problem representation form.(3)Under the without system depletion condition,elementary school students did better in mental arithmetic with low interaction problem representations;under the with system depletion condition,elementary school students did better in mental arithmetic with high interaction problem representations.