数学焦虑、问题形式对乘法估算的影响

The Impact of Math Anxiety and Problem Type on Multiplication Computational Estimation

采用由研究者修订的数学焦虑量表和自行设计的估算问题,通过团体测验,考察了在纯数字运算和应用题两种情境中数学焦虑对大学生估算加工的影响以及估算中的问题大小效应。结果显示:(1)数学焦虑情绪在纯数字与应用题两种情境下都对估算有显著影响;(2)情境对估算准确性影响显著,纯数字情境下的估算准确性显著高于应用题情境;(3)在应用题情境估算中发现明显的问题大小效应,在纯数字情境估算中却未发现该效应。

As one of the basic forms of mathematical estimation,computational estimation gives new perspectives for investigating individual＇s arithmetic cognition.It is very important to reveal the mechanisms of arithmetic cognition and the development of cognition.As a negative emotion,math anxiety influences not only the development of personal emotion,but also the development of arithmetic cognition.Previous studies about computational estimation have shown that context can make it easier or harder,but the researchers have not come to a conclusion yet.The problem-size effect refers to the phenomenon that it is harder to solve large problems than small problems.In order to investigate the problem-size effect in computational estimation,simple and complex problems were both adopted. 388 participants were randomly sampled from a university in Ji＇nan City.Firstly,they were administered with the Revised Mathematics Anxiety Rating Scale.According to their level of math anxiety,they were divided into three groups,i.e.,high,middle and low.After that,60 students were randomly sampled from each group to attend the computational estimation experiment.The problems presented by computers involved two contexts,i.e.,pure digital and word problem.In addition,both contexts contained simple problems and complex problems. The results showed that 1） On the whole,math anxiety had a significant impact on the performance of computational estimation in two different contexts.The average RT of the low math anxiety group was significantly lower than that of the middle and high groups;the average accuracy of the high math anxiety group was the lowest among the three groups both in the pure digital context and in the word problem context.2） In the pure digital context,there were significant differences in the RTs of the high,middle and low math anxiety groups only in complex problems;in the word problem context,there were significant differences in the RTs of the three groups both in simple problems and complex problems,that is,the average RT of low anxiety individuals was significantly lower than the other two groups,and the accuracy was significantly higher than the other two.3） Context had a significant impact on the accuracy of estimation;the accuracy in the pure digital context was significantly higher than in the word problem context.4） There were significant differences in estimation accuracy between simple and complex problems in different contexts.No significant difference in accuracy between simple and complex problems in the pure context was found;however,the average accuracy on one-digit × two-digit was significantly higher than two-digit × two-digit in the word problem context.5） A problem-size effect in computational estimation was found in the word problem context,but not in the pure digital context. Based on these findings,the following conclusions were drawn,1） math anxiety was an important factor in the process of computational estimation both in the pure digital context and in the word problem context.2） Context posed a clear constraint on the accuracy of estimation.3） Situational cues in word problems could promote the problem-size effect in computational estimation.