The Effect Of Number Sense And Anchoring Type On Mathematical Estimation For Primary School Children

Estimation and number sense are two major topics of modern mathematical education; they also offer a new perspective for us to reveal the regularity of individual's cognitive development. Previously the study about estimation and number sense were carried out by most researches as two independent issues, but there was little comprehensive study of the two. Estimation and number sense had been put forward in"Standard of Mathematical Curriculum"in China in 2002. Nevertheless, researches about these two topics are little in China, and we have no normal rating scale of number sense adapted to our country at present. Anchoring effect is a phenomenon that as we judge the number of the target the former number may influence our judgment. Since 1974, it has been found in various materials. Besides, researchers consider it to be one of the potential causes of other psychological phenomena, thus, understanding anchoring effect is very important in theory and in practice.This study includes two sub studies. The purpose of the first study is to design a"Rating Scale of Number Sense for High Graders"and construct the reliability and the validity of this scale. The second study is a 3(number sense level)×3(anchoring type)×3(estimation type) experiment, which is to review whether there are differences if individuals at different number sense levels as well as under different anchoring manners and different estimation tasks; and examine the degree of influence of anchoring effect on students at different number sense level.The collected data are analyzed by SPSS14.0. The results are as follows:1."The High Grade Number Sense Rating Scale"includes 5 components: Understanding numbers meanings and relationship, applying number and comparing magnitude in real context, representing numbers in various means, developing the computational strategies and judging the reasonableness.2. The scale has good reliability and validity. The reliability consists of the coefficient of internal consistency and the test-retest reliability. The validity includes the specialist validity, content validity and construct validity.3. Main effect of number sense in RT is not significant, but there is significant difference between the high and the low individuals; main effect of number sense in the correct rate is significant, there are significant differences between high, middle and low individuals, but there is no significant difference between high and middle individuals.4. There are significant main effects of anchoring manner in both RT and correct rate. The average RT in basic anchoring is significant lower than that in no anchoring and traditional anchoring. The correct percent in no anchoring is significant lower than that in traditional and basic anchoring. But data of descriptive statistics shows that the RTs become shorter and the correct percents become higher with increase of the number sense level.5. There are significant main effects of estimation task in both RT and correct rate. There are significant differences among three estimation tasks. The order of RT from long to short is computational estimation, measurement estimation and numerosity estimation; the order of correct rates from high to low was computational estimation, measurement estimation and numerosity estimation.6. There are significant interaction effects between anchoring manner and estimation task in both RT and correct rate. There are significant interaction effects between number sense and anchoring manner, and among these three independent variables only in correct rate.To sum up, the following conclusions are drawn:1. Number sense of primary school high grade students includes 5 components:2. There are significant main effects of number sense, anchoring manner and estimation in correct percent. But in RT, the main effect of number sense is not significant.3. There are significant interaction effects between anchoring manner and estimation task both in RT and correct percent. There are significant interaction effects between number sense and anchoring manner, and among these three independent variables only in correct percent.