Estimated By The Number Of Primary School Children Line Development Research

Numerical estimation is a pervasive process in both school and everyday life. It is also a process that many children feel difficult. This difficulty has been ascribed to inadequate central conceptual structures, mindlesssymbol manipulation, lack of number sense and misunderstanding of arithmetic and so on. Another factor that may play a large role is reliance on inappropriate representation of numbers. Different investigators have proposed the logarithmic representation, line representation and multiple representations hypothesis. Number line estimation has been regarded as an ideal task to study representation models of estimation. Learning from abroad scholars' research procedure, the paper examined primary school children's developmental progression of representation models of estimation in our country. It also examined which experiences can improve the accuracy of estimation.The paper mainly included three experiments about number line estimation. The purpose of experiment 1 was to examine the representation models of estimation and used strategies with the second, fourth and sixth grade children. The experiment 2 was used to test developmental progression of estimation and the correlation between estimation accuracy and math scores with first, second and third grade children. The experiment 3 was used to test the influence of fadback experiences with second grade children, then we can know how malleable and accurate is young children's estimation? Based on the three experiments, the conclusions were as follow:(1) The primary school children exactly possessed multiple representations models of estimation in our country. On the 0—1000 number lines, second graders' median estimates were fit equally well by the logarithmic and linear two models; fourth and sixth graders' median estimates fitted the linear model far better than the logarithmic one. With increasing age and numerical experience, children relied increasingly on appropriate linear representations rather than intuitive logarithmic ones. The same number can elicit either a logarithmic or a linear pattern of estimates depending on the numerical context. The landmark-based proportionality strategy and experimental task both appeared to be specific means of implementing the linear representation.(2) The developmental sequence of representations models of estimation had the consistency. On the 0—100 number lines, first through third graders'estimates presented the developmental sequence-from reliance on a mixture of reliance on logarithmic and linear representations to predominant reliance on a linear representation. Each Child's estimation accuracy and variance accounted for by the linear function with math scores both had significant correlations at all three grade levels. With increasing age, the linearity and accuracy of estimates showed the expected increase, but the variability of estimates showed the expected decrease.The increasing linearity of estimates appeared to be the sole source of the improvement in estimation accuracy.(3) The fadback experiences received by second graders exactly improved their estimation accuracy. The estimation accuracy of children in all three feedback conditions improved more than accuracy of children in the no-feedback group; children in the 150-feedback group had the highest rates of learning; children in the no-feedback group had the lowest rates of learning; the largest and fastest change occurred on numbers around 150 received feedback. Trial block 0 marked the point at which children switched from a logarithmic representation to a linear one; from trial block -1 to trial lock 0, there was a significant increase in the fit of the linear equation to individual children's estimates. In all three feedback conditions, the largest improvements occurred on numbers where the discrepancies between the logarithmic and linear representations were greatest rather than numbers which children received feedback.