Abstract: Numerical estimation is a pervasive process, both in school and in everyday life. Because of the ease of use and good ecological validity, the number line estimation task becomes of the most popular paradigms in the researches on number estimation. In this task, participants are required to estimate the placement of numbers on number lines. Some of the lines start at 0 and end at 100, whereas others have start point of 0 and endpoint of 1000. In both conditions, the lines were unmarked between the start point and endpoint. The second-year primary school students of America and the first-year students of China manifested the same behavioral patterns in the number line estimation tasks: they both depended on linear representations on 0-100 context while depended on log representations on 0-1000 context. In the current study, we aimed at investigating why the junior year primary school students use different types of number representation for different context. We hypothesized that the reason behind is that they trend to map low end number with fixed distance during number estimation, which is defined as mental distance.
Two experiments were correspondingly designed to examine whether mental distance exists in children’s number estimation. In experiment 1, we examined whether the children used fixed distance to represent low end numbers when the actual length of the number lines were the same while the scale of the numbers varied. Twenty-six first-year primary school students were randomly selected. They were asked to estimate the placement of numbers on 15cm number lines with two contexts: 0-100 or 0-1000. By contrast in experiment 2, we examined whether the children used fixed distance to represent low end numbers when the scale of the numbers were the same while the actual length of the number lines varied. Thirty new first-year students were selected. They were asked to estimate the placement of numbers 0-1000 on number lines with two line lengths: 10cm or 20cm. The low end numbers were oversampled to maximize discriminability of logarithmic and linear functions, and to examine whether mental distance exists.
Paired t-tests of low end numbers showed that there was no significant difference for nine of the ten comparisons on different contexts in experiment 1 and all ten comparisons on different number line lengths in experiment 2. These results suggested that first-year students mapped the low end numbers with fixed distance. Although the context varied from 0-100 to 0-1000, and the lengths of the number lines varied from 10cm to 20cm in the two experiments, the mental distances that low end numbers were mapped to remained constant. Mental distance thus exists in children’s number estimation, and it determines the selection of number representations for different number contexts and number line lengths.
The two experiments came to the same conclusion: mental distance in children’s number estimation is the possible reason why children depend on different representations on different number contexts. Mental distance is a special characteristic emerging when the development of numerical concept in children has reached the interval level.

Key words: mental distance, numerical estimation, linear representation, logarithmic representation