Development of the Mental Number Line Representation of Numbers 0-10 and Its Relationship to Mental Arithmetic.

Anat Feldman,Andrea Berger

doi:10.3390/brainsci12030335

Abstract

The internal representation of numbers on the mental number line (MNL) was demonstrated by performing the computerized version of the number-to-position (CNP) task on a touchscreen while restricting response time. We found that the estimation pattern is best fit by a sigmoid function, further denoted as the “sigmoidal model”. Two developmental leaps occurring during elementary school were recognized: (1) the division of the number line into two segments and (2) consistent use of different anchor points on the number line—the left endpoint in first grade, the right endpoint in second grade, and finally the midpoint in third grade. Additionally, when examining the differences between the breakpoints, we found that first graders demonstrated a breakpoint close to 6, which linearly decreased over the years until stabilizing close to 5. The relation between the ability to place individual numbers on a number line and performance of mental arithmetic showed that the consistent use of anchor points correlated significantly with faster responses in mental arithmetic.

Highlights

Many studies investigating mental number representation assume that numbers and quantities are spatially organized along a mental number line (MNL; e.g., [1–3])
In order to demonstrate the internal representation of numbers on the MNL, we used the computerized version of the number-to-position (CNP) task, which restricts response time and is performed on a touchscreen
We found that the estimation pattern was best fit by the sigmoidal function, which we termed the “sigmoidal model.”

Summary

Introduction

Many studies investigating mental number representation assume that numbers and quantities are spatially organized along a mental number line (MNL; e.g., [1–3]). Siegler and Opfer [4] attempted to understand this developmental process by using a number-to-position (NP) task with participants of different ages In this task, in each trial, a number was presented, and the participant was asked to mark the corresponding position on a bounded number line (on paper/screen), which was labeled with numbers only at its endpoints. In each trial, a number was presented, and the participant was asked to mark the corresponding position on a bounded number line (on paper/screen), which was labeled with numbers only at its endpoints They found that accuracy of the number position changed with numerical range and participant age. Adults produced a linear distribution when placing numbers on a 0–1000 number line [4] This developmental change is known as the logarithmic-to-linear representational shift, and it was replicated in a number of subsequent studies [5–8]

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