title: Place-value understanding in number line estimation predicts future arithmetic performance.
abstract: In multi-digit numbers, the value of each digit is determined by its position within the digit string. Children's understanding of this place-value structure constitutes a building block for later arithmetic skills. We investigated whether a number line estimation task can provide an assessment of place-value understanding in first grade. We hypothesized that estimating the position of two-digit numbers requires place-value understanding. Therefore, we fitted a linear function to children's estimates of two-digit numbers and considered the resulting slope as a measure of children's place-value understanding. We observed a significant correlation between this slope and children's performance in a transcoding task known to require place-value understanding. Additionally, the slope for two-digit numbers assessed at the beginning of grade 1 predicted children's arithmetic performance at the end of grade 1. These results indicate that the number line estimation task may indeed constitute a valid measure for first-graders' place-value understanding. Moreover, these findings are hard to reconcile with the view that number line estimation directly assesses a spatial representation of numbers. Instead, our results suggest that numerical processes involved in performing the task (such as place-value understanding) may drive the association between number line estimation and arithmetic performance.
authors.affiliation: Leibniz-Institut für Wissensmedien, Tuebingen, Germany. julia.dietrich@iwm-tuebingen.de.|Department of Psychology, Eberhard Karls University, Tuebingen, Germany. julia.dietrich@iwm-tuebingen.de.
authors.forename: Julia F
authors.initials: JF
authors.lastname: Dietrich
authors.affiliation: Leibniz-Institut für Wissensmedien, Tuebingen, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Huber
authors.affiliation: Leibniz-Institut für Wissensmedien, Tuebingen, Germany.
authors.forename: Tanja
authors.initials: T
authors.lastname: Dackermann
authors.affiliation: Leibniz-Institut für Wissensmedien, Tuebingen, Germany.|Department of Psychology, Eberhard Karls University, Tuebingen, Germany.|LEAD Graduate School, Eberhard Karls University, Tuebingen, Germany.
authors.forename: Korbinian
authors.initials: K
authors.lastname: Moeller
authors.affiliation: Leibniz-Institut für Wissensmedien, Tuebingen, Germany.|University of Regensburg, Germany.
authors.forename: Ursula
authors.initials: U
authors.lastname: Fischer
mesh_terms: D000073978:Academic Performance; D002648:Child; D032882:Comprehension / Q000502:physiology*; D005260:Female; D006801:Humans; D008297:Male; D055641:Mathematical Concepts; D008433:Mathematics; D013850:Thinking / Q000502:physiology*
keywords: arithmetic; number line estimation; numerical development; place-value understanding; transcoding