title: An integration of competing accounts on children's number line estimation.
abstract: Children's estimation patterns in bounded number line estimation (NLE) reveal marked developmental changes. Three different theoretical accounts were proposed to explain these changes: a log-to-linear shift account, a proportion-judgment account and a two-linear account considering familiarity with numbers or the understanding of the place-value structure of the Arabic number system. However, only the first two accounts are considered prominently in the ongoing scientific debate. Therefore, we first present a reanalysis of NLE data of Austrian first-graders contrasting all three accounts. Results indicate that the two-linear account is a reliable alternative to the log-to-linear shift as well as the proportion-judgment account. However, we do not claim the two-liner account to provide an exhaustive explanation for the observed developmental changes. We rather introduce the idea that aspects of all three accounts may complement - instead of exclude - each other. Jointly considering conceptual (i.e., familiarity, place-value) and procedural (i.e., proportion-judgments) aspects will allow for a more comprehensive understanding of children's development in NLE.
authors.affiliation: Knowledge Media Research Center Tuebingen, Germany.
authors.forename: Tanja
authors.initials: T
authors.lastname: Dackermann
authors.affiliation: Knowledge Media Research Center Tuebingen, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Huber
authors.affiliation: Knowledge Media Research Center Tuebingen, Germany ; Eberhard Karls University Tuebingen Tuebingen, Germany.
authors.forename: Julia
authors.initials: J
authors.lastname: Bahnmueller
authors.affiliation: Knowledge Media Research Center Tuebingen, Germany ; Eberhard Karls University Tuebingen Tuebingen, Germany.
authors.forename: Hans-Christoph
authors.initials: HC
authors.lastname: Nuerk
authors.affiliation: Knowledge Media Research Center Tuebingen, Germany ; Eberhard Karls University Tuebingen Tuebingen, Germany.
authors.forename: Korbinian
authors.initials: K
authors.lastname: Moeller
keywords: mental number line; model fitting; number line estimation; numerical development; spatial representation of number magnitude