Representational change and strategy use in children's number line estimation during the first years of primary school

BACKGROUND: The objective of this study was to scrutinize number line estimation behaviors displayed by children in mathematics classrooms during the first three years of schooling. We extend existing research by not only mapping potential logarithmic-linear shifts but also provide a new perspective by studying in detail the estimation strategies of individual target digits within a number range familiar to children. METHODS: Typically developing children (n = 67) from Years 1-3 completed a number-to-position numerical estimation task (0-20 number line). Estimation behaviors were first analyzed via logarithmic and linear regression modeling. Subsequently, using an analysis of variance we compared the estimation accuracy of each digit, thus identifying target digits that were estimated with the assistance of arithmetic strategy. RESULTS: Our results further confirm a developmental logarithmic-linear shift when utilizing regression modeling; however, uniquely we have identified that children employ variable strategies when completing numerical estimation, with levels of strategy advancing with development. CONCLUSION: In terms of the existing cognitive research, this strategy factor highlights the limitations of any regression modeling approach, or alternatively, it could underpin the developmental time course of the logarithmic-linear shift. Future studies need to systematically investigate this relationship and also consider the implications for educational practice.This research was conducted as part of the PhD project completed by Sonia White at the University of Cambridge, who was supported by the Cambridge Commonwealth Trust. This research was also partly funded by the Medical Research Council, Ref. G90951

Symbolic number: the integration of magnitude and spatial representations in children aged 6 to 8 years

The process of learning symbolic Arabic digits in early childhood requires that magnitude and spatial information integrates with the concept of symbolic digits. Previous research has separately investigated the development of automatic access to magnitude and spatial information from symbolic digits. However, developmental trajectories of symbolic number knowledge cannot be fully understood when considering components in isolation. In view of this, we have synthesized the existing lines of research and tested the use of both magnitude and spatial information with the same sample of British children in Years 1, 2, and 3 (6-8 years of age). The physical judgment task of the numerical Stroop paradigm demonstrated that automatic access to magnitude was present from Year 1 and the distance effect signaled that a refined processing of numerical information had developed. Additionally, a parity judgment task showed that the onset of the spatial-numerical association of response codes effect occurs in Year 2. These findings uncover the developmental timeline of how magnitude and spatial representations integrate with symbolic number knowledge during early learning of Arabic digits and resolve inconsistencies between previous developmental and experimental research lines

Measurements of the semileptonic decays (B)over-bar -> Dl(nu)over-bar and (B)over-bar -> D*l(nu)over-bar using a global fit to DXl(nu)over-bar final states

Semileptonic (B) over bar decays to DXl (nu) over bar (l = e or mu) are selected by reconstructing D(0)l and D(+)l combinations from a sample of 230 x 10(6) Y(4S) --> B (B) over bar decays recorded with the BABAR detector at the PEP-II e(+)e(-) collider at SLAC. A global fit to these samples in a three-dimensional space of kinematic variables is used to determine the branching fractions B(B- --> D(0)l (nu) over bar = (2.34 +/- 0.03 +/- 0.13)% and B(B- --> D*(0)l (nu) over bar) = (5.40 +/- 0.02 +/- 0.21)% where the errors are statistical and systematic, respectively. The fit also determines form-factor parameters in a parametrization based on heavy quark effective theory, resulting in rho(2)(D) = 1.20 +/- 0.04 +/- 0.07 for (B) over bar --> Dl (nu) over bar and rho(2)(D*) = 1.22 +/- 0.02 +/- 0.07 for (B) over bar --> D*(0)l (nu) over bar. These values are used to obtain the product of the Cabibbo-Kobayashi-Maskawa matrix element |V-cb| times the form factor at the zero recoil point for both (B) over bar --> Dl (nu) over bar decays, G(1)|V-cb| = (43.1 +/- 0.8 +/- 2.3) x 10(-3), and for (B) over bar --> D*l (nu) over bar decays, F(1)|V-cb| = (35.9) +/- 0.2 +/- 1.2) x 10(-3)