An integrated theory of whole number and fractions development.

By Robert S. Siegler, Clarissa A. Thompson, Michael Schneider. Cognitive Psychology, 2011

696 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7f0b0fe641fe015209d24bd100e52a99a19edbaf

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Citations in the corpus

Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge? (2014, background): “Students can have problems related to both their procedural and conceptual understanding of fractions (Aksu 1997, Bulgar 2003, Hecht 1998, Post et al. 1993, Prediger 2008, Siegler et al. 2011).”
Using Relational Reasoning to Learn About Scientific Phenomena at Unfamiliar Scales (2016, background): “Learning about fractions often results in a deeper understanding of numerical properties because students must reconcile properties of fractions with their previous understanding of number (Siegler and LortieForgues 2014; Siegler et al. 2011).”
Supported Self-Explaining during Fraction Intervention. (2015, methodology): “Does Supported Self-Explaining Compensate for Limitations in Cognitive Processes?”
Interventions to Improve Fraction Skills for Students With Disabilities: A Meta-Analysis (2019, background): “The implications of this are that fraction knowledge should evolve with numerical development rather than as a secondary domain, as has been the case in other frameworks (Siegler et al., 2011).”
Improving At-Risk Learners' Understanding of Fractions (2013, background): “Number line is Siegler et al. (2011).”
Does working memory moderate the effects of fraction intervention? An aptitude–treatment interaction. (2014, background): “(2011), modeled after Siegler et al. (2011), for 0–2 number lines.”
Early Predictors of High School Mathematics Achievement (2012, result): “Consistent with this analysis, studies have shown that accurate estimation of fraction magnitudes is closely related to correct use of fractions arithmetic procedures (Hecht & Vagi, 2010; Siegler et al., 2011).”
Why Is Learning Fraction and Decimal Arithmetic so Difficult (2015, methodology): “…less knowledge of the magnitudes of individual fractions also tend to have less knowledge of fraction arithmetic (Byrnes & Wasik, 1991; Hecht, 1998; Hecht et al., 2003; Hecht & Vagi, 2010; Jordan et al., 2013; Siegler & Pyke, 2013; Siegler et al., 2011; Torbeyns, Schneider, Xin, & Siegler, 2014).”
Neurocognitive Architectures and the Nonsymbolic Foundations of Fractions Understanding (2016, positive): “Over time, these links strengthen, providing intuitive knowledge of fraction magnitudes, precisely the sort of magnitude knowledge which Siegler et al (2011) have shown to be predictive of fractions arithmetic proficiency and overall scores on mathematics achievement tests.”
Making Connections in Math: Activating a Prior Knowledge Analogue Matters for Learning (2015, background): “Children’s errors on fraction division problems suggest negative transfer from other operations on fractions, specifically, addition and subtraction (i.e., operating on only the numerators when the fraction denominators are equal; Siegler et al., 2011).”
Putting fractions together. (2020, background): “…(i.e., sizes) of fractions seems to be at the heart of many difficulties with fractions and fraction arithmetic, including the whole number bias and confusing different fraction arithmetic operations (Fuchs et al., 2013; Hamdan & Gunderson, 2017; Hansen et al., 2015; Siegler et al., 2011).”