How Many Decimals Are There Between Two Fractions? Aspects of Secondary School Students’ Understanding of Rational Numbers and Their Notation

By Xenia Vamvakoussi, Stella Vosniadou. 2010

231 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/369531bb9e5e4a8607096dff2a24b379703031a2

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Citations in the corpus

Conceptual Limitations in Curricular Presentations of Area Measurement: One Nation’s Challenges (2016, result): “In contrast to perspectives that frame students’developing knowledge inmathematics and science as theorylike (Vamvakoussi & Vosniadou, 2010; Vosniadou, Vamvakoussi, & Skopeliti, 2008), the knowledge-inpieces perspective views students’ knowledge as loosely structured collections of many different…”
Improving fraction understanding in sixth graders with mathematics difficulties: Effects of a number line approach combined with cognitive learning strategies. (2019, background): “Students often incorrectly apply whole number logic to fractions (DeWolf & Vosniadou, 2015; Siegler, Thompson, & Schneider, 2011; Vamvakoussi & Vosniadou, 2010), and the problem seems to be especially pervasive in low-achieving students (Malone & Fuchs, 2017).”
Are secondary school students still hampered by the natural number bias? A reaction time study on fraction comparison tasks (2013, background): “Rational numbers: a stumbling block in mathematics education Research has repeatedly shown that children and adults have difficulties with rational numbers (e.g. Vamvakoussi and Vosniadou 2010; Vamvakoussi, Van Dooren, and Verschaffel 2012).”
Diagnosing misconceptions: Revealing changing decimal fraction knowledge. (2015, background): “Conceptual change and misconceptions According to the framework theory approach to conceptual change, children first form framework theories about the world based on their everyday experiences (e.g., Vamvakoussi & Vosniadou, 2010; Vosniadou & Verschaffel, 2004).”
An integrated theory of whole number and fractions development. (2011, unknown): “For example, Vamakoussi and Vosniadou (2010) proposed that before encountering rational numbers, children form a ''coherent explanatory framework of number as counting number which, in terms of the theoretical framework that we propose, constitutes an initial, domain-specific theory of number''…”
Neurocognitive Architectures and the Nonsymbolic Foundations of Fractions Understanding (2016, unknown): “A third common misunderstanding is the failure to recognize that fractions have different properties than whole numbers (Siegler et al., 2013; Vamvakoussi & Vosniadou, 2010).”
Inhibiting natural knowledge in fourth graders: towards a comprehensive test instrument (2015, background): “The framework theory approach towards conceptual change assumes that people interpret their experiences in everyday life and organize them in a coherent framework theory (Vamvakoussi and Vosniadou 2010).”
What Fills the Gap between Discrete and Dense? Greek and Flemish Students' Understanding of Density. (2011, methodology): “These findings replicate those of the original study (Vamvakoussi & Vosniadou, 2010) in a different population, providing supporting evidence for their generality.”
Naturally Biased? In Search for Reaction Time Evidence for a Natural Number Bias in Adults. (2012, background): “…natural number bias affects rational number reasoning, but these studies focus only on specific tasks such as the comparison of fractions (Stafylidou & Vosniadou, 2004) or the density property (Hartnett & Gelman, 1998; Smith et al., 2005; Vamvakoussi & Vosniadou, 2010; Vamvakoussi et al., 2011).”
What Kinds of Numbers Do Students Assign to Literal Symbols? Aspects of the Transition from Arithmetic to Algebra (2012, background): “Students' initial framework theory of number encompasses a number of interrelated beliefs that underlie students' expectations about what counts as number and how it is supposed to behave—namely, that numbers have a distinct symbolic representation, refer to absolute quantities, have a distinct succ”