The development of students’ understanding of the numerical value of fractions

By Stamatia Stafylidou, Stella Vosniadou. 2004

376 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d9e084d0cb9a3b234bbd6e1c1f461a8a2a21927c

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Citations in the corpus

Conceptual knowledge of fraction arithmetic. (2015, background): “This well-documented error involves treating fraction numerators and denominators as independent whole numbers, as when claiming that 1/2 + 1/2 = 2/4 (Gelman, 1991; Hecht & Vagi, 2010; Mack, 2005; Ni & Zhou, 2005; Stafylidou & Vosniadou, 2004; Van Hoof, Lijnen, Verschaffel, & Van Dooren, 2013).”
Developmental changes in the comparison of decimal fractions (2010, methodology): “…have applied the conceptual change theory to other mathematical reorganizations, like extensions of number systems (Merenluoto & Lehtinen, 2002; Stafylidou & Vosniadou, 2004; Vamvakoussi & Vosniadou, 2004) or extension of a mathematical symbol and the related operation (Prediger, 2008;…”
How Many Decimals Are There Between Two Fractions? Aspects of Secondary School Students’ Understanding of Rational Numbers and Their Notation (2010, background): “Thus students are found, for example, to interpret the symbol a / b as two unrelated natural numbers, or focus on the additive, rather than the multiplicative, aspect of the relation between a and b ; or they appear to think that “longer decimals are bigger” or “the bigger the terms, the bigger”
Vicious Cycles of Identifying and Mathematizing: A Case Study of the Development of Mathematical Failure (2015, background): “Such a view would draw on studies that point to the different pitfalls and misconceptions that are prevalent in school algebra (Burton, 1988; Kieran, 1992) and in the learning of fractions and rational numbers (Hasemann, 1981; Pantziara & Philippou, 2011; Stafylidou & Vosniadou, 2004).”
Drawing on a Theoretical Model to Study Students’ Understandings of Fractions (2007, background): “Thereby, assigning the concept of numberhood to fractions is regarded as a fundamental step for number theory reconceptualization and proficiency in the additive operations of fractions (Brousseau et al., 2004; Stafylidou and Vosniadou, 2004).”
Naturally Biased? In Search for Reaction Time Evidence for a Natural Number Bias in Adults. (2012, background): “On the other hand, students deal effectively with rational number tasks when these are compatible with natural number strategies (e.g., Nunes & Bryant, 2008; Stafylidou & Vosniadou, 2004).”
What Fills the Gap between Discrete and Dense? Greek and Flemish Students' Understanding of Density. (2011, neutral): “…conceptual organization of number, namely conceptual change (Desmet, Grégoire, & Mussolin, 2010; Gelman, 2000; Hartnett & Gelman, 1998; Merenluoto & Lehtinen, 2002; Moss, 2005; Ni & Zhou, 2005; Smith, Solomon, & Carey, 2005; Stafylidou & Vosniadou, 2004; Vamvakoussi & Vosniadou, 2004, 2007).”
Neurocognitive Architectures and the Nonsymbolic Foundations of Fractions Understanding (2016, positive): “…most important is a difficulty accessing the holistic magnitudes of symbolic fractions (Bonato, Fabbri, Umiltà, & Zorzi, 2007; Kallai & Tzelgov, 2009, 2012; Stafylidou & Vosniadou, 2004) – a difficulty that even expert mathematicians face (Obersteiner, Van Dooren, Van Hoof, & Verschaffel, 2013).”
The Cognitive-Situative Divide and the Problem of Conceptual Change (2007, background): “…have also shown that synthetic models can be observed in many subject-matter areas, from astronomy and mechanics, to history, economics, and mathematics (Christou & Vosniadou, 2005; Gelman, 1990; Vosniadou & Brewer, 1992, 1994; Vosniadou & Ioannides, 1998; also Stafylidou & Vosniadou, 2004).”
Engineering Design and Conceptual Change in Science: Addressing thermal energy and heat transfer in eighth grade (2011, background): “Alternative conceptions may actually be generated by students in school to solve problems, reorganize ideas, and make sense of new information (Stafylidou & Vosniadou, 2004 ).”
Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge? (2014, background): “A main difficulty in learning fractions is the interference with students’ prior knowledge about natural numbers (Behr et al. 1992, Grégoire and Meert 2005, Stafylidou and Vosniadou 2004).”
The relevance of didactic categories for analysing obstacles in conceptual change: Revisiting the case of multiplication of fractions (2008, background): “Its generalization to fractional and decimal numbers offers an obstacle for activating the multiplicative Difficulties like the one of Gareth have been explained by conceptual change in the last years (like in Stafylidou and Vosniadou, 2004).”