Understanding the structure of the set of rational numbers: a conceptual change approach

By Xenia Vamvakoussi, Stella Vosniadou. 2004

274 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5ffea6fd07831d3f2a1661dac13fe6e24a5d6e3d

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Citations in the corpus

How Many Numbers are there in a Rational Numbers Interval? Constraints, Synthetic Models and the Effect of the Number Line (2007, methodology): “Based on the findings of a previous study ( Vamvakoussi & Vosniadou, 2004 ) we suggest that these students converted 4/8 into 1/2, and then assumed that 1/2 is not between 3/8 and 5/8, based on the difference between the symbolic representations.”
Diagnosing misconceptions: Revealing changing decimal fraction knowledge. (2015, methodology): “For example, in one study students were asked to think-aloud when answering questions such as “How many numbers are there between .005 and .006?” and to explain their answers (Vamvakoussi & Vosniadou, 2004).”
Inhibiting natural knowledge in fourth graders: towards a comprehensive test instrument (2015, background): “This can result in problems and misconceptions when rational numbers are introduced, because the characteristics and rules accounting for rational numbers do not always correspond with those for natural numbers (Gelman 2000; Saxe et al. 2013; Smith et al. 2005; Vamvakoussi and Vosniadou 2004).”
Naturally Biased? In Search for Reaction Time Evidence for a Natural Number Bias in Adults. (2012, background): “…that the idea of infinitely many numbers in an interval is difficult for students at various levels of instruction (Giannakoulias et al., 2007; Hannula et al., 2006; Hartnett & Gelman, 1998; Merenluoto & Lehtinen, 2002; Smith et al., 2005; Tirosh et al., 1999; Vamvakoussi & Vosniadou, 2004, 2010).”
Student Teachers’ and Experienced Teachers’ Professional Vision of Students’ Understanding of the Rational Number Concept (2020, unknown): “However, increasing research evidence shows that students tend to overgeneralise their natural number knowledge to rational numbers (McMullen et al. 2015; Van Dooren et al. 2015; Vamvakoussi and Vosniadou 2004).”
How Many Decimals Are There Between Two Fractions? Aspects of Secondary School Students’ Understanding of Rational Numbers and Their Notation (2010, methodology): “In comparison to our previous studies (Vamvakoussi & Vosniadou, 2004, 2007), we broadened our age sample to include seventh graders in addition to ninth and eleventh graders.”
Teaching and Learning About Whole Numbers in Primary School (2016, background): “…for example, whether teachers’ realization that rational numbers do not have a next number is a matter of content or pedagogical content knowledge (Vamvakoussi and Vosniadou 2004): do teachers need to be more aware of this difference between whole and rational numbers themselves or do they need…”
Developing Conceptual and Procedural Knowledge of Mathematics (2015, unknown): “…of concepts Define the equal sign (Knuth, Stephens, McNeil, & Alibali, 2006; Rittle-Johnson & Alibali, 1999) (Star & Rittle-Johnson, 2009; Vamvakoussi & Vosniadou, 2004) (Izsák, 2005) b. Explain why procedures work Explain why ok to borrow when subtract (Fuson & Kwon, 1992) (Berthold &…”
Developmental changes in the comparison of decimal fractions (2010, methodology): “Several studies have indicated that the extension of the number concept to rational or real numbers requires a conceptual change (Lehtinen, Merenluoto, & Kasanen, 1997; Merenluoto & Lehtinen, 2002; Merenluoto & Palonen, 2007; Stafylidou & Vosniadou, 2004; Vamvakoussi & Vosniadou, 2004).”
Mental number line, number line estimation, and mathematical achievement : Their interrelations in grades 5 and 6 (2009, background): “Facing this rationale, recent efforts to broaden the scope of conceptual change approaches from science to mathematics learning seem especially worthwhile (Merenluoto & Lehtinen, 2004; Vamvakoussi & Vosniadou, 2004).”
Spontaneous Focusing on Quantitative Relations in the Development of Children's Fraction Knowledge (2014, background): “…with many concepts related to fractions (McMullen, Laakkonen, Hannula-Sormunen, & Lehtinen, 2014; Merenluoto & Lehtinen, 2004; Obersteiner, Van Dooren, Van Hoof, & Verschaffel, 2013; Siegler, Fazio, Bailey, & Zhou, 2013; Vamvakoussi, Van Dooren, & Verschaffel, 2012; Vamvakoussi & Vosniadou, 2004).”