Conceptual Change in Mathematics: Understanding the Real Numbers

By Kaarina Merenluoto, Erno Lehtinen. 2002

68 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/5121eb9ee439961a27ab3af89541401bb9d048d8

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Citations in the corpus

The relevance of didactic categories for analysing obstacles in conceptual change: Revisiting the case of multiplication of fractions (2008, background): “Their results have been replicated and explained within the conceptual change approach by Vamvakoussi and Vosniadou (2002), Merenluoto and Lehtinen (2002), and Stafylidou and Vosniadou (2004).”
Understanding the structure of the set of rational numbers: a conceptual change approach (2004, background): “Empirical research on the concept of rational and real numbers and the concept of infinity (Hannula, Maijala, Pehkonen & Soro, 2001; Malara, 2001; Merenluoto & Lehtinen, 2002, this issue ) shows that misconceptions associated with the idea of discreteness are robust.”
How Many Numbers are there in a Rational Numbers Interval? Constraints, Synthetic Models and the Effect of the Number Line (2007, background): “Our results agree with previous findings showing that the idea of discreteness is a barrier to the understanding of the dense structure of the rational numbers set (Malara, 2001; Merenluoto & Lehtinen, 2002, 2004; Neumann, 1998; Tirosh et al., 1999).”
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).”
What Fills the Gap between Discrete and Dense? Greek and Flemish Students' Understanding of Density. (2011, unknown): “…or point to the successor of a particular rational number (Giannakoulias, Souyoul, & Zachariades, 2007; Hartnett & Gelman, 1998; Hannula, Pehkonen, Maijala, & Soro, 2006; Malara, 2002; Merenluoto & Lehtinen, 2002; Tirosh, Fischbein, Graeber, & Wilson, 1999; Vamvakoussi & Vosniadou, 2004, 2007).”
Developmental changes in the comparison of decimal fractions (2010, methodology): “Previous studies 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,…”
How Many Decimals Are There Between Two Fractions? Aspects of Secondary School Students’ Understanding of Rational Numbers and Their Notation (2010, background): “…the idea of discreteness is a major constraint on students’ understandings of density (Giannakoulias, Souyoul, & Zachariades, 2007; Hartnett & Gelman, 1998; Malara, 2001; Merenluoto & Lehtinen, 2002; Neumann, 2001; Pehkonen et al., 2006; Tirosh et al., 1999; Vamvakoussi & Vosniadou, 2004, 2007).”
Extending the conceptual change approach to mathematics learning and teaching (2004, background): “One could argue that the cognitive developmental approach to conceptual change is not very different from the classical conceptual change approach put forward by Posner et al. (1983). But this is not the case.”