The construction of an iterative fractional scheme: the case of Joe

By John Olive, Leslie P. Steffe. 2001

96 citations recorded by the source corpus.

Subfields: Applied Mathematics, Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6d0b72db67c8e2b2a5eaf5acbfebfd4226f56c23

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In Applied Mathematics

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Citations in the corpus

Mathematical Knowledge for Teaching Fraction Multiplication (2008, background): “In subsequent work, Steffe and Olive (Olive 1999; Olive & Steffe, 2001; Steffe 2001, 2003, 2004) have examined how elementary students modified their knowledge of whole-number counting and multiplication to construct knowledge of fractions when engaged in tasks involving lengths and rectangular…”
Students’ Reasoning With Reversible Multiplicative Relationships (2010, methodology): “To justify these claims requires a brief discussion of cognitive anticipation, or foresight, which Piaget (1967/1971) believed was “one of the essential functions of knowing” (p. 191).4 von Glasersfeld (1998) has identified three kinds of anticipation based on humans’ “mysterious” (p.”
Towards understanding the origins of children's difficulties in mathematics learning (2011, background): “…is necessary for further development of multiplicative concepts, including the base ten system and unitising (Confrey, 1994; Lamon, 1996; Mulligan & Watson, 1998; Nunes et al., 2007; Steffe, 1994; Thomas et al., 2002) or fractions and units of measurement (Battista, 2003; Olive & Steffe, 2002).”
Teaching and Learning About Whole Numbers in Primary School (2016, background): “Studies in which teaching starts from analyzing relations between quantities often focus on a single but broadly defined concept—for example, proportions (Kaput and West 1994), fractions (Olive and Steffe 2002; Nunes et al. 2007), speed (Thompson 1994), or rate of change (Confrey 1994).”
Students' Whole Number Multiplicative Concepts: A Critical Constructive Resource for Fraction Composition Schemes. (2009, background): “Olive, Steffe, and colleagues have confirmed their hypothesis in analyses of data from a teaching experiment with students in their third through fifth grades (e.g., Biddlecomb, 2002; Olive & Steffe, 2002; Steffe, 2003, 2004; Tzur, 1999, 2004).”
Units coordination and the construction of improper fractions: A revision of the splitting hypothesis (2007, methodology): “This also seemed to be the case for other students participating in Olive and Steffe’s research project (1990) who, upon constructing a splitting operation, also constructed an iterative fractional scheme (Leslie P.”
Teaching and Learning Fraction Addition on Number Lines (2008, background): “Iterating (Olive & Steffe, 2001; Steffe, 2001) involves taking a segment and joining copies end to end to recreate an already established unit.”