On the Construction of Learning Trajectories of Children: The Case of Commensurate Fractions

By Leslie P. Steffe. 2004

127 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/de5aed306455f6b89bd79f37ceedc3a0210da0a0

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Citations in the corpus

Mathematical Knowledge for Teaching Fraction Multiplication (2008, background): “Steffe (2003, 2004) has defined recursive partitioning to be taking a partition of a partition in the service of a non-partitioning goal.”
Obstacles and Affordances for Integer Reasoning: An Analysis of Children's Thinking and the History of Mathematics (2014, background): “…literature (e.g., Carpenter et al., 1999; Carpenter, Fennema, Peterson, Chiang & Loef, 1989; Fennema et al., 1996), Steffe’s work on rational number (Steffe, 1994, 2002, 2004; Steffe & Olive, 2010), and Fuson and her colleagues’ work on supporting ten-structured thinking (Fuson & Briars, 1990;…”
Teaching and Learning Fraction Addition on Number Lines (2008, background): “Recursive partitioning (Steffe, 2003, 2004) is defined to be taking a partition of a partition in the service of a nonpartitioning goal.”
Units coordination and the construction of improper fractions: A revision of the splitting hypothesis (2007, methodology): “Once he could split, at the start of his fifth grade, he could use his splitting operation in constructing commensurate fractional schemes and fractional composition schemes, which indicated he was coordinating three levels of units prior to activity (Steffe, 2003, 2004).”
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).”
An Exponential Growth Learning Trajectory: Students’ Emerging Understanding of Exponential Growth Through Covariation (2016, methodology): “We borrow the term stage from Steffe (2012) and Glasersfeld and Kelly (1981), who”
Putting fractions together. (2020, methodology): “For example, Tzur (1999) described the approach of constructing fractions by iterating unit fractions, and Steffe (2001) noted the analogy between iterating unit fractions and counting with whole numbers (see also Steffe, 2004; Tzur & Hunt, 2015).”
A hypothetical learning trajectory for conceptualizing matrices as linear transformations (2017, unknown): “The construct of an HLT was initially developed for and has primarily been used by both instructors and researchers with a focus on individual student learning in particular content domains [2,11,33,34].”
Conceptualizing Mathematically Significant Pedagogical Opportunities to Build on Student Thinking. (2015, background): “Documents such as the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices [NGA] & Council of Chief State School Officers [CCSSO], 2010) and research on learning trajectories (e.g., Clements & Sarama, 2009; Maloney, Confrey, & Nguyen, 2014; Steffe, 20”
The Splitting Group (2012, background): “Psychologically, the splitting loope describes the composition of iterating and partitioning, which constitutes splitting (Steffe, 2004).”