Fractions and multiplicative reasoning

By Patrick Thompson, L. Saldanha. 2003

286 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6573417ccd730a2f37cce3ef55ce5c8be859fac6

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Citations in the corpus

Decentering: A construct to analyze and explain teacher actions as they relate to student thinking (2016, background): “As research in the area has revealed (Lamon 2005; Thompson and Saldanha 2003), students can hold numerous meanings for ‘‘proportion,’’ many of which are limited to a procedural execution of calculations.”
Teaching and Learning Fraction and Rational Numbers: The Origins and Implications of Whole Number Bias (2005, background): “…the part-whole scheme associated with the equal sharing approach is less convenient to demonstrate the making of improper fractions (Steffe, 2002; Thompson & Saldanha, 2003; Tzur, 1999) as it is difficult to perceive within the scheme how it is possible that the number of parts (the numerator)…”
Relationships between Students' Fractional Knowledge and Equation Writing. (2015, background): “We attribute reciprocal reasoning to a student if, given that y is 3/5 of x, she can reason that x must be 5/3 of y because each 1/5 of x is equal to 1/3 of y, and so 5/5 of x is equal to 5/3 of y (Hackenberg, 2010, 2014; Thompson & Saldanha, 2003).”
Students’ Reasoning With Reversible Multiplicative Relationships (2010, background): “Understanding these relationships means a student knows that if quantity A is 2/3 times the size of quantity B, then B must be 3/2 times the size of A, because each of the thirds of B are exactly half of the size of A (Behr et al., 1993; Thompson & Saldanha, 2003).”
Students' Whole Number Multiplicative Concepts: A Critical Constructive Resource for Fraction Composition Schemes. (2009, background): “…other researchers have found evidence for connections between students’ whole number multiplicative concepts and students’ fraction knowledge (e.g., Empson, Junk, Dominguez, & Turner, 2006; Hackenberg, 2007; Hunting, Davis, & Pearn, 1996; Kieren, 1995; Thompson & Saldanha, 2003; Vergnaud, 1988).”
CONCEPTUAL ANALYSIS OF MATHEMATICAL IDEAS: SOME SPADEWORK AT THE FOUNDATION OF MATHEMATICS EDUCATION 1 (2008, methodology): “Thompson & Saldanha (2003) employed conceptual analysis to show how a person’s understandings of multiplication, division, measurement, and fraction could each be expressions of a core scheme of conceptual operations, all entailed by multiplicative reasoning.”
Key Developmental Understandings in Mathematics: A Direction for Investigating and Establishing Learning Goals (2006, background): “Thompson and Saldanha (2004) asserted that “conditions for improved instruction entail an enduring discussion of what the community Correspondence should be sent to Martin Simon, Penn State University, Chambers 266, University Park, PA16802.”
Physically Distributed Learning: Adapting and Reinterpreting Physical Environments in the Development of Fraction Concepts (2005, unknown): “Researchers have identified several interpretations of rational numbers, including part–whole, ratio, quotient, and operator (e.g., Carpenter, Fennema, & Romberg, 1993; Confrey & Smith, 1995; Kieren, 1995; Moss & Case, 1999; Streefland, 1993; Thompson & Saldanha, 2003 ).”
Secondary mathematics teachers’ meanings for measure, slope, and rate of change (2017, background): “A person with an image of multiplication as making multiple or partial copies of a quantity is positioned to understand the connection between multiplication and quotient as described by Thompson and Saldanha (2003).”
The design of tasks in support of teachers’ development of coherent mathematical meanings (2007, background): “See Thompson & Saldanha (2003) for a discussion of magnitude versus measure. are lengths.4 Third, angles can be measured in any unit that is proportional to a circle’s circumference.5 To return to the theme of this article, the design of tasks in support of teachers’ development of coherent…”
Units coordination and the construction of improper fractions: A revision of the splitting hypothesis (2007, background): “Kamii & Housman, 2000; Kaput & West, 1994; Steffe, 1992; Thompson & Saldanha, 2003 ).”
On the idea of Learning Trajectories: Promises and Pitfalls (2011, background): “2a) dominate instruction on fractions, children learn to think about fractions in terms of counting parts rather than as magnitudes (Thompson & Saldanha, 2003).”
Advanced Mathematical-Thinking at Any Age: Its Nature and Its Development (2005, background): “Perhaps introducing multiplication as meaning “copies of” would serve the students better ( Thompson & Saldanha, 2003 ): 2 × 4 tells you how many are in 2 copies of 4, and 2/3 × 6 tells you how many are in 2/3 of a copy of 6— thus enveloping repeated-addition and fractional-part-of-an-amount interpr”
How reform curricula in the USA and Korea present multiplication and division of fractions (2010, background): “This understanding can become the basis of multiplicative reasoning that students need to develop by conceiving multiplication as about quantifying something made of identical copies of some quantity or taking a part of a part ( Thompson & Saldanha, 2003 ).”
Explicating a Mechanism for Conceptual Learning: Elaborating the Construct of Reflective Abstraction (2004, unknown): “From her previous work with 5 Thompson and Saldanha (2003) described this limited view of fractions as an additive rather than a multiplicative r lationship.”