Building on Informal Knowledge through Instruction in a Complex Content Domain: Partitioning, Units, and Understanding Multiplication of Fractions

By Nancy K. Mack. 2001

127 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6c570b313bb32e11f9f6c3da183e6ece6b6030b5

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Citations in the corpus

Students' Whole Number Multiplicative Concepts: A Critical Constructive Resource for Fraction Composition Schemes. (2009, background): “In a similar vein, Mack (2001) found that fifth grade students’ informal knowledge of partitioning and conceptualizing units could be a basis for solving fraction multiplication problems.”
A Comparative Analysis of the Addition and Subtraction of Fractions in Textbooks from Three Countries (2010, background): “when (1) it fails to build on students’ prior knowledge (Mack, 2001), (2) it emphasizes rote learning at the expense of conceptual understanding (Ball, 1993; Mack, 2001), (3) it introduces formal symbols and algorithms before familiarizing students with the different aspects of the notion of fractio”
Students’ Reasoning With Reversible Multiplicative Relationships (2010, background): “…(Behr, Wachsmuth, Post, & Lesh, 1984; Saenz-Ludlow, 1994), construct improper fractions (Hackenberg, 2007; Olive & Steffe, 2002; Steffe, 2002; Tzur, 1999), and compose fractions additively and multiplicatively (Hackenberg & Tillema, 2009; Mack, 2001; Steffe & Olive, 2010; Streefland, 1991).”
Relationships between Students' Fractional Knowledge and Equation Writing. (2015, background): “…whole into some number of equal pieces; disembedding, removing a part from a whole without mentally destroying the whole; and iterating, repeatedly instantiating a part to make a larger amount (Kieren, 1980; Lamon, 1996; Mack, 2001; Pothier & Sawada, 1983; Steffe & Olive, 2010; Tzur, 1999, 2004).”
Units coordination and the construction of improper fractions: A revision of the splitting hypothesis (2007, background): “Other researchers have emphasized the importance of real-world contexts and the informal knowledge that students bring to their activity with fractions in helping students develop fractional knowledge (e.g., Mack, 1990, 1995, 2001; Streefland, 1991).”