The construction of number concepts

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Extraneous perceptual information interferes with children's acquisition of mathematical knowledge (2013, background): “Understanding of the relationship between counting and cardinality emerges gradually over the preschool years (Baroody & Price, 1983; Briars & Siegler, 1984; Fuson, 1988; Gelman & Gallistel, 1978; Mix, 2002; Wynn, 1990, 1992).”
Bootstrapping the Mind: Analogical Processes and Symbol Systems (2010, background): “The learning is at first slow and piecemeal—even after binding two to sets of cardinality two, weeks or months may ensue before the child realizes that three refers to a set with three items (Carey, 2004; Mix, 2002; Mix et al., 2005).”
Promoting broad and stable improvements in low-income children's numerical knowledge through playing number board games. (2008, background): “Even everyday routines that do not explicitly involve numbers, such as passing out napkins during dinner, promote concepts that are foundational for understanding numbers, such as one-to-one correspondence (Mix, 2002).”
Teaching and Learning Fraction and Rational Numbers: The Origins and Implications of Whole Number Bias (2005, methodology): “…there is no single approach that would be the “best” method for helping children “penetrate the concepts of fraction” given the fact that most learning following a particular instructional approach has shown to be more or less context-dependent (Mack, 1995; Mix, 2002; Streefland, 1991, 1993).”