The development of arithmetic principle knowledge: How do we know what learners know?

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Defining and measuring conceptual knowledge in mathematics (2014, methodology): “Third, for the domains of equivalence and inversion, we screened the sources cited in previous literature reviews (McNeil, 2014, for equivalence; Prather & Alibali, 2009, for inversion) to identify additional, potentially relevant sources.”
Variability in the natural number bias: Who, when, how, and why (2015, background): “…both involve making groups as big as the divisor”) (Sidney & Alibali, 2014), or implicit knowledge of regularities that occur when the operation is applied (e.g., the sum of two natural numbers is larger than either addend) (Dixon & Bangert, 2005; Dixon et al., 2001; Prather & Alibali, 2009; 2011).”