Students' Verification Strategies for Combinatorial Problems

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Student connections among counting problems: an exploration using actor-oriented transfer (2011, background): “Research on the teaching and learning of combinatorics confirms this fact (e.g., Batanero, Navarro-Pelayo, and Godino, 1997; Eizenberg & Zaslavsky 2004; English, 1991), indicating that, across ages, students struggle with various types of counting problems.”
A model of students' combinatorial thinking (2013, unknown): “…addressed combinatorial strategies among young students (e.g., English, 1991; Piaget & Inhelder, 1975), examined students’ verification strategies (Eizenberg & Zaslavsky, 2004), explored student-generated connections among counting problems (Lockwood, 2011b), and emphasized students’ potential…”
Seizing the Opportunity to Create Uncertainty in Learning Mathematics (2005, background): “In the case of combinatorial tasks uncertainty is associated with the difficulty to verify the result and to estimate the number of cases under question (Fischbein and Grossman, 1997; Mashiach-Eizenberg and Zaslavsky, 2004).”
Patterns, Sets of Outcomes, and Combinatorial Justification: Two Students’ Reinvention of Counting Formulas (2015, background): “Additionally, Eizenberg and Zaslavsky (2004) and Lockwood (2014a) have pointed out the fact that counting problems, with their large numerical answers, can be difficult to verify.”