“…Although some view errors as part of the “messiness” of doing mathematics (e.g., Brown, 2000), student errors are often considered as catalysts for mathematics learning (Ashlock, 1986; Borasi, 1994; Lannin, Barker, & Townsend, 2007). In keeping with this latter way, teachers need to identify students' specific errors or learning difficulties and provide appropriate responses (e.g., Ashlock; Gable & Coben, 1990; Gable & Hendrickson, 1990).…”