Correctness, however, is a slippery idea in mathematics. Resnick and Ford (1981) specify correctness to be that which is 'defined by the consensus of mathematicians' (p. 206). Although it seems reasonable, this definition ignores two critical issues. First, mathematicians do not reach consensus on some questions. And second, ideas are not absolutely true in mathematics (Davis and Hersh, 1981; Kline, 1980). Often they depend on the particular context. Furthermore, even some ideas about which many mathematicians agree are ultimately fallible (Lakatos, 1976). Having "correct" knowledge, therefore, entails knowing the conditions and limits of an idea. Parallel lines never meetbut this "fact" is not true in nonEuclidean geometry. Firstgrade teachers may tell pupils that 0 is the smallest number or that 3 is the next number after 2but these ideas are true only if the domain is the counting numbers. 
Nicole M.

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