In this paper, an attempt is made to determine if peer collaboration increases student achievement in teaching elementary mathematics. Empirical evidence and philosophical problems with constructivist epistemology are considered. Two things are argued: first, it is reasonable to think, for elementary mathematics, peers collaboration is useful (especially in heterogeneous groups). Peer collaboration is an appendage to instruction, not a replacement for the didactics of an expert, or individual problem solving (which occurs both at its inception, when mathematics is discovered as well as advanced levels). There is reciprocity between individual and social settings in learning mathematics. Second, for the teaching of mathematics an adequate epistemology will guide, to some extent, a successful pedagogy.