Vol. 32 Num. 1 (2012) Boris Koichu Enhancing an intellectual need for defining and proving: a case of impossible objects ABSTRACT 2 Dor Abrahamson Discovery reconceived: product before process ABSTRACT 8 Tim Rowland Contrasting knowledge for elementary and secondary mathematics teaching ABSTRACT 16 Ami Mamolo , Rina Zazkis Communication: Continuing conversations towards the horizon22 Mercedes García , Victoria Sánchez Communication: Thinking about a mathematics for mathematics teachers23 Ilana Seidel Horn Communication: Teacher discourse and the construction of school mathematics25 Alexandre Pais , Elsa Fernandes , João Filipe Matos , Ana Sofia Alves Recovering the meaning of "critique" in critical mathematics education ABSTRACT 28 Mary Beisiegel , Elaine Simmt Formation of mathematics graduate students' mathematician-as-teacher identity ABSTRACT 34 - Contributor affiliations and contact information40