This research forum addresses the question: what is the nature of the mathematical knowledge that is needed for secondary teaching? Six international contributors: (1) Australia (Kaye Stacey); (2) Brazil (Marcelo Borba); (3) Israel (Ruhama Even); (4) Norway (Bodil Kleve and Barbara Jaworski); (5) Taiwan (Fou-Lai Lin); and (6) USA (Helen Doerr) respond by making two claims (one related to an area where progress in research has been made and the other related to dilemmas facing researchers): (1) preparing teachers; (2) teaching practice; (3) research designs and methodologies. This structure provides a way of focusing the discussion among forum participants and a means to develop international points of view on the nature of the mathematical knowledge that is needed for secondary teaching. Contained in this document are the following titles: (1) Preparing Teachers--Progress and Dilemmas; (2) Practicing Teachers--Progress and Dilemmas; and (3) Research Design--Progress and Dilemmas. [For complete proceedings, see ED489178.]