Vol. 20 Num. 2 (2000) Monica Villarreal Mathematical thinking and intellectual technologies: the visual and the algebraic2 Peter Huckstep The utility of mathematics education: some responses to scepticism8 Helen Featherstone "-Pat + Pat = 0": intellectual play in elementary mathematics14 Roza Leikin ,  Greisy Winicki-Landman On equivalent and non-equivalent definitions: part 224 Inés Cruz ,  Ma Febles ,  José Diaz Kevin: a visualiser pupil30 Michael D. Hardy Communication: Co-operation, silence and the quest for 'cool' ideas37 Liz Bills Politeness in teacherstudent dialogue: a socio-linguistic analysis40