Vol. 8 Num. 3 (1988) Susan Pirie Understanding: instrumental, relational, intuitive, constructed, formalized ...? How can we know?2 Hans-Georg Steiner Two kinds ofelements and the dialectic between synthetic-deductive and analytic-genetic approaches in mathematics7 Roger Säljö , Jan Wyndhamn A week has seven days. Or does it? On bridging linguistic openness and mathematical precision16 Jane M. Watson Three hungry men and strategies for problem solving20 Peter Galbraith Mathematics education and the future: a long wave view of change27 Nitsa Movshovits-Hadar School mathematics theorems -- an endless source of surprise34 Caleb Gattegno Reflections on forty years of work on mathematics teaching41