Vol. 2 Num. 2 (1982) Ken Clements Visual imagery and school mathematics2 Jean Dhombres Pédagogie et utilisation de l'histoire: des tensions contradictoires10 David Tall Comments on the difficulty and validity of various approaches to the calculus16 Jeremy Kilpatrick The reasonable ineffectiveness of research in mathematics education22 Jan van den Brink Mutual observation29 David Swanson ,  Robert Schwartz ,  Herbert Ginsburg ,  Nancy Kossan The clinical interview: validity, reliability and diagnosis31 Ipke Wachsmuth Two modes of thinking - also relevant for the learning of mathematics?38 Stuart Plunkett Fundamental questions for teachers46 Larry Copes Communication: Educational mathematics48 David Sturgess Communication: Teacher-student interactions49 Arthur Morley Communication: Teaching and learning algorithms50