Beginning and established teachers of mathematics as well as teacher educators will all find this book a rich resource when focusing on the crucial issue of designing and using tasks to provoke real learning in mathematics. It has become a central feature of our PGCE course in mathematics'. David Wright, Tutor in mathematics education, University of Newcastle Mathematics seems, on the face of it, a cut and dried subject. But does being able to do mathematics mean being competent at techniques? Understanding how ideas and techniques fit together? Using basic principles in problem-solving? Something else...or all of these? This book addresses these questions through a definition of learning as transformation in the way that learners perceive or think. Learners increase their choice of actions and develop their powers to think mathematically and their competence and fluency in using specific techniques and language and their appreciation of how ideas fit together. Contents include: Introduction: learning, teaching and behaviour theory and practice Mathematical topics Mathematical tasks Mathematical activity Interaction Progression in mathematics