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.