Book excerpt: Challenging Mathematical Tasks supports the idea that students learn best when they work on problems that they do not yet know how to solve. Peter Sullivan's research shows that many students do not fear challenges in mathematics, but welcome them. And rather than having teachers instruct them, these students prefer to work out solutions for themselves.Challenging Mathematical Tasks:includes activities that allow for sustained thinking, decision-making and risk-taking by the studentsfeatures a 'Learning Focus', 'Key Mathematical Language', 'Pedagogical Considerations', 'Enabling and Extending Prompts' for each task, plus 'Supplementary Tasks' and 'Possible Solutions'is written by a well-established expert in the field of teaching and learning mathematicsfollows a set structure to help students approach and work through the tasks.For a preview, see the Sample Pages tab.